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A systematic literature review and meta-analysis on cross project defect prediction

Research output : Contribution to journal › Article › Research › peer-review

Background: Cross project defect prediction (CPDP) recently gained considerable attention, yet there are no systematic efforts to analyse existing empirical evidence. Objective: To synthesise literature to understand the state-of-the-art in CPDP with respect to metrics, models, data approaches, datasets and associated performances. Further, we aim to assess the performance of CPDP vs. within project DP models. Method: We conducted a systematic literature review. Results from primary studies are synthesised (thematic, meta-analysis) to answer research questions. Results: We identified 30 primary studies passing quality assessment. Performance measures, except precision, vary with the choice of metrics. Recall, precision, f-measure, and AUC are the most common measures. Models based on Nearest-Neighbour and Decision Tree tend to perform well in CPDP, whereas the popular naive Bayes yield average performance. Performance of ensembles varies greatly across f-measure and AUC. Data approaches address CPDP challenges using row/column processing, which improve CPDP in terms of recall at the cost of precision. This is observed in multiple occasions including the meta-analysis of CPDP vs. WPDP. NASA and Jureczko datasets seem to favour CPDP over WPDP more frequently. Conclusion: CPDP is still a challenge and requires more research before trustworthy applications can take place. We provide guidelines for further research.

Bibliographies
Context modeling
Cross Project
Data models
Defect Prediction
Fault Prediction
Measurement
Meta-analysis
Object oriented modeling
Predictive models
Systematic Literature Review
Systematics
Within Project

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10.1109/TSE.2017.2770124

A Systematic Literature Review and Meta-Analysis on Cross Project Defect Prediction

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Background: In recent studies, Cross Project Defect Prediction (CPDP) has proven to be feasible in software defect prediction. When both the source as well as the target projects have the same metric sets, it is termed as a homogeneous CPDP. Current CPDP strategies are difficult to implement through projects with a variety of different metric sets. Aside from that, training data often has a problem with class imbalance. The number of defective/bug-ridden and non-defective/clean instances of the source class is usually unbalanced. To address this issue, we propose a heterogeneous cross-project defect prediction framework that can predict defects across projects with different metric sets. Methods: To construct a prediction framework between projects with heterogeneous metric sets, our heterogeneous cross project defect prediction approach uses metric selection, metric matching, class imbalance (CIB) learning followed by ensemble modelling. For our study, we have considered six open-s...

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A systematic literature review and meta-analysis on cross project defect prediction

Hosseini, seyedrebvar; turhan, burak; gunarathna, dimuthu (2019-02-01).

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S. Hosseini, B. Turhan and D. Gunarathna, "A Systematic Literature Review and Meta-Analysis on Cross Project Defect Prediction," in IEEE Transactions on Software Engineering, vol. 45, no. 2, pp. 111-147, 1 Feb. 2019. doi: 10.1109/TSE.2017.2770124

Tiivistelmä

Background: Cross project defect prediction (CPDP) recently gained considerable attention, yet there are no systematic efforts to analyse existing empirical evidence.

Objective: To synthesise literature to understand the state-of-the-art in CPDP with respect to metrics, models, data approaches, datasets and associated performances. Further, we aim to assess the performance of CPDP versus within project DP models.

Method: We conducted a systematic literature review. Results from primary studies are synthesised (thematic, meta-analysis) to answer research questions.

Results: We identified 30 primary studies passing quality assessment. Performance measures, except precision, vary with the choice of metrics. Recall, precision, f-measure, and AUC are the most common measures. Models based on Nearest-Neighbour and Decision Tree tend to perform well in CPDP, whereas the popular naïve Bayes yields average performance. Performance of ensembles varies greatly across f-measure and AUC. Data approaches address CPDP challenges using row/column processing, which improve CPDP in terms of recall at the cost of precision. This is observed in multiple occasions including the meta-analysis of CPDP versus WPDP. NASA and Jureczko datasets seem to favour CPDP over WPDP more frequently. Conclusion: CPDP is still a challenge and requires more research before trustworthy applications can take place. We provide guidelines for further research.

Avoin saatavuus [31658]

Selaa kokoelmaa

Omat tiedot.

Systematic Review
Open access
Published: 01 April 2024

Role of bariatric surgery in reducing periprosthetic joint infections in total knee arthroplasty. A systematic review and meta-analysis

D. De Mauro 1 , 2 , 3 ,
G. Balato 1 ,
E. Festa 1 ,
A. Di Cristo 1 ,
L. Marasco 1 ,
G. Loffredo 1 ,
P. Di Lauro 1 ,
D. Di Gennaro 1 ,
G. Maccauro 2 , 3 &
D. Rosa 1

BMC Musculoskeletal Disorders volume 25 , Article number: 248 ( 2024 ) Cite this article

Metrics details

Obesity represents an epidemic of rising numbers worldwide year after year. In the Orthopedic field, obesity is one of the major causes leading to osteoarthritis needing Total Joint Arthroplasty (TJA). Still, contextually, it represents one of the most significant risk factors for joint replacement complications and failures. So, bariatric Surgery (BS) is becoming a valuable option for weight control and mitigating obesity-related risk factors. This review of the literature and meta-analysis aims to evaluate periprosthetic joint infections (PJI) and surgical site infections (SSI) rates in patients who underwent TKA after BS compared to obese patients without BS.

Systematic review was performed according to Preferred Reporting Items for Systematic Review and Meta-Analyses (PRISMA) guidelines up to October 2023. We included longitudinal studies comparing obese patients who underwent total knee arthroplasty after bariatric surgery (study group) and obese patients who underwent TKA (control group). The surgical site infection and Periprosthetic joint infection rate were compared among groups using a meta-analytical approach.

The online database and references investigation identified one hundred and twenty-five studies. PJI rate differed significantly among groups, (z = -21.8928, p < 0.0001), with a lower risk in the BS group (z = -10.3114, p < 0.0001), for SSI, instead, not statistically significance were recorded (z = -0.6784, p = 0.4975).

Conclusions

The current Literature suggests that Bariatric Surgery can reduce infectious complications in TKA, leading to better outcomes and less related costs treating of knee osteoarthritis in obese patients.

Peer Review reports

Obesity represents an epidemic plague, rising its numbers worldwide year after year [ 1 ]. High Body Mass Index (BMI) patients have increased risk of developing several diseases, such as diabetes, hypertension, and joint arthritis [ 2 ]. Obesity stands as a paradoxical factor in Orthopedics due to its role as one of the major causes leading to a Total Joint Arthroplasty (TJA), and contextually, one of the most significant risk factors for joint replacement complications and failures [ 3 , 4 ]. International guidelines suggest joint replacement for patients with BMI > 40 kg/m2 should be avoided because the risk of postoperative complications may outweigh the benefit of the TJA [ 5 ]. Thus, surgeons must aim to induce BMI reduction in patients before the procedure [ 2 ]. Among tools for weight control, Bariatric Surgery (BS) is becoming a valuable option for those patients who present morbid obesity. Literature is still unclear about its use in Orthopedic patients, with conflicting results regarding complications rates and re-revisions incidence [ 6 ]. Although mechanical failures and post-operative re-admissions were often analyzed, BS’s impact on Periprosthetic Joint Infection (PJI) rates remains unclear. PJI still represents the most feared complication in prosthetic surgery [ 7 , 8 , 9 , 10 ], and its higher incidence in obese patients was assessed and confirmed in several studies. The number of papers relating TKA complications and bariatric surgery before TKA is increasing [ 11 , 12 , 13 , 14 ]. Given the benefits of BS for patients’ general health, it is necessary to establish if weight loss provided by metabolic surgery can also lead to an overall decrease of infection rates, both in PJI and surgical site infection (SSI). This review of the literature and meta-analysis aims to evaluate infections and SSI rates in patients who underwent TKA after BS compared to obese patients without BS.

Materials and methods

Search strategy and eligibility criteria.

Systematic review was performed according to Preferred Reporting Items for Systematic Review and Meta-Analyses (PRISMA) guidelines [ 15 ] up to October 2023. Research papers investigating clinical outcomes and complications rate in patients treated with bariatric surgery before or after total knee arthroplasty were conducted in three different online databases: MEDLINE, Web of Science, Scopus. The keywords used for the research were combined as follow: (“BS” OR “Bariatric surgery” OR “metabolic surgery”) AND (“TKA” OR “TKR” OR “Total Knee Arthroplasty” OR “Total Knee Replacement”) AND (“Infection” OR “PJI” OR “SSI”).

All articles written in English were included, with no limitations for date of publication. Reference lists of selected articles were searched for additional articles that were not identified in the database search. Longitudinal studies (retrospective and prospective) and randomized controlled trials were evaluated and added to the final reference list. The exclusion criteria required the omission of case reports, expert opinions, prior systematic reviews, letters to the editor, studies that did not include patients who underwent TKA, studies that included different total joint arthroplasty (such as hip arthroplasty, shoulder etc.) and wherein TKA data could not be extrapolated. Studies not including infectious complications in the post-operative analysis were also excluded.

Study assessment and data extraction

Initially, the titles and abstracts of the studies were screened by two independent reviewers. Full text was obtained for all abstracts that appeared to meet the inclusion criteria or those with any uncertainty. Then, each study was assessed based on the inclusion criteria by two independent reviewers, and the evaluation of the article by the senior author resolved any disagreement regarding the inclusion of any study. Relevant data were extracted from each study. Data describing participant demographics, sample size, and failure rate regarding SSI and PJI were recorded. The methodological quality of the studies included in this meta-analysis was assessed. The methodological quality of the studies included in this meta-analysis was assessed using the Methodological Index for Non-Randomized Studies (MINORS) score that yields a maximum score of 16 and 24, respectively, for non-comparative and comparative studies [ 16 ]. Two authors independently determined the MINORS score; the final score was obtained through consensus.

Statistical analysis

The comparison between the infection rate in the study groups and the infection rate in the control group with a 95% confidence interval (CI) represented the primary outcome. Secondary outcomes were the rate of surgical site infections at follow-up in both groups. The analysis was carried out using the log odds ratio as the outcome measure. A random-effects model was fitted to the data. The amount of heterogeneity (i.e., τ²), was estimated using the restricted maximum-likelihood estimator [ 17 ]. In addition to the estimate of τ², the I² statistic are reported. In case any amount of heterogeneity is detected (i.e., τ² > 0), a prediction interval for the true outcomes is also provided. Studentized residuals and Cook’s distances are used to examine whether studies may be outliers and/or influential in the context of the model. Studies with a studentized residual larger than the 100 × (1–0.05/(2 X k))th percentile of a standard normal distribution are considered potential outliers (i.e., using a Bonferroni correction with two-sided alpha = 0.05 for k studies included in the meta-analysis). Studies with a Cook’s distance larger than the median plus six times the interquartile range of the Cook’s distances are influential. The rank correlation test and the regression test, using the standard error of the observed outcomes as predictors, are used to check for funnel plot asymmetry. Jamovi version 2.3 [ 18 ] and SPSS version 29 (SPSS, Chicago, IL, USA) for all statistical analyses. P ≤ 0.05 was considered significant.

A flow diagram of the search strategy is presented (Fig. 1 ). One hundred twenty-five studies were identified from the online database and reference investigation. After the duplicate removal and first screening based on titles and abstracts, the search produced a 32 papers list of full text to analyze. Six studies [ 19 , 20 , 21 , 22 , 23 , 24 ] were then included in the meta-analysis, 4 for the evaluation of PJI rate and 4 for the surgical site infection (SSI) rate (Table 1 ). Most of the studies were written and developed in USA, with only one other country represented (China).

A total amount of 3.045.096 patients was considered in the study, with a mean age of 60,1 years. The BS-group included 58.463 patients, 2.986.633 in the obese-group, instead. The mean percentage of patients with SSI in the study group and in the control, group was 4,2% and 3,9%, respectively, with a slightly lower rates of incidents in obese group. For what concerns the PJIs, the percentage in bariatric surgery group was lower (2.2%) than in control group (4.6%).

Study flowchart

Surgical site infections

Four studies were eligible for meta-analysis [ 19 , 21 , 22 , 24 ], for a total amount of 44.236 patients in BS-group and 2.896.662 in obese group, with 1.265 and 64.879 cases of surgical site infection, respectively. The observed log odds ratios (OR) ranged from − 0.6936 to 0.3518, with the majority of estimates being negative. The estimated average log odds ratio based on the random-effects model was µ = -0.1734 (95% CI: -0.6742 to 0.3275). Therefore, the SSI rate did not differed significantly from zero (z = -0.6784, p = 0.4975). According to the Q-test, the true outcomes appear to be heterogeneous (I² = 96.44%, p < 0.0001). According to the Cook’s distances, none of the studies could be considered as overly influential. Neither the rank correlation nor the regression test indicated any funnel plot asymmetry ( p = 0.7500 and p = 0.7011, respectively) (Fig. 2 ).

Rates of surgical site infections in patients treated by bariatric surgery before TKA and obese control group. The summary estimates presented were calculated using random-effects models; CI, confidence interval (bars)

Periprosthetic joint infections

Four studies were eligible for meta-analysis [ 19 , 20 , 22 , 23 ], for a total amount of 32.406 patients in BS-group and 310.648 in obese group, with 1.003 and 23.027 cases of infections, respectively. The observed log odds ratios (OR) ranged from − 1.0405 to -0.3733, with the majority of estimates being negative. The estimated average log odds ratio based on the random-effects model was µ = -0.7110 (95% CI: -0.8462 to -0.5759). Therefore, the PJI rate differed significantly from zero (z = -10.3114, p < 0.0001), with a lower risk in the BS-group. According to the Q-test, there was no significant amount of heterogeneity in the true outcomes (I² = 11.69%, p = 0.398). A 95% prediction interval for the true outcomes is given by -0.9018 to -0.5203. Hence, even though there may be some heterogeneity, the true outcomes of the studies are generally in the same direction as the estimated average outcome. According to the Cook’s distances, none of the studies could be considered as overly influential. There was no indication of outliers in the context of this model. Neither the rank correlation nor the regression test indicated any funnel plot asymmetry ( p = 0.750 and p = 0.387, respectively) (Fig. 3 ).

Rates of infection in patients treated by bariatric surgery before TKA and obese control group. The summary estimates presented were calculated using random-effects models; CI, confidence interval (bars)

Patients with BMI > 40 Kg/m 2 are unanimous considered as worst candidates to joint replacement, especially to total knee arthroplasty. Nevertheless, obese patients suffers more often than non-obese patients of knee osteoarthritis, leading to a surgical indication to knee replacement. Due to this paradoxical situation, in Literature are becoming more commons studies comparing TKA outcomes in obese patients treated with bariatric surgery and obese patients without BS [ 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 ]. Existing reviews of the literature about this topic [ 27 , 28 ] consider mechanical failures and re-admissions into the Hospital for early complications as main endpoints, without focusing on infectious complications. For what we know, this is the first review of the literature and meta-analysis specifically about PJI and SSI rates in TKA. Therefore, the strength of this paper is solid and current about such a dramatic topic in daily activity of Orthopedic surgeon [ 8 ].

Smith et al. [ 28 ] collected cases from 5 studies, highlighting a significant difference in wound infection, with lower rates in BS patients. However, they performed a literature review and meta-analysis considering both TKA and total hip arthroplasty (THA), we opted, instead, to evaluate single TKA procedures, in order to compare homogeneous groups and same joint.

More recently, Yan et al. [ 27 ] provided a more updated review of the literature about this topic, involving more studies than us in the meta-analysis for infections (7). However, they considered all infectious complications under a general label “infection”, without going into details of the pathology. We analyzed two different outcomes, PJI and SSI, providing a meta-analysis for each of them.

The correct outcome to evaluate the risk of septic failures was chosen according to the data found in the Literature. First endpoint was to assess periprosthetic joint infection rates, considering it as the mean diagnosis when it comes to septic complications [ 29 ]. Surgical site infections, instead, were less related to actual septic failure, but the available data allowed us to use this information to better define the impact of bariatric surgery as prevention of infections in joint arthroplasty. The choice of performing a meta-analysis using random-effects models rather than fixed-effects, due to the heterogeneous data and the size of the studies, according to Nikolakopoulou et al. [ 30 ].

Our data allowed us to deliver a statistically significant statement about first outcome, not for the SSI rates, instead. Thus, obese patients underwent bariatric surgery before TKA seem to have a lower risk of PJI, compared to patients who underwent TKA without a BS before. SSI risk seems to be different, but p -value > 0.05.

This data suggests lack of correlation between Bariatric surgery and SSI risk in TKA, thus superficial wound infections cannot be addressed through BS, unlike the PJI.

As matter of facts, SSI includes partially those infections who later became deeper infections, often representing an early manifestation of PJI. Thus, even if the SSI-risk remain similar in both groups, it seems less probable for the infections to affect deeper layers and the prosthesis itself in BS-group, rather than in Obese-group, and this represents an important result of our meta-analysis.

Even if included studies are heterogeneous, none of them is overly influential compared to others, according to our analysis. Each paper contained enough data to reach inclusion criteria and make it to the final draft for the meta-analysis, considering surgical site infection and periprosthetic infection among complications in TKA.

Some studies [ 21 , 24 ] offered a further comparison between BS-patients and non-obese patients, matching patients underwent bariatric surgery with patients with the same BMI they reached after the surgery. Due to the low numerosity of these studies, meta-analysis was not performed, but comparing the straight numbers, seems to be still higher infection risk in BS-group. This can suggest that BMI reduction alone is not able to grant an adequate return to pre-obesity condition. Further studies comparing obese, non-obese and BS patients are needed to better analyze relations among metabolic disorders, obesity and TKA complications.

Main limitation of the study is clearly the studies number, not allowing a more appropriate and accurate meta-analysis. All the included studies are, moreover, not specifically sets for infectious outcomes, but mostly on early complications and revisions. Thus, the data we analyzed were often not clear determined and highlighted. Bariatric Surgery can be a solid ally for orthopedic surgeons in facing joint osteoarthritis in obese patients, but more and stronger studies are needed, to allow this procedure to be included in treatment algorithm.

The current Literature suggests that Bariatric Surgery can reduce infectious complications after TKA. Indeed, Obese patients treated with BS before TKA are less prone to surgical site infections and periprosthetic joint infections compared to morbidly obese patients.

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Abbreviations

Total Joint Arthroplasty

Total Knee Arthroplasty

Periprosthetic Joint Infection

Bariatric Surgery

Surgical site infection

Confidence Interval

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Environmental migration? A systematic review and meta-analysis of the literature

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Published: 30 March 2024

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Maria Cipollina ORCID: orcid.org/0000-0002-1454-4039 1 ,
Luca De Benedictis 2 &
Elisa Scibè 3

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This article provides a comprehensive quantitative overview of the literature on the relationship between environmental changes and human migration. It begins with a systematic approach to bibliographic research and offers a bibliometric analysis of the empirical contributions. Specifically, we map the literature and conduct systematic research using main bibliographic databases, reviews, and bibliometric analysis of all resulting papers. By constructing a citation-based network, we identify four separate clusters of papers grouped according to certain characteristics of the analysis and resulting outcomes. Finally, we apply a meta-analysis to a sample of 96 published and unpublished studies between 2003 and 2020, providing 3904 point estimates of the effect of slow-onset events and 2065 point estimates of the effect of fast-onset events. Overall, the meta-analytic average effect on migration is small for both slow- and rapid-onset events; however, it is positive and significant. Accounting for the clustering of the literature, which highlights how specific common features of the collected studies influence the magnitude of the estimated effect, reveals a significant heterogeneity among the four clusters of papers. This heterogeneity gives rise to new evidence on the formation of club-like convergence of literature outcomes.

The impact of climate change on migration: a synthesis of recent empirical insights

David J. Kaczan & Jennifer Orgill-Meyer

Labour Migration from Nepal: Trends and Explanations

Migration and Immigrants in Europe: A Historical and Demographic Perspective

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1 Introduction

In a world of changing climate and increasing occurrence of natural hazards, the role of environmental factors in shaping migration patterns has become a most debated topic within institutions and academia. As opposed to a simplistic vision of a general direct role of environmental factors in determining migration flows from environmentally stressed areas and regions hit by calamities, more complex scenarios have emerged, with analyses reporting different and sometimes opposite outcomes. This may not only be due to the intrinsic complexity of their extent and scale, but also to differences in specific characteristics of scientific contributions (International Organization for Migration, 2021 ).

The literature on the relationship between environmental factors and human mobility is characterized by heterogeneous findings: some contributions highlight the role of climate changes as a driver of migratory flows, while others underline how this impact is mediated by geographical, economic, and the features of the environmental shock. This paper aims to map the economic literature on these topics moving away from a classical literature review and offering a methodology that integrates three approaches in a sequence, in this way we believe that our contribution improves the existing literature on several dimensions. First, the analysis starts with systematic research of the literature through main bibliographic databases and collecting previous reviews and meta-analyses, followed by a review and bibliometric analysis of all resulting papers. This step produces a sample of 151 papers empirical and non-empirical contributions, spanning the last 20 years and focusing on different geographical areas, taking into account different socio-economic factors, applying different methodologies and empirical approaches to the analysis of slow-onset climatic events and/or fast-onset natural catastrophic events. Most importantly, the sample provides a variety of different outcomes on the impact of climatic changes and hazards on migration, revealing three main possible scenarios: (1) active role of environmental factors as a driver of migration; (2) environmental factors as a constraint to mobility; (3) non-significant role of environmental factors among other drivers of migration.

Second, to investigate the determinants of this extreme heterogeneity of outcomes, we postulate the assumption that the inter-connectivity of papers may play a role in shaping such different conclusions. Considering the ensemble of papers referenced by each contribution included in the sample, as a second step, we build a bibliographic coupling network, where papers are linked to each other according to the number of shared references. This citation-based method allows for the formation of a network of contributions in the literature space and highlights some potential common grounds among papers. We then run a community detection of the resulting network that produces four main clusters that gather papers together according to not only certain characteristics of the analysis but also resulting outcomes.

Finally, we use the clustered structure in the last step of the analysis: a Meta-Analysis (MA) to summarize and analyze all estimated effects of environmental variables on human mobility. The MA is a “quantitative survey" of empirical economic evidence on a given hypothesis, phenomenon, or effect, and provides a statistical synthesis of results from a series of studies (Stanley, 2001 ). The MA can be applied to any set of data and the synthesis will be meaningful only if the studies have been collected systematically (Borenstein et al., 2009 ). A highly significant result can be potentially considered as a consensual indication of the external validity of the correlation of the phenomena under scrutiny.

Therefore, from the original 151 paper we build - through a replicable process of screening, eligibility, and inclusion of contribution based on PRISMA guideline (see Fig. 1 ) - a unique dataset that synthesises the estimated coefficients of 96 empirical papers released between 2003 and 2020, published in academic journals, working papers series, or unpublished studies, providing 3904 point estimates of the effect of slow-onset events (e.g. climate change) and 2065 point estimates of the effect of fast-onset natural events(e.g. catastrophes) on different kinds of human mobility (international, domestic, and with a clear pro-urban directionality). Overall, the meta-analytic average effect estimates a small impact of slow- and rapid-onset variables on migration, however positive and significant. When the communities of papers are accounted for, however, a significant heterogeneity emerges among the four clusters of papers, giving rise to new evidence on the limits of a consensual effect of climatic shocks on permanent human displacement and the formation of club-like convergence of literature outcomes.

PRISMA Diagram. Note : PRISMA Diagram (Page et al., 2021a ) of identification, screening, eligibility and inclusion stages of academic contributions. The resulting sample is obtained through a search on Scopus, Web of Science, Google Scholar, IDEAS RePEc, and previous meta-analyses (Hoffmann et al., 2020 ; Beine & Jeusette, 2021 )

This is not the first MA on environmental migration. Concerning previous published reviews (Hoffmann et al., 2020 ; Sedova & Kalkuhl, 2020 ; Beine & Jeusette, 2021 ; Hoffmann et al., 2021 ) our article contributes and adds to the existing literature: (a) providing systematic research of the literature through main bibliographic databases, followed by a review and bibliometric analysis of all resulting papers; (b) building a citation-based network of contributions, that allows identifying four separate clusters of papers; (c) applying MA methods on a much larger sample of both micro- and macro-level estimates of environmental factors (slow- and fast-onset events) as a driver of migration (international and internal, including urbanization). Moreover, our overview highlights the role of the interconnectivity of studies in driving some main findings of the environmental migration literature.

Section 2 offers a systematic review of the literature and gives a detailed description of the data collection process; Sect. 3 analyses the structural characteristic of the network of the bibliographically coupled papers; Sect. 4 summarizes and discusses the results of the MA, finally, Sect. 5 concludes and offers some possible future extensions of the analysis.

2 Systematic review

This section reports the different phases of the systematic review. We do it schematically to facilitate the understanding of the proposed procedure.

Setting the boundaries of the literature This first step provides the most comprehensive sample of economic contributions on the relationship between climatic variations (and natural hazards) and human mobility, in all its different forms. We implement a systematic review aimed at mapping the body of literature and defining the boundaries of our focus. Systematic reviews have become highly recommended to conduct bibliographic overviews of specific literature because they provide a tool to report a synthesis of the state of the art of a field through a structured and transparent methodology (Page et al., 2021b ). To allow for comparability with previous MA and reviews, we also add to our sample all articles included in two recently published MA, Hoffmann et al. ( 2020 ) and Beine and Jeusette ( 2021 ) Footnote 1 . We begin with the definition of the research question and the main keywords, to gather and collect data in a sample of contributions. After the definition of inclusion and exclusion conditions, we proceed with a screening by title to exclude off-topic contributions and then to a screening of the text to assure the uniformity of contributions. The resulting sample is then the object of a preliminary bibliometric analysis.

Defining the research question and keywords The purpose of our systematic search is to collect all possible economic contributions to the impact of environmental factors on migration determinants. We define three keywords of the three phenomena under analysis:

climate change, as the most investigated environmental factor in the literature. The events connected to climate change are hereby intended as slow-onset events that gradually modify climatic conditions in the long run. We specifically focus on variations of temperature, precipitation, and soil quality (such as desertification, salinity, or erosion), factors that are not expected to cause an immediate and sudden expected impact, but slowly modify environmental conditions;

natural disasters, defined as fast-onset events that introduce a sudden shock (see Appendix Table 5 );

migration, which captures all possible patterns of human mobility, including within the borders of a country, which might be a potential response to environmental change. Most importantly, internal mobility includes also the process of urbanization of people moving out of rural areas to settle in cities.

Collecting data and initial search results To collect data we use two main literature databases, namely Scopus and Web of Science. Footnote 2 Exploiting the specific indexing and keyword definition of both sources, the search is run allowing for any kind of document type (articles in journals, book chapters, etc.) but limiting the area to economic literature in English. Footnote 3 The obtained sample only includes published documents, however since we perform a MA, it is important to take into account also non-published documents, as a way to control for a well-known publication bias in meta-analytic methodology (see Sect. 4 ). Therefore, we use the bibliographic database IDEAS, based on RePEc and dedicated to Economics, to include unpublished and working papers. Footnote 4 A selection of the contributions is made manually. Finally, to meet the purpose of comparability with other recent meta-analyses on the impact of environmental factors on migration, we also include all the contributions that have been reviewed in two main articles: Hoffmann et al. ( 2020 ) that provide a MA on 30 empirical papers focusing on country-level studies and Beine and Jeusette ( 2021 ) that review 51 papers and offer an investigation of the role of methodological choices of empirical studies (at any level) on the sign and magnitude of estimated results. Merging the results gives a sample of 203 records.

Screening of the results. We manually and meticulously screen the collected items through Scopus and Web of Science by title and we exclude papers on the migration of animals, plants, or other species, or focusing on topics different from human mobility (i.e. discrimination, crime, wars) or on the impact of environmental variables not corresponding to our definition of environmental factors (air pollution, mineral resources). All the papers in Beine and Jeusette ( 2021 ), Hoffmann et al. ( 2020 ) and those manually selected from IDEAS RePEc are automatically included in the sample with no concern of incoherence. The screening by title leads to the exclusion of 20 papers. The remaining 183 documents underwent a text screening process, which involved a careful and thorough reading of each paper to isolate eligible content. This stage leads to the removal of additional 32 documents covering on the one hand the analysis of the impact of environmental variables at destination countries (thus not focusing on their role on migration determinants at origin). We also exclude all the papers in which the dependent variable of the empirical exercise is not a measure of human mobility (i.e. remittances, poverty, wealth, employment, etc.). After duplicates removal, the sample results in 151 documents of different kinds: 35 records are non-empirical and contain an ensemble of literature reviews, qualitative analysis, theoretical modeling, and policy papers; 116 records are categorized as empirical, in which the dependent variable is a measure of human mobility and at least one environmental variable is an independent variable.

The PRISMA flow diagram (Moher et al., 2009 ) in Fig. 1 shows the process of identification, screening, eligibility, and inclusion of contributions in the final sample. It is important to note that there are two levels of inclusion: the first level identifies the sample of contributions included in our network analysis, while the second level is restricted to quantitative analyses suitable for the MA. To conduct a MA it is crucial to select only comparable papers that provide complete information (mainly on estimated coefficients and standard errors) that can then be used to recover the average effect size Footnote 5 . This implies the exclusion of papers that do not comply with the requirements of a MA. However, those excluded papers can be of interest in building the taxonomy of the whole concerned literature, as they may play a role in building links between different contributions (see Sect. 3 ). Similarly, non-quantitative (policy, qualitative or theoretical) papers may participate as well in the development of research fronts or give a direction to a certain thread of contributions and incidentally affect the detection of clusters. These reasons led us to build our citation-based network and perform the network analysis and the community detection on the whole sample, while only the sample for the MA is restricted only to quantitative contributions that meet the coding requirements. Our final database of point estimates for the MA includes 96 papers released between 2003 and 2020, published in an academic journal, working papers series, or unpublished studies, providing 3,904 point estimates of the effect of slow-onset events (provided by 66 studies) and 2,065 point estimates of the effect of fast-onset events (provided by 60 studies). The list of articles is in the Appendix Table 6 .

2.1 Bibliometric analysis

This section summarizes the most relevant features of the ensemble of economic literature collected in our sample. Footnote 6

The economic literature started to pay attention to the potential relevance of environmental events on migration in the early 2000s, although the topic had already gained some relevance in global debate decades before, and scientific production increased sharply in the last 17 years. Figure 2 shows that the scientific production in the specific field is quite recent, spanning from 2003 to 2020, with a peak of 20 contributions in 2016 and an annual growth rate for the overall period at 18.5 percent. Taking a closer look at the cited references, it is possible to trace back an article published before 2003 (Findley, 1994 ), that provides a qualitative analysis of drought-induced mobility in Mali (finding no evidence of any role of 1983-85 droughts on migration). As our research of documents is based on keywords, naturally the three most repeated are those put in the search key (“migration", “climate change" and “natural disasters"). Footnote 7 Within the topic of migration, there’s a greater emphasis on international mobility compared to internal migration. However, internal migration may include also urbanization or rural-urban migration, and when combined, they are as common as international migration (counting 21 repetitions per group). Environmental migration is also explored as a form of forced migration , originating refugees, or specifically environmental refugees. The keywords related to environmental issues are more focused on slow-onset events like ( rainfall, temperature, global warming and climate variability ) rather than rapid-onset events. Although, some of the latter are more recurrent than others, such as drought, floods and ultimately earthquakes .

Number of documents per year. Note : Sample of academic contributions about migration and environmental factors from Scopus, Web of Science, Google Scholar, IDEAS RePEc, and previous meta-analyses (Hoffmann et al., 2020 ; Beine & Jeusette, 2021 ) collected, merged, screened and included by the authors

Overall 288 authors have contributed to this literature, with 372 appearances, 34 documents are single-authored, the mean number of authors per document is 1.88; when considering exclusively multi-authored documents, the number of co-authors per document rises to 2.16, with a maximum of co-authors of 9. Various disciplines have put attention to the topic. Despite journals specializing in economics and econometrics representing the majority of the sources of publication, the literature includes also other disciplines (Fig. 3 ).

The 20 most relevant publication sources by field. Note : Sample of academic contributions about migration and environmental factors from Scopus, Web of Science, Google Scholar, IDEAS RePEc, and previous meta-analyses (Hoffmann et al., 2020 ; Beine & Jeusette, 2021 ) collected, merged, screened and included by the authors

Specifically, economic environmental migration is the object of publication in journals specialized in environmental sciences, geography, and social sciences such as urban studies, agriculture, demography, and political studies. A special mention has to be done for development studies: many reviews and journals specialized in development have issued contributions on the topic, highlighting the trend of observing the topic through development lenses. As an example, 14 documents in our sample are published in World Development , a multi-disciplinary journal of development studies.

A picture of the most relevant documents included in the sample is provided by simple measures, such as the number of global citations as reported in Scopus (at the moment of the bulk download of all sources), and the number of local citations, which shows how many times a document has been cited by other papers included in the sample. Measures for the most cited documents (global and local citation scores) in the sample are reported in Appendix Table 7 . The difference between global and local citation scores (almost four times higher) reveals that the documents have been cited by papers not included in our sample. It means that environmental migration has attracted the interest of different disciplines or they became part of the two main strands of literature, climate change, and migration, separately. 58 papers have not been cited in any of our samples, while 52 have zero citations globally. A part of it can be explained by the 18 papers that have been published recently in 2020, which could not have been cited yet because of timing (except for some contributions published in early 2020 such as Mueller et al. ( 2020 ) and Rao et al. ( 2020 ). Footnote 8 Position and the number of citations confirm the central role of papers published by Gray Clark and Valerie Mueller (Gray & Mueller, 2012b , a ; Mueller et al., 2014 ), receiving high citations both globally and internally. Some papers seem to be more relevant locally than globally: Marchiori et al. ( 2012 ) and Beine and Parsons ( 2015 ) had a bigger influence on our sample of economic environmental migration literature rather than globally, scoring the highest number of local citations. Conversely, Hornbeck ( 2012 ) seems to be cited more in literature outside the specific literature of environmental migration.

2.2 Overview of major results

The literature on the effects of climate and natural disasters on migration is characterized by a rich variety of studies both in micro- and macro-economic analyses. Country-level analyses tend to find evidence of a direct or indirect impact of environmental factors on migration patterns, either internally or internationally. Barrios et al. ( 2006 ) and Marchiori et al. ( 2012 ) find evidence of an increase in internal migration, especially towards urban areas in the case of Sub-Saharan Africa, according to many specific historical and developmental factors. Both contributions highlight how worsening climatic conditions correspond to a faster urbanization process. Marchiori et al. ( 2012 ) add also that this climate-driven urbanization process results also in higher international migration rates, acting as a channel of transmission of the effect of climate.

The macro literature, in line with most validated theoretical models of migration, also investigates whether the effect is conditioned to income levels of the country of origin of potential migrants (Marchiori et al., 2012 ; Beine & Parsons, 2015 , 2017 ). The role of income in a specific origin country experiencing the effects of environmental events is found to be crucial to determine the sign and the magnitude of the impact. Cattaneo and Peri ( 2016 ) support from one side the active role of those events in fostering migration, but show how this effect is conditioned to middle-income countries. The effect is the opposite when conditioning the analysis to poor countries, highlighting the existence of certain constraints to mobility. Worsened environmental conditions may exacerbate liquidity constraints or lack of access to credit aimed at financing the migratory project, which lead to what has been called poverty trap . Furthermore, these conditioned results seem to be robust even when another important channel is controlled, agricultural productivity. Climatic conditions and disruptive hazards may constitute major drawbacks for agricultural productivity, leading the agriculture-dependent part of the population to move out from rural areas: Cai et al. ( 2016 ) and Coniglio and Pesce ( 2015 ) provide evidence of an indirect link between worsened temperature and precipitation conditions and migration, mediated by the level of agricultural dependency of the country of origin. Sudden and fast-onset hazards, on the other side, are not found to contribute significantly to human mobility, except in the case of a higher-educated population, more mobile than other groups after the disruption of a natural disaster (Drabo & Mbaye, 2015 ).

Number of case studies covered by the micro-level sub-sample per country. Note : Sub-sample of micro-level studies about migration and environmental factors from Scopus, Web of Science, Google Scholar, IDEAS RePEc, and previous meta-analyses (Hoffmann et al., 2020 ; Beine & Jeusette, 2021 ) collected, merged, screened and included by the authors

Micro-level literature provides a vast variety of case studies on different potential impacts of environmental factors on mobility. In our sample, they almost double macro-level contributions (86 contributions against 47) and provide different scenarios. Firstly, while macro-level studies mostly provide analyses at the global level or for some groups of countries or macro-regions, micro-level analyses tend to observe a specific phenomenon hitting a specific area or to study differences in the impact of a common phenomenon in different areas. The most covered region as a whole is Sub-Saharan Africa, with 65 case studies included in the contributions (Fig. 4 ). Footnote 9 When the level of analysis is less aggregated than the national or sub-national level, and individual or household behavior is observed through the use of surveys, the picture gains complexity and less generalized conclusions. This seems clear in Gray and Wise ( 2016 ) who analyze a series of comparable surveys across five Sub-Saharan countries, which have consistent differences. The heterogeneity of responses to climatic variations across those countries is strictly linked to the characteristics of the area and of the specific households. Poorer countries (such as Burkina Faso) mainly experience internal and temporary migration, often on a rural-rural channel as a way to diversify risk (Henry et al., 2003 , 2004 ). Long-distance migration seems to be constrained by liquidity and access to credit to finance those expensive journeys. Migratory trends of Nigerian households are pushed in times of favorable climatic conditions, while the effect of adverse conditions interacts with a negative effect on income and traps populations at origin (Cattaneo & Massetti, 2019 ). Overall, micro-level studies focused on the African continent highlight the importance of considering the interplay of a variety of factors when it comes to the analysis of the role of environmental factors, defining the new path toward hybrid literature.

The single countries that receive singularly the most attention are Mexico, with 10 case studies, and the U.S., with 9 case studies. This should not be a surprise because of two reasons: firstly, the stock of Mexican emigrates has been constantly the highest in the world (in absolute terms) as well as the migratory flow between Mexico and the U.S. But there might also be a publication-related reason based on the fact that the vast majority of journals in our sample are U.S. based. Major findings support the relevance of environmental drivers (mainly precipitation shortage) on push factors from Mexico ( Feng et al. ( 2010 ) estimates that a 10% reduction of agricultural productivity driven by scarce rainfall corresponds to the rise of 2% of emigrants).

Southern and Eastern Asia, representing by far the most disaster-prone area in the world. Footnote 10 also provide a variety of heterogeneous scenarios. The case of Vietnam (Koubi et al., 2016 ; Berlemann & Tran, 2020 ) shows how the Vietnamese population chooses different coping strategies in response to different kinds of environmental stressors. While gradual climatic variations lead to mechanisms of adaptation in loco to new climatic conditions, sudden shocks drive the decision to migrate elsewhere. However, mobility responses to different types of hazards might be different according to their specific consequences and duration (Berlemann & Tran, 2020 ). On the contrary, the case of Bangladesh supports the hypothesis that the existence of previous barriers to access to migration is worsened by the occurrence of disasters, specifically in the face of recurrent and intense flooding (Gray & Mueller, 2012b ).

The specific case of earthquakes across the world (El Salvador in Halliday ( 2006 ), Japan in Kawawaki ( 2018 ) and Indonesia in Gignoux and Menéndez ( 2016 ) for instance) shows a common trend of outcomes: highly disruptive disasters such as earthquakes tend to decrease mobility from the hit area. An interesting mechanism to explain this common trend found in three very different contexts is given by, not only the already mentioned financial constraints but also the possibility of higher local employment opportunities due to post-disaster reconstruction (Gignoux & Menéndez, 2016 ; Halliday, 2006 ). Moreover, households are found to respond to hazard by using the labor force as a buffer to the damages and redistributing labor within the household, with female mobility drastically dropping more than males and being substituted with increased hours of domestic labor (Halliday, 2012 ).

Analyses on South American countries also contribute to giving a hint of the complexity of the phenomenon. Thiede et al. ( 2016 ) show how internal migration is indeed impacted by rising temperature when considering the general effect; however, it hides an extreme heterogeneity of outcomes when specific characteristics of the areas and individuals are taken into account, resulting in a non-uniform effect.

An evident gap in the literature emerges in Fig. 4 : European countries have rarely been the object of study of the impact of environmental factors on mobility. This might be motivated by the fact that the European continent is mostly seen as a destination for migrants than an origin. It should not surprise that the two articles covering European countries, namely Italy (Spitzer et al., 2020 ) and the Netherlands (Jennings & Gray, 2015 ) analyze historical data of mobility at the beginning of the XX century (respectively earthquake in Sicily and Calabria and climate variability associated with riverine flooding in the Netherlands). Nevertheless, figures show that Europe is not unrelated to the occurrence and frequency of hazards as well as to sizable internal mobility that should receive some attention.

3 The inter-connectivity of papers

Our quantitative approach aims at analyzing the connectivity that exists among papers according to a citation-based approach and detecting the existence of communities or clusters. Since our target literature is characterized by a high heterogeneity of results, both in the direction and magnitude of the impact, we try to investigate the existence of potential specific patterns that lead to a certain type of analysis, methodology, or result under network-analysis lenses. We then use all information from this section to implement the meta-analysis.

3.1 Bibliographic coupling and citation-based approaches

The citation-based approach we choose is called bibliographic coupling. Footnote 11 Two scientific papers “bear a meaningful relation to each other when they have one or more references in common". Thus, the fundamentals of the link between two papers are depicted by the number of shared papers they both include in their references, which constitute the strength of the connectivity they have. In other words, a reference that is cited by two papers constitutes a “unit of coupling between them" (Kessler, 1963a ). Two articles are then said bibliographically coupled if at least one cited source appears in both articles (Aria & Cuccurullo, 2017 ). Bibliographic coupling is increasingly becoming widely used in citation analysis, thanks to some specific advantages (and despite some disadvantages). Conceptually, through the linkages established, it gives a representation of the basic literature of reference and, incidentally, implies a relation between two papers that reveals a potential common intellectual or methodological approach (Weinberg, 1974 ). The constancy of the links between the papers over time, being based on cited references which, once published and indexed, is also an asset (Thijs et al., 2015 ). Most importantly, the bibliographic coupling is more suitable for recent literature than other citation-based approaches. For reasons of timing and extension of the time window, Footnote 12 using any other citation-based approach would have resulted in a very sparse matrix and created many isolated observations which would not be inter-connected for reasons other than conceptual, but just for the fact that they could not have been cited yet. Not only do the characteristics of our sample motivate the choice of the approach: keeping in mind that this stage of the analysis aims to investigate and map current research fronts in the target literature rather than to look at historical links or the evolution of school of thoughts, bibliographic coupling seems to be the best tool to capture them (Klavans & Boyack, 2017 ).

To obtain the network of bibliographically coupled papers, we initially extract the list of cited references from each article and build a bipartite network, a rectangular binary matrix \(\textbf{A}\) linking each paper in the sample to their reference (Aria & Cuccurullo, 2017 ):

The matrix \(\textbf{A}\) is composed of 151 rows i representing the papers belonging to the sample and 5.433 columns j representing the ensemble of references cited in each paper in the sample. Each element \(a_{ij}\) of the matrix equals 1 when paper i cites paper j in its bibliography; \(a_{ij}\) is equal to 0 otherwise. Starting from matrix \(\textbf{A}\) , we can derive the bibliographic coupling network \(\textbf{B}\) as follows:

where \(\textbf{A}\) is the cited reference bipartite network and \(\mathbf {A^T}\) is its transpose. \(\textbf{B}\) is a symmetrical square matrix 151 \(\times\) 151, where rows and columns are papers included in the sample. Element \(b_{ij}\) of the matrix \(\textbf{B}\) contains the number of cited articles that paper i and paper j have in common. By construction, the main diagonal will contain the number of references included in each paper (as element \(a_{ii}\) defines the number of references that a paper has in common with itself).

The resulting matrix displays an undirected weighted network in which the 151 vertices are the set of papers included in our sample and the edges represent the citation ties between them. An existing tie implies that common reference literature exists between vertex i and j . When two nodes are not linked, the corresponding value of their tie is zero, as they do not share any common reference. Therefore, the network is weighted with the strength of the connections between papers i and j being measured by the weights associated with each tie. To avoid loops, which would be meaningless for our investigation, Footnote 13 we set the main diagonal to zero. Few ties exceed 20 shared cited references, with a maximum value of 48. Footnote 14 It can be argued that the number of references included in an article is not neutral to the resulting tie with any other article. Measuring the correct relatedness of nodes is of primary importance to produce an accurate mapping of literature (Klavans & Boyack, 2006 ). Citation behaviors of authors may interfere with the observation of core reference literature at the basis of coupled nodes. An author may opt for an extensive approach of citations and include a consistent number of references to display some particular links or details of a paper; authors may also decide for a less inclusive approach and include just essential cited references in the list. In other words, the number of included references in one article may dissolve meaningful information about the ties. Furthermore, specific formats or types of articles lead to broader or narrower bibliographies. To address these concerns, a process of normalization is needed so that data can be corrected for differences in the total number of references. Bibliometric literature has dealt with this issue through the calculation of different similarity measures . An accurate overview of the possible measures of similarity is provided in van Eck and Waltman ( 2009 ). Overall, such indices aim to determine the similarity between two units according to their co-occurrence (value of association between them, which in our case, is the number of common references in the bibliography) adjusted in different ways for the number of total occurrences of the single units. However, despite the need to correct data for many purposes in citation-based networks and obtain a size-independent measure of association, there is no consensus on which measure is the most appropriate (van Eck & Waltman, 2009 ): tests of accuracy and coverage proposed by different authors have reached different conclusions (Klavans & Boyack, 2006 ; van Eck & Waltman, 2009 ; Sternitzke & Bergmann, 2009 ). We apply a simple ratio between the observed number of commonly shared references and the product of the number of cited references in each of the two coupled papers. It has been defined as a measure of association strength (van Eck & Waltman, 2009 ) and it can be expressed as:

where \(b_{ij}\) corresponds to the weights of the tie between i and j in the original bibliographic coupling network; \(b_{ii}\) and \(b_{jj}\) are respectively the number of cited references included in paper i ’s bibliography and in paper j ’s bibliography, which corresponds to the original value on the diagonal. The obtained weighted network will serve to detect communities of papers through their common references and investigate if referring to a certain (group of) paper(s) creates meaningful clusters of items aggregating around certain common characteristics.

3.2 Community detection

We intend to identify the existence of communities in our network. The assumption is that papers citing the same references aggregate into a group that shares certain features, which could be methodological approach, level of analysis, specific sub-topics of the literature, and outcomes. The extreme heterogeneity of outcomes in this specific literature may be motivated partially by the heterogeneity of the events themselves (type of environmental factor, type of mobility, preexisting conditions in the specific area) or the theoretical and empirical modeling; it may also be motivated by other factors, that can be traced in some patterns linked to the characteristics of single publications. The procedure of community detection is aimed at investigating which are the “forces" that aggregate or disperse papers with each other, primarily through the direct observation of main characteristics, and then running separate MAs on each cluster. Community detection in the bibliographic network is often made through Louvain community detection algorithm (Blondel et al., 2008 ). In this analysis, a community is thought of as a group of contributions that share common references and form strong common ties with each other, while others have less shared characteristics and structure. The algorithm can detect clusters of contributions with dense interaction with each other and sparse connections with the rest of the network (Fig. 5 ).

Bibliographic coupling network and detected communities Note : Bibliographic coupling network of 151 documents included in the sample obtained from Scopus, Web of Science, Google Scholar, IDEAS RePEc and previous meta-analyses (Hoffmann et al., 2020 ; Beine & Jeusette, 2021 ). Each node represents a paper included in our sample and its size corresponds to its weighted degree. Nodes are tied by links whenever two nodes share at least one common reference. The thickness of links is given by the association strength of the tie between two nodes (to provide a clear visualization, only nodes with weights higher than the mean are displayed). Colors correspond to communities of belonging of each paper: Cluster 1 is represented in violet, Cluster 2 in green, Cluster 3 in blue, and Cluster 4 in yellow. The description of each Cluster is presented in the text

The procedure identifies four main clusters. Our network being relatively small allows analyzing the main characteristics of each cluster. Following the full-text screening made in the first step of our threefold approach, we summarized some meaningful indicators about the analysis (such as type - quantitative, qualitative, theoretical, policy, literature review -, level - macro or micro for quantitative and qualitative studies -, unit - country, household, individual, territorial units), the object of the analysis (concerning the type of migration and environmental factors studied and the area) and theoretical and empirical approach (empirical approach and whether it is theory-based, estimation strategy and potential channel investigated). Finally, we recorded a synthetic indicator of the concluding effect of environmental factors on migration patterns: for each paper, we assigned the value “positive", “negative", “not significant" or a combination of the three (in case a paper contains multiple analysis of different migration or environmental factors that lead to different outcomes). Thanks to these indicators we were able to have a picture of the main common characteristics of the papers included in a cluster (Appendix Table 8 ), which will be tested and eventually confirmed in the MA.

The first cluster (Cluster 1) is the most populated, counting 51 papers spanning the entire period considered (from 2003 to 2020). In terms of the type of analysis, it contains the largest variety: as in all clusters, quantitative studies represent the majority (as they are the 76% of the full sample), but this cluster contains also most of the qualitative analyses (10 out of 13) and policy papers (5 out of 7) of the full sample. Published papers are predominant (47 out of 50). Except for a few papers, the analysis is mainly carried from a micro perspective, with individuals as units of analysis, based on surveys. Interestingly, most of the micro-level studies included in Beine and Jeusette ( 2021 ) can be found in this cluster. Authorship is very concentrated around two main authors, Clark Gray, (co-)authoring 9 papers, and Valerie Mueller, (co-)authoring 4 papers. Many of their co-authors appear in this community, which indeed scores the highest collaboration index of all communities (2.86), much higher than the full sample (2.16). Another important feature is that Cluster 1 includes the micro-level papers with the highest global citations: Gray and Mueller ( 2012b ), Feng et al. ( 2010 ), Gray and Mueller ( 2012a ), Mueller et al. ( 2014 ), Henry et al. ( 2004 ), Henry et al. ( 2003 ) and Gray ( 2009 ). This is also shown by the fact that the number of average citations per document is the highest among all clusters (34.84). Journals are also quite concentrated around a few of them, World Development and Population and Environment mainly. The content of the analyses is mainly focused on climatic change exclusively (precipitation and temperature), while few studies include also natural disasters. All corridors of migration are investigated, with no specific predominance of internal or international migration (which is a characteristic of individual-level studies, mainly based on surveys). Even though the majority of outcomes show a positive coefficient, that can be translated into finding an active role of environmental factors in pushing migrants out of their origin areas, it is not consensual to every paper: variation among results is high compared to other clusters, most paper finding complex relations between the two phenomena and different directions according to different dimensions. Empirical strategies are often based on discrete-time event history models estimated through multinomial logit. This reflects the approach of the main authors included in this community. A strong accent is put on the importance of the agricultural channel and the theme of adaptation to the change in environmental conditions.

The second community (Cluster 2) counts 28 papers, mostly published, except for 4 of them. It is composed of mostly quantitative papers, accompanied by 5 literature reviews. As in the previous cluster, most studies are at a micro level, with all kinds of units of analysis and aggregations. Both patterns of migration are explored, but with special attention to urbanization and internal mobility. Contrarily, it seems to put a stronger accent on natural disasters rather than on slow-onset events. The majority of papers in Cluster 2 have been excluded from Beine and Jeusette ( 2021 ) (only 5 included, compared to the 21 in Cluster 1) and Hoffmann et al. ( 2020 ) (only 1, all others being in Cluster 4). All papers analyzing the impact of different kinds of natural disasters in the U.S. are included in this cluster. Empirical approaches such as the differences-in-difference model and instrumental variable are often used. The papers explore a large variety of potential channels and mechanisms of transmission of the impact of environmental factors on migration (income, agriculture, employment, liquidity constraints), and only in a few cases, a negative direction is found.

The third cluster (Cluster 3) includes the most recent papers: only one paper dates 2011, all other ones are published or issued after 2015. This is part of the reasons why the average citations per document in this cluster is the lowest (10.89) compared to any other cluster. Half of the overall unpublished papers are included in this cluster. In terms of kind of analysis, this cluster appears to be very heterogeneous: even if the micro-level analysis is the majority, 12 papers apply a macro-level analysis on countries. Both cross-country and internal migration are considered, but the majority of them investigate the impact of slow-onset events rather than fast-onset. Many of the analyses are theory-based, especially on classic economic migration theories (Roy-Borjas model, New Economics of Labor Migration), or general or partial equilibrium models. This cluster is also peculiar for the heterogeneity of empirical outcomes, which are often multiple for a single paper: outcomes vary according to the different channels explored, i.e. different levels of agricultural dependency, presence of international aid, and level of income. In many cases, environmental factors are an obstacle to the decision to migrate from an area, or completely neutral. Comparatively, outcomes from this cluster tend to show a complex picture and highlight the many dimensions that may intervene in determining the direction of the impact.

Contrary to the previous one, Cluster 4 is extremely homogeneous. It contains almost exclusively quantitative (32 out of 35) and macro-level studies (30 out of 35). It covers equally slow- and fast-onset events and their impact on mobility. Most importantly, it aggregates 23 of the 30 papers reviewed in Hoffmann et al. ( 2020 ), making this cluster very representative and comparable to Hoffmann et al. ( 2020 )’s MA. Additionally, this community appears to be solid also in terms of theoretical and empirical approaches, as micro-founded gravity or pseudo-gravity models are widely used in it (more than half of them use such models). None of the studies find a negative impact of environmental factors on migration, they mainly estimate positive and significant outcomes, with few not-significant results for specific cases. The most locally cited macro papers are included in this cluster, which also receive high global citations with an average of citations per document 24.91 (even though lower than Cluster 1).

This description of cluster composition serves as a preliminary investigation of which are the main characteristics linking papers together through their citation behavior. It emerges that stronger links are given by diverse indicators varying across clusters. To test which are the sources of heterogeneity between clusters that aggregate papers within a cluster and their impact on the estimated effect size, in the next section, we will use this partitioning to run four separate MAs and compare the conclusions.

4 Meta-analysis

The purpose of our MA is to summarize the results of collected studies and, at the same time, highlight any possible sources of heterogeneity. The analysis is based on four assumptions: (i) our parameter of interest, which we call \(\beta\) , is the effect of climate change on migration; (ii) most researchers believe that \(\beta\) is greater than zero, and this is indeed true; (iii) the sign is not enough for decision-makers; (iv) this has attracted a large literature that has obtained a large number of estimates \(\hat{b}\) of \(\beta\) . Each of the 96 selected papers contains one or more equations that estimate the migration effect due to environmental factors. Footnote 15 In addition to the characteristics specific to migration itself, the estimated impact on migration can also be distinguished according to different features of environmental factors. Since comparability among studies, and more specifically among estimated \(\beta\) s, is a crucial issue for the MA, we group all collected estimates and conduct two separate analyses according to the type of environmental phenomenon: gradual or slow-onset events and sudden or fast-onset events. To compare the estimates and correctly interpret the synthetic results we need to standardize all collected effect sizes \(\beta\) in a common metric. In this MA the estimates from separate, but similar studies, are converted into partial correlation coefficients ( pcc ):

and its standard error, \(se_i\) :

where \(t_i\) and \(df_i\) are the t-value and the degrees of freedom of the i-th estimate \(\beta _i\) . The pcc is commonly used in MA literature (Doucouliagos, 2005 ; Stanley & Doucouliagos, 2012 ; Doucouliagos & Ulubasoglu, 2006 ; Brada et al., 2021 ) and allows to analyze within a single framework of all available studies on the effects of environmental stressors on migration regardless of the specification or measure of migration used. Footnote 16 Summarizing all the different estimates together in a single coefficient raises the question of heterogeneity within the same study and between studies. The summary effect is calculated as follows:

where \(\hat{b}_i\) is the individual estimate of the effect and weight, \(w_i\) , in a fixed effects model (FEM) is inversely proportional to the square of the standard error, so that studies with smaller standard errors have greater weight than studies with larger standard errors. The FEM is based on the assumption that the collected effect sizes are homogeneous (the differences observed among the studies are likely due to chance). Unlike in the FEM, random-effects model (REM) takes into account the heterogeneity among studies and weights incorporate a “between-study heterogeneity", \(\hat{\tau }^2\) . In the presence of heterogeneity, the two models likely find very different results, and it may not be appropriate to combine results. A test of homogeneity of the \(\beta _i\) is provided by referring to the statistic Q to a \(\chi ^2\) -distribution with n - 1 degrees of freedom (Higgins & Thompson, 2002 ): if the test is higher than the degrees of freedom, the null hypothesis is rejected (and thus there is heterogeneity). Another test commonly used is the \(I^2\) inconsistency index by Higgins and Thompson ( 2002 ) describing the percentage of the variability of the estimated effect that is referable to heterogeneity rather than to chance (sample variability). Values of the \(I^2\) range from 0 percent to 100 percent where zero indicates no observed heterogeneity. Since most computer programs report \(I^2\) , and so it is readily available, it is largely used to quantify the amount of dispersion. However, it is a proportion and not an absolute measure of heterogeneity in a meta-analysis (Borenstein et al., 2017 ). To understand how much the effects vary and report the absolute values, we compute the prediction interval as suggested by Borenstein et al. ( 2017 ). The results of the meta-synthesis of the collected estimates (Table 1 ) are statistically significant, except for findings of the slow onset effect of paper included in Cluster 2 (where the most of studies focus on the fast onset effect), in which both FEM and REM give statistically insignificant averages.

The preliminary result of the basic MA is that environmental factors seem to influence migration positively, even if the magnitude is very small and the REM mean is statistically significant only in the case of fast-onset events. The mean effect by cluster becomes negative in the case of estimates of slow-onset events in Clusters 1 and 3 and for the estimates of fast-onset events in Cluster 2.

4.1 Meta-regression tests of publication selection bias

Different findings of the same phenomenon can be explained in terms of heterogeneity of studies’ features, however, the literature also tends to follow the direction consistent with the theoretical predictions causing the so-called publication bias. Footnote 17 Meta-regression tests, such as the funnel asymmetry test (FAT), allow for an objective assessment of publication bias:

Weighted least squares (WLS) corrects the previous equation for heteroskedasticity (Stanley & Doucouliagos, 2017 ) and it can be obtained by dividing \(pcc_i\) by the standard errors:

Results are used to test for the presence of publication selection ( \(H_0:\beta _1 = 0\) ) or a genuine effect beyond publication selection bias ( \(H_0:\beta _0 = 0\) ). According to the Funnel Asymmetry and Precision-Effect Tests (FAT-PET), in the absence of publication selection the magnitude of the reported effect will vary randomly around the “true” value, \(\beta _1\) , independently of its standard error (Stanley & Doucouliagos, 2012 ). Replacing in eq. ( 7 ) the standard error \(se_i\) with the variance \(se_i^2\) , as the precision of the estimate, gives a better estimate of the size of the genuine effect corrected for publication bias (Stanley & Doucouliagos, 2014 ). This model is called “precision-effect estimate with standard error” (PEESE) and the WLS version is:

Table 2 shows results of the FAT-PET using multiple methods for sensitivity analysis and to ensure the robustness of findings. To take into account the issue of the dependence of study results, when multiple estimates are collected in the same study, the errors of meta-regressions are corrected with the “robust with cluster" option, which adjusts the standard errors for intra-study correlation.

Column (1) of Table 2 presents the FAT-PET coefficients, column (2) shows the results of the WLS model to deal with heteroskedasticity, columns (3) and (4) present the results of the panel-random effect model (REM) and multilevel mixed-effect model that treats the dataset as a panel or a multilevel structure.

Looking at the estimates of the effect of climate change on migration, the FAT coefficients ( \(\hat{\beta }_1\) ) are not statistically significant, implying that there is no evidence of publication bias, while the positive and statistically significant PET coefficient ( \(\hat{\beta }_0\) ) indicates a genuinely positive slow-onset effect exists, in particular in the case of Cluster 4. Conversely, in the case of Cluster 3 the REM and multilevel mixed-effect model find that, even if in presence of publication bias, the impact on migration is negative. Table 2 provides evidence of publication bias in the literature focusing on the effect of natural disasters on migration. The estimated FAT coefficient is statistically significant in the overall sample, especially due to papers in clusters 1 and 3, and there is insufficient evidence of a genuinely positive effect (accept \(H_0: \hat{\beta }_0\) ).

4.2 Multiple meta-regression analysis: econometric results and discussion

The multiple meta-regression analysis (MRA) includes an encompassing set of controls for factors that can integrate and explain the diverse findings in the literature. To capture possible sources of bias among all analyses, we code all differences in the features of the various studies and regressions and include a set of dummies to control for them. Specifically, we code left- and right-hand side characteristics of regressions estimated in the collected papers and generate a set of dummies for paper features, dependent variables, independent variables, sample characteristics, and regression characteristics. Footnote 18

The overall sample includes both unpublished and published papers, so we add some moderators variables describing different features of the studies that are published. In particular, we introduce a dummy for Published articles and a control for the quality of the journal in which the study is published by adding the variable Publication Impact-factor . In reporting the main results, some authors emphasize a benchmark regression that produces a preferred estimate, thus we add the dummy preferred specification equal to 1 when the reported effect size is obtained from the main specification. Concerning the measure of migration, the dependent variable in the left-hand side of the regression, original studies mainly distinguish migration by corridor , which are mainly two, internal and international migration. In this context, we distinguish also a special internal corridor, the one characterized by rural-urban mobility, to investigate the potential impact of an environmental variable on the urbanization process. Whenever the corridor is not specified, the variable is categorized as undefined (which will be the reference category in the estimation). Dependent variables differ also in terms of measurement of the phenomenon: specifically, we separate measures that express flows from those expressing stocks. The first category includes both studies that use flows (or an estimation of flows) and rates of migration. The second category captures those cases in which migration is measured as a stock of migrants at the destination. The reference category is direct measures, which mainly capture whether migration has occurred or not (typically dummy variables used on survey-based samples equal to 1 when the individual migrates and 0 otherwise). We also include information about the countries of origin and the destination of migrants. Origins are categorized by macro-regions: Africa, Asia, Europe, Latin America and Caribbean, Middle East and North Africa, and North America. The reference category is “world", identified whenever origin countries are not specified (typically in multi-country settings). Destinations are categorized by level of income. The choice of this categorization is led by the aim to identify differences in the possibility to choose a destination. Categories are divided into high, higher-middle, lower-middle, and low-income.

The specific objective of the study is the impact of environmental variables on migration, thus on the right-hand side of the regression a proxy of the environmental change is included. Slow-onset events are typically defined as gradual modifications of temperature, precipitation, and soil quality. Respectively, three dummies temperature, precipitation and soil degradation are created. Each of these phenomena is measured in different ways, and the use of a specific kind of measurement is relevant to the outcome. Both temperature and precipitation have been measured in levels (simple level or trend of temperature/precipitation); deviation, as the difference between levels and long-run averages; and anomalies, mostly calculated as the ratio of the difference between the level and the long-run mean and its standard deviation. Soil degradation includes events such as desertification, soil salinity, or erosion. Additionally, we also code the time lag considered concerning the time units of the dependent variable: whenever the period considered corresponds to the same period of the dependent variable the lag is zero, while it takes values more than zero for any additional period before the dependent variable time-span. This control also allows us to account for varying time-frames in different studies, including situations where migration spans several years or occurs suddenly in the aftermath of a natural disaster. The second battery of coded variables refers to fast-onset events, which can be also defined as natural hazards or extreme events. The main classification of fast-onset events reflects the one reported in Sect. 2 : geophysical (earthquakes, mass movements, volcanic eruptions), meteorological (extreme temperature, storms - cyclones, typhoons, hurricanes, tropical storms, tornadoes), hydrological (floods and landslides) and climatological (droughts or wildfires). Fast-onset events also differ in the way they are measured. Possible measures are occurrence (when the measure is a dummy capturing if the disaster happened or not), frequency (the count of events that occurred in the area), intensity (i.e. Richter scale for earthquakes, wind speed for tornadoes, etc.), duration (length of the occurrence of the event) and losses (when the disaster is measured in terms of the affected population, number of deaths or injured people, number of destroyed houses or financial value of the damaged goods). As for slow-onset events, we code a continuous variable capturing the time lag of the event concerning the dependent variable. A dummy capturing whether the coefficient refers to multiple disasters is also included.

Characteristics of the sample are one of the main sources of heterogeneity. The level of the analysis varies considerably from paper to paper, as we include both micro-and macro-level studies. we code variables capturing both the specific unit of analysis and the source of the data. Typically micro-level studies use data coming from censuses or surveys where households or individuals are the units of analysis. Country-level studies usually take the source of their data from official statistics . Other kinds of sampling are included in the reference group (for example small territorial aggregates such as districts, provinces, or grid cells). We also code a variable capturing the time span of the analysis, subtracting the last year of observation from the first one. The role of econometric approaches may have an impact on resulting outcomes. Beine and Jeusette ( 2021 ) emphasized in their work the importance of methodological choices, with differentiated results depending on estimation techniques. First of all, we code a panel dummy to capture whether the structure of data and related estimation techniques has an impact. Furthermore, we distinguish Poisson estimations that include the Pseudo Poisson Maximum Likelihood (PPML) estimator and Negative Binomial Models; linear estimators, both Ordinary Least Squares (OLS), linear probability models and maximum likelihood models; conventional Instrumental Variables (IV) estimators, two-stage least squares (2SLS), and other cases of estimators as Generalized Method of Moments (GMM) used to control for endogeneity; and finally, logit which comprises multinomial logit models. Any other estimator (i.e. Tobit, panel VAR) is less frequent and grouped in a category other estimators used as the reference group.

Theoretically, the impact of environmental variables on migration may be mediated, channe-led, or transmitted through other phenomena that can be controlled for or interacted with. Most of models investigating general migration determinants usually control for several possible determinants to recover the effect of the specific objective variable, with all potential other factors being controlled for. The majority of these additional controls are suggested by theoretical models and then introduced in the empirical model. Furthermore, methodological approaches in our sample are found to often include interaction terms to specifically address the combined effect of an environmental variable with other potential factors. Thus, we introduce two groups of variables, controls and interacted terms , categorized both to capture factors or channels such as income, agriculture, conflicts, political stability, cultural or geographical factors. Among the list of controls, we also include a dummy that captures whether both slow- and fast-onset events are included in the regression.

Table 3 shows the results of the multiple MRA on the literature in slow-onset events (precipitation, temperature, and soil quality) in which potential biases are filtered out sequentially by the addition, in a stepwise manner, of statistically significant controls. Column (1) presents results for the whole sample of studies estimating the impact of climatic variations on migration, and columns (2) to (5) show the results of papers grouped by clusters to highlight how specific features characterizing the cluster influence the magnitude of the estimated effect. The results are unfolded below.

Column (1) refers to the overall sample and shows a coefficient of the main variable of interest ( \(\hat{\beta }_0\) ) negative and statistically significant, implying that climatic variations may decrease incentives for migration by exacerbating credit constraints of potential migrants. Looking at results for different clusters (columns 2-5) such a negative effect is generated by studies that are included in clusters 1 and 3. The MRA of papers in clusters 2 and 4, instead, gives positive and statistically significant PET coefficients ( \(\hat{\beta }_0\) ) implying that climate changes induce people to migrate. Concerning the FAT-test, the intercept ( \(\hat{\beta }_1\) ) might deviate from zero confirming the presence of publication bias: the peer-review process seems to particularly affect the magnitude of the estimated effect of studies in all clusters except for Cluster 3.

Most of the papers included in the MRA for slow-onset events are published (52 articles out of 66), indeed the estimated coefficients of controls for published articles are useful to evaluate if the peer-review process exerts some influence on reported results in the collected studies. In Cluster 3 estimates obtained by the Preferred specification tend to be slightly lower while articles published in journals with higher impact factors report lower estimates of the impact of slow-onset events on migration. In Cluster 4, instead, results of Published articles are lower, even if the mean effect of this group of studies remains positive.

From the other sets of controls emerges that specific features of studies included in the MRA differently explain the diversity in the results within clusters. The positive coefficients of controls for corridors such as Internal and Urbanization state that people respond to adverse climatic change with increased internal migration. The only exception is for studies included in Cluster 3, this is the most heterogeneous cluster of most recent papers, where heterogeneous approaches (micro-and macro-level and type of migration) lead to a large heterogeneity in outcomes, varying according to different channels explored. Findings obtained when mobility is measured by Flows seem to be lower in the overall sample. In macroeconomic literature, usually, the measurement of migration is a stock variable, since it is generally easier to find and measure the number of foreign citizens born or resident in a country at any given time. Data on flow variables and migration rates, or the number of people who have moved from an origin to a destination in a specific period, are less available, and analyses often rely on estimates and computations of this data. Therefore, the opposite sign of the coefficient of the variable Flows in Cluster 1 is not surprising since this cluster collects all micro-level studies (where the migration variable refers to the movements of individuals as a unit, based on surveys).

Controls for how the climatic phenomenon is measured, Precipitation measures and Temperature measures , seem to differently affect the heterogeneity of results and, in many cases, the estimated coefficients are statistically significant but very close to zero.

The estimated coefficients of dummies for country groups included in our multiple MRA indicate how results from analyses focusing on specific regions of origin differ. In particular, positive coefficients of controls Asia and Europe support the idea that the results of analyses that focus on the migration from these regions are likely to be positive (with exception of Cluster 1), while if the people move from a country in the region of North America the impact of climate changes on migration is lower and can be negative. The climate impact on migration from LAC (Latin America and the Caribbean) countries are higher in Cluster 3 (where the PET coefficient is negative) and lower in Cluster 4 (where the PET coefficient is positive).

Regarding the heterogeneity produced by the fact that studies use different sources of data for migration, we add dummies for sources used. All estimated coefficients of this set of controls are statistically significant in Cluster 1: the use of different databases might influence the wide variety of findings. Effect sizes in Cluster 2, instead, are not affected by the source of data used.

Since it is natural to expect the adjustment of migratory flows in response to climate change is not instantaneous, especially in the case of gradual phenomena, most of the studies use a panel structure with a macroeconomic focus and attempt to assess the impact of changes in climatic conditions on human migratory flows in the medium-long term. Microeconomic analyses mostly use cross-section data to explain causal relationships between specific features of individuals, collected through surveys and censuses, and various factors determining migration by isolating the net effect of the environment. Analyses at Individual level tend to capture a more negative impact of climate changes on migration, whereas analyses at Country level tend to find a more positive effect. As already said, for micro-level analyses in Cluster 1 controls related to sample characteristics have opposite signs. Looking at dummies for the estimation techniques, our evidence suggests that the diversity in the effect sizes is in part explained by differences in techniques. In particular, positive and significant coefficients are found for controls as OLS and ML estimators for cross-section analyses, same for panel studies that use Panel estimation techniques, and Instrumental Variables ( IV ) or GMM estimators to correct for endogeneity. Micro-economic analyses (Cluster 1) use more disaggregated data, while the high presence of zeros in the dependent variable is treated with a Poisson estimator, which tends to produce lower estimates.

Many authors highlight the importance of variables of political, economic, social, and historical nature, in influencing the impact of climatic anomalies on migration processes, emphasi-zing the role of important channels of transmission of the environmental effect to migrations. We include in the multiple MRA a set of dummies for Controls included in the estimation of the model of migration and dummies for Channels through which the climatic event determines migration phenomena. The idea is that studies based on the same theoretical framework tend to include the same set of control variables or interacted terms and we find that many of these controls may positively and negatively affect the effect size of climate changes on migration.

Table 4 shows the results of the MRA for fast-onset events, or rather natural disasters, more or less related to climate change, which appear as destructive shocks of limited duration and for which the ability to predict is reduced. Footnote 19

The coefficient of \(\hat{\beta }_0\) , is positive and statistically significant in the overall sample and clusters 2 and 4, providing evidence of an increase in migration due to sudden natural hazards. It is worth noting that papers in Cluster 2 (column 3) mainly focus on fast-onset events and the summarized effect size is positive and very high. On the other side, the summarized effect of papers in clusters 1 and 3 is negative and statistically significant.

Results show evidence of publication bias for the overall sample and in Cluster 3, with \(\hat{\beta }_1\) statistically significant signaling that the reported effect is not independent of its standard error. The significant and positive coefficient found for the published dummy confirms that there is a general Publication Impact , so the peer-review process seems to affect the magnitude of the estimated effect, especially in clusters 1 and 2. Articles published in journals with higher Impact-factor get higher estimates of the effects of natural disasters on migration, with exception of published articles in Cluster 2, suggesting that editors prefer to publish results that have a positive but more limited effect. Natural disasters affect domestic and international migration flows. The positive coefficients of the group of controls related to the type of migration, in clusters 2 and 3 confirm that people respond to natural disasters with any kind of mobility. Specifically in Cluster 2 natural disasters increase both Internal and Urbanization migration, while studies in Cluster 3 find a greater effect on Internal and International movements of people. In Cluster 4, instead, estimates of the impact of natural disasters are lower in the case of Internal migration. Hydrological events have a greater impact on migration, the estimated coefficient is statistically significant in all clusters; if the fast-onset event refers to Geophysical , Meteorological and Climatological disasters the effect on migration is lower.

The severity of natural disasters, such as hurricanes, landslides, or floods, affects regional agricultural production and it also has direct effects on employment and income in the agricultural sectors of the affected regions pushing people to migrate. However, on the one hand, natural disasters, such as droughts, floods, and storms, push individuals to move to find new sources of income or livelihood, on the other hand, natural disasters such as earthquakes, tsunamis, or hurricanes cause losses to populations that might lead people into a poverty trap, with potential migrants not having the resources to finance the trip. These effects, already highlighted by the literature, seem to be confirmed. Also in this literature, indeed, various controls and transmission channels analyzed in the original empirical models have a role in determining heterogeneity in results.

5 Conclusions

The present meta-analysis, aimed to systematically review and synthesize the empirical evidence on the relationship between environmental change and human migration, suggests that while there is a small, positive, and significant effect of slow- and rapid-onset environmental variables on migration, the heterogeneity of results in the existing economic literature highlights the need for a nuanced understanding of the causes and effects of environmental migration, as well as the specific characteristics of the places and populations involved.

If a key function of meta-analysis is to challenge and test the results of empirical studies, our study provides important insights that can inform both researchers and policymakers on the relationship between human migration and environmental changes or shocks. Specifically, our findings suggest that a more nuanced and context-specific understanding of environmental migration is needed. Future research could profit from our work by exploring the average effect of specific environmental shocks, such as droughts or floods, and the important role of mediating factors that influence the decision to migrate, such as specific economic and social conditions.

The paper also offers an encompassing methodology for the empirical analysis of very heterogeneous outcomes of a research field. The sample collected through a systematic review of the literature, the bibliometric analysis, the construction of a co-citation network and the community detection on the structure of the network of essays, allow the inspection of a scientific area also in absence of a uniform and cohesive literature. In the case of environmental migration, the too many different characteristics in terms of object of analysis, empirical strategy, and mediating covariates render the meta-analytic average effect estimates just a first approximation of the quantitative evidence of the literature.

As shown in the present meta-analysis, when the level of heterogeneity in the outcome of a literature is relevant, as for the four clusters of papers that compose the economic literature on environmental migration, a group-by-group analysis has to be preferred and compared with the results of an overall meta-analysis.

Moreover, our analysis highlights the need for greater collaboration and standardization of methods in the study of environmental migration. We report a lack of uniform and cohesive literature, with different studies using different methods, covariates, and definitions of key variables. This limits the external validity of existing results and calls for greater efforts by scholars and institutions to validate existing studies and improve the quality of data and methods used in future research.

Overall, our meta-analysis contributes to a better understanding of the complex relationship between slow or rapid environmental change and human migration. The implications of this work extend beyond the academic community to inform public policy and action. As environmental change and human migration continue to characterize the global system, it is crucial for decision-makers to consider the insights provided by scientific research and for the scientific community to continue to produce results that improve the external validity of existing studies and help delineate evidence-based policies.

A detailed table highlighting specific studies featured in other meta-analyses, along with their citations, that have been reviewed in our study is provided in the Supplementary material, Section A.

The extraction is made through bibliometrix , an R tool for science mapping analysis that reads and elaborates the information exported by Scopus and Web of Science (Aria & Cuccurullo, 2017 ).

Scopus: key (“migration" and (“natural disasters" or “climate change")) and ( limit-to ( subjarea ,“econ")) and ( limit-to ( language ,“English")), Date: 24/11/2020. Web of Science: (( AK =(migration and (“natural disasters" or “climate change"))) or ( KP = (migration and (“natural disasters" or “climate change")))) and language : (English) Refined by: web of science categories : (“economics"), Date: 24/11/2020.

We use the Advanced Search tool, searching by Keywords and Title: migration and (“natural disasters" or “climate change").

Our inclusion criteria prioritize studies reporting outcomes in an appropriate and consistent manner. In particular, we have excluded studies that do not rely on a complete set of objective measures. For instance, studies that only present estimated coefficients, solely indicating the significant level, without reporting standard errors or t -ratios have been excluded because they do not allow for the calculation of a meta-synthesis.

All records have been uploaded and summary statistics produced using the R tool bibliometrix (Aria & Cuccurullo, 2017 ). Scopus and Web of Science allow for the download in the bulk of records in .bibtex format, ready to be converted in R objects. Other records are manually entered, depending on the publication status of the single record: for published documents additional research of the specific document is made on Scopus and the relative .bibtex file is downloaded and added to the other results; for unpublished papers, which cannot be found in the two sources, a .bibtex is manually created following the structure of fields and information in the downloaded ready-to-use files. After merging each file and removing duplicates we obtain the data source that contains the bibliographic information of all articles, including publication year/latest draft, author(s), title, journal, keywords, affiliations, and references.

Variants of words or concepts have been aggregated in a unique item i.e. climate change and climatic change or environmental migrants and environmental migration .

The issue of timing will be addressed in the network analysis, choosing a specific type of citation-based network, the bibliographic coupling network, to minimize the risk of missing connections between papers.

Some contributions are not single-case studies.

Asia suffered the highest number of disaster events. In total, between 2000 and 2019, there were 3,068 disaster events in Asia, followed by the 1,756 events in the Americas and 1,192 events in Africa (UNDRR, 2020 ).

Bibliographic coupling, first introduced by (Kessler, 1963b , a ), belongs to the broader class of citation-based approaches to science mapping. Co-citation is based on the relationship established by citing authors of a paper: two papers are linked whenever they jointly appear in the cited references of at least a third paper. Direct citation is the most intuitive approach, linking two papers if one has cited a precedent one. As co-citation, direct citation performs better for long time windows to visualize historical connections (Klavans & Boyack, 2017 ). In terms of accuracy, it has been established that direct citation provides a more accurate representation of the taxonomy of scientific production (Klavans & Boyack, 2017 ), but for the specific requirements the methodology imposes, it has not gained much success (Boyack & Klavans, 2010 ).

Our sampled literature starts in 2003 and ends at the moment the research has been done (November 2020), testifying the recent interest of economic literature on the topic.

It is trivial to observe the value of ties that link a paper with itself, which naturally corresponds to the number of listed references.

This number seems very high, but at a closer look, the two papers that register the highest value are two consecutive papers published by the same author (Naudé, 2008, 2010).

Detailed information on collected coefficients and standard errors are provided in the Supplementary material, Section B.

A summary of the distribution of computed partial correlation coefficients is provided in the Supplementary material, Section C.

The publication bias occurs when (i) researchers, referees, or editors prefer statistically significant results and (ii) it is easier to publish results that are consistent with a given theory. However, the consequences of the peer-review process refer more to a general “publication impact" rather than a “bias" (Cipollina & Salvatici, 2010 ).

The complete description of coded variables is available in Supplementary material, section D.

Potential biases are filtered out sequentially by the addition, in a stepwise manner, of statistically significant controls.

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Cipollina, M., De Benedictis, L. & Scibè, E. Environmental migration? A systematic review and meta-analysis of the literature. Rev World Econ (2024). https://doi.org/10.1007/s10290-024-00529-5

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A Systematic Literature Review and Meta-Analysis on Cross Project Defect Prediction

Summary ( 12 min read), 1 introduction.

In the realm of software quality control, defect prediction in general and cross project defect prediction in particular, have attracted a lot of attention.
Panies do not consider using defect prediction in practice [84] - this is also why researchers usually conduct in vitro studies.
In addition, experiments by Zimmerman et al. [82] revealed extensive insights as well as challenges for CPDP.

1.1 Prior Research

To the best of their knowledge, there does not exist any SLRs and formal meta-analysis on CPDP, however, three secondary studies have already been performed on defect prediction [1], [3], [5].
The first one by Fenton and Neil [5] covered defect prediction studies up to 1999 and provided a critique of the field with an emphasis on good and bad practices in statistical data analysis, though their review did not follow a systematic approach.
Of the 30 primary studies that passed quality assessment in this review, only 4 were published before 2010, which is the last year covered by the latest secondary study.
As a result, rather than mere applications of existing techniques, data manipulation approaches become of utmost interest and importance in CPDP settings.
The authors should caution the reader that, different than the systematic literature review part, their meta-analysis covers only those studies that benchmark CPDP vs. WPDP, i.e., they did not include pure CPDP or WPDP studies in the metaanalysis.

1.2 Research Goals

The objective of this study is to summarise, analyse and assess the empirical evidence regarding metrics, modelling techniques, different approaches and performance evaluation criteria in the context of CPDP.
Further, the authors want to explore the relative performance of CPDP vs. Within Project Defect Prediction (WPDP) models.
The authors defined five research questions to achieve these goals.
Table 1 shows those research questions and the motivation behind each question.

1.3 Contributions

This SLR contributes to the existing literature in the following ways: Community can use this set as a starting point to conduct further research on CPDP.
Personal use is permitted, but republication/redistribution requires IEEE permission.
These studies can act as a reliable basis for further comparisons and benchmarks.
The authors synthesis covers the following themes: metrics, prediction models, different approaches and performance evaluation in CPDP research.
To increase the validity of the meta-analysis, the authors use both fixed and random effects analysis and account for the differences within and between different studies.

2 RESEARCH METHODOLOGY

To achieve their research goals, the authors conducted a Systematic Literature Review (SLR) following the guideline provided by Kitchenham and Charters [36].
In addition to this guideline, the authors followed the structure of Hall et al. [1] for conducting the review and presenting the results.
Particularly, the authors used Hall et al.’s set of criteria (with slight modifications) for inclusion/exclusion and quality assessment of defect prediction studies with customisation for cross project defect prediction context.
All steps of their research are documented and the related data are available online for further validation, exploration and replication.
Scripts for the data analysis part of this SLR are also available online as part of the replication package for their SLR [100].

2.1 Selection of Primary Studies

A set of search strings were identified based on the research questions.
This search term was modified to suit the specific requirements of different electronic databases.
Search was performed on the full text of the papers, if allowed by the digital library, i.e., ACM Digital Library, IEEExplore, Google Scholar.
For Scopus and ISI Web of Science, the search was conducted on title, abstract, and keywords.
After applying inclusion/exclusion criteria to digital library search results (explained in the next section), the authors used the resulting set as input for the snowballing process, recommended by Wohlin [28], to identify additional studies (with potential hits to papers published after the initial search date).

2.2 Inclusion and Exclusion Criteria

Studies must report empirical CPDP research (learning and prediction) to be included.
Prediction outcome must include defect related information, for example, defect labels, number of defects, etc.
The inclusion and exclusion criteria, also summarised in Table 2, were applied and piloted by two researchers starting with the assessment of 15 randomly selected primary studies from the initial set of identified papers.
The agreement rate in the pilot study was “moderate” (0.59).

2.3 Selection Results

Figure 1 illustrates the overview of the study selection process.
In total, 1889 studies were detected based on their defined search terms.
After discarding the duplicate studies, 962 of them were left for further assessment.
Applying the inclusion and exclusion criteria to the title and abstract of each paper, decreased the pool of the papers for full-text reading from 962 to 41 studies.
Finally, 5 and 12 relevant primary studies were found using backward and forward snowballing, respectively, resulting in 46 studies to be included in this SLR.

2.4 Quality Assessment

The quality of each primary study was assessed based on a quality checklist.
The resulting six stages of assessment criteria are provided below.
Suitable performance measures must be reported for both Categorical and Continuous models.
11 studies did not meet the quality assessment criteria (failed in one or more steps) and this phase resulted in 35 studies to proceed with the data extraction phase.

2.5 Data Extraction

The data extraction form was designed to collect the data from primary studies and consequently, answering the research questions.
The data extraction process was piloted on a sample of five randomly selected primary studies to assess the completeness and usability of the data extraction form, as well as to guarantee the consistency between the researchers.
The extracted data for each study were held in tables, i.e., an Excel sheet per study.
The performance values are recorded in terms of original, average, and median values.

2.6 Data Analysis

There are many potential confounding factors that may challenge and affect the results of the synthesis performed in secondary studies.
In their case, these are different defect prediction models build for addressing different aspects of CPDP and evaluated in different contexts.
Hence, as long the results are interpreted in the light of stated limitations, they would be valid in their scope.
Rather, their results for theme X should be interpreted with assuming that other factors do not affect the outcome (directly or as a result of interplay of many factors) or that their impact is uniformly distributed across different studies cancelling out a systematic bias.
Specifically, their meta-analysis includes those studies that passed the quality assessment stage and if they reported results of experiments that compare CPDP with WPDP.

2.6.1 Performance Indicators

The authors mainly used violin plots [31] to illustrate the results of their analysis centred around performance indicators.
In the plots, the solid horizontal lines indicate the mean of the values for each case whereas the thin continuous lines represent the median.
These distinctions are taken into consideration when generating the violin plots.
//www.ieee.org/publications_standards/publications/rights/index.html for more information, also known as See http.

2.6.2 Modelling Techniques

Different modelling techniques are extracted for each model reported in the primary studies.
The authors present them in tabular form and their performances with violin plots.

2.6.3 CPDP Approaches

CPDP approaches correspond to data processing approach by each study and are presented in tabular form and in violin plots.
The authors discuss these in two categories: row processing and column processing.
Primary studies usually use a combination of these approaches.
These approaches will be discussed in the next section.
When a study reports multiple models with different approaches, its relevant performance data rows are included in the category of both approaches when plotting violin plots.

2.6.4 Meta-analysis and Forest Plots

Meta-analysis and, specifically, both fixed and random effect models are considered to compare the results of CPDP and WPDP studies.
Forest plots are used to demonstrate the results of their meta-analysis visually.
These comparisons are performed for precision, recall, f-measure, and AUC performance measures as they are among the top five frequently used measures in the studies.
These additional analyses can provide useful insights on how CPDP (vs. WPDP) behave on specific datasets and learners.
Finally, the authors included both fixed and random effect models, not only to provide more validity and insight into the results, but also to reveal possible sources of bias as will be explained in Section 4.
To start with an overview of primary studies, the majority of the CPDP studies were published during the past five years.
Figure 2 shows the frequency of the papers published each year.
43% of the studies are published in 2015, indicating that more contemporary studies are included in this SLR.
This paper presents the results of the categorical studies in depth .
The authors start each subsection with a summary of the findings to provide an insight about the results and then these summaries are expanded and explained in detail.

3.1 Theme: Independent Variables

All performance measures vary in relation to the choice of set of independent variables.
Many different sets of independent variables are used in the primary studies.
As shown in the table, most studies use a combination of different metric sets.
Lastly, two continuous model studies have mainly used Process and OO metrics when constructing prediction models.

3.1.1 Performance in relation to independent variables

Figure 3 presents the violin plots for the performance trends of the prediction models with respect to the independent variables used in each study.
In most cases, one can see a degree of instability in the plots especially with respect to the precision and recall.
In the AUC plot, OO+SCM+LOC has the lowest median value; lower than Process metrics which has the lowest fmeasure and recall medians.

3.2 Theme: Modelling Techniques

There are few studies which use various optimisation techniques on top of the base learners.
Naı̈ve Bayes (NB) is the most commonly used modelling technique in the categorical studies (513 data rows in 12 studies).
Study [S4] has the highest amount of contribution to the ensemble LR predictions by providing 264 of 344 data rows.
Two of these studies ([S18], [S44]) use NB and boosting as a part of their proposed CPDP approaches.

3.2.1 Performance in relation to modelling techniques

Figure 4 shows the model performances in relation to the modelling techniques.
Later, [S42] assessed the usefulness of Meta-learner LR with respect to alternative performance measures, i.e., f-measure and Nof20 and concluded that its performance is comparable to other composite algorithms except for MAX voting.
Ensemble techniques seem to affect the performance of LR, one of the most common learning techniques in the studies.
Boosting has not improved NB dramatically in terms of the median, but the stability is improved.

3.3 Theme: Performance Evaluation Criteria

Table 11 presents the most widely used performance measures used in the categorical studies.
Cost related measures such as inspection cost ([S8], [S11]), cost effectiveness ([S42]), and expected cost of misclassification ([S14]) were used in multiple studies and their importance were justified.

3.4 Theme: CPDP Approaches

Different studies have used different processing methods to build their models.
In the following, these methods are presented.

3.4.1 Data Related Issues and Approaches

Among them, data heterogeneity is the most frequently addressed CPDP specific issue (68% of studies), while the remaining ones are not unique to CPDP, e.g., class imbalance (25%), noise in data (7%), redundant (14 %), or correlated features (14%).
Collinearity and multicollinearity among independent variables might decrease the effectiveness of the prediction models.
The categorisation of the studies into column and row processing groups is illustrated in Tables 13 and 15.

3.4.2 Column Processing Methods

Column processing techniques addressing data related issues, and the studies they appear in, are listed in Table 13.
The study conducted in 2013 by Nam et al. [S24] proposed another transformation approach called TCA+ which tries to make feature distributions in source and target projects similar by transforming both source and target data to the same latent feature space.
Nam et al. [S37], have used various feature selection approaches such as gain ratio, chi-square, reliefF, and attribute significance evaluation.
Two types of normalisation, namely min-max and z-score, are commonly used of which z-score normalisation is more popular.

3.4.3 Row Processing Methods

Table 15 lists the row processing techniques, which targets data instances as opposed to data features, along with the studies in which they appear.
Later in 2013, they confirmed the usefulness of the filtering method in CPDP [S13].
Recently published study by Chen et al. [S18] also takes advantage of filtering method to avoid irrelevance instances in source dataset.
The minority class instances are weighted in a way that a more balanced distribution of data is achieved.

3.4.4 Other CPDP Approaches

The majority of the categorical studies have mentioned specific names for their proposed approaches such as TNB[S25], DTB[S18], VCB-SVM[S26], and CODEP[S8].
The majority of the studies (19 studies) present some models without any data specific approach.
They concluded that, when limited project history data is available, defect prediction models based on the mixed data are useful.
During their experiments, the authors combined five, ten, and 25 percent of WP data with CP data for model construction and concluded that there is no significant performance difference between using 25 and five percent of WP data.
The data from the local models benchmark appear under clustering category and association rule learning technique as used in [S11].

3.4.5 Performance in relation to data approach

Data oriented approaches seem to improve f-measure through improvements in recall with no visible trend on precision.
For the second part, the combinations of the approaches as they are proposed in the studies are used .
According to the plots in Figure 5, Normalization (N) has the highest median f-measure while its stability is not very good.
The recall based nature of data approaches is observed again in this set of plots as the plots for no data approach have the second best median precision and the worst median recall values.

3.5 Theme: Overall Paper Approach

The authors categorize the studies based on their main focus for further analysis.
Metrics are also another target for such models.
The focus of this set of studies is on optimising the learning approach and they usually present sophisticated learning methods toward CPDP.
Different optimisation/ensemble techniques such Bagging, Boosting, Voting, Meta-Learning, and other ensembles are utilised in this category.
Additionally, multiple models in the categorical studies are presented (mostly as benchmarks for the proposed methods) with no clear focus (e.g simple NB).

3.5.1 Performance in relation to overall paper approach

Targeting learner, data and metric can potentially lead to better predictions (in terms of f-measure, recall, AUC) and more stable models (with regard to recall).
Figure 7 represents the results of this categorization in the extracted data.
Especially in the case of recall, this approaches can provide more stable models with significant boosts in performances.

3.6 Theme: Datasets and Levels of Granularity

Datasets form open source projects are dominant in CPDP studies.
The table distinguishes among different kinds of datasets, i.e., open source, industrial, student, and proprietary.
See [49] for the detailed information regarding (the quality of) these datasets.
Finally, 17 academic projects, with one release each, also belong to the same category.
These datasets contain 29 static code metrics as well as manually verified defect labels for different systems.

3.6.1 Performance in relation to levels of granularity

In all three, function and file level predictions have the highest and the lowest median values respectively.
With respect to AUC, the class level achieves the top median value while the file level predictions still have the lowest.
Except for AUC, class level predictions have less stability as they cover a higher range.
With these in mind, one can argue that function level predictions could potentially lead to better performance while being more effective in practice.

4 CPDP VS. WPDP

To measure the effect and power of the proposed approaches, the authors collected both within and cross project data for all the models that pass through their quality checklist.
The comparisons however are not limited to the proposed approaches in the studies as the authors have combined the data from all of the reported models with enough information.
Usually, the simplest WPDP models are considered in the studies when they act as benchmarks for proposed CPDP approaches and no rigorous and sophisticated optimisation or data manipulation methods are applied.
Finally, the authors have to consider the fact that no set of evaluation measures and none of the types of reporting (median, average, original) are shared among all of the studies that contribute to this analysis.

4.1 Meta-analysis

In its essence, a meta-analysis incorporates statistical approaches to combine multiple studies in an effort to increase power over individual studies while improving the estimates of the effect sizes and resolve uncertainties when different studies disagree [50], [69], [76].
On the contrary, these small steps can be extremely important and provide significant benefits if applied under suitable circumstances.
In software engineering, Kitchenham et al. endorses the use of meta-analysis [95].
Different weighting models exist for meta-analysis, most notably, the inverse variance method.

4.2 Fixed and Random Effect Models

Two popular methods of performing meta-analysis are fixed and random effect models [76].
The assumption of a common effect shared by the studies does not usually hold.
The description of the random effect model and its procedures will be discussed after presenting the required calculations for the fixed effect model.
Specifically, Q which represents the total variance, and df , which represents the expected variance if all studies have the same true effect need to be calculated first.

4.3 Meta-analysis Results

CPDP challenges WPDP only with respect to recall, but that is at the cost of precision.
The thin dashed line shows the line of no effect for the random effect model, i.e., the average overall random model effect size.
The fixed and random effect models do not agree on the significance of the overall effect for recall.
With precision and AUC, WPDP is significantly better than CPDP while in both cases, wider confidence intervals can be observed.

5 DISCUSSION

By synthesizing both qualitative and quantitative data, this section provides answers to their defined research questions.
The authors follow a similar approach used by Hall et al. [1] when discussing model performance in relation to certain factors (e.g., independent variables, modeling techniques, etc.).
First, the performance within individual studies is discussed.
This helps to figure out the major predictive performance impact within each particular study.
A similar approach is considered for comparing WPDP and CPDP performances.

5.1 Independent Variables in CPDP (RQ1)

The independent variables used in the categorical studies can be mainly categorized as traditional metrics (size and complexity metrics), process metrics (code delta, code churn), and Object-Oriented metrics.
Analysis of the model performance across the categorical studies suggests that the combinations involving LOC, OO, and SCM improve the predictive performance of their respective models.
Kamei et al. [S39] asserted that the defect prediction models built with process metrics are more useful in comparison with the traditional defect prediction models as they are done at a finer level of granularity and the responsible developers for inspections can be determined more rapidly.
Their results showed that WPDP models built with code changes outperform CPDP counterparts in terms of AUC, precision, recall, and fmeasure.

5.2 Modeling Techniques in CPDP (RQ2)

Naı̈ve Bayes (NB) and Logistic Regression (LR) are the most commonly used modeling techniques in CPDP.
They later observed that simple classifiers like NB could perform well in CPDP context with respect to the overall performance [S3].
They presented these results by comparing GPbased models against 17 non-GP models.
Moreover, base learners perform better with respect to fmeasure compared with the ensembles.

5.3 Performance Evaluation in CPDP (RQ3)

Analysing performance evaluation criteria of 28 categorical studies disclosed that the majority studies had computed various compound performance measures using the confusion matrix to evaluate the performance of their prediction models.
Multi-objective Defect Prediction, on the other hand, targets multiple goals at once.
MODEP [S11] uses a multiobjective approach to target both cost and effectiveness.
The justifications for using particular performance measures were collected when possible for the primary studies.

5.4 CPDP Approaches (RQ4)

A variety of approaches are proposed in CPDP, addressing different data and learner related issues.
Some approaches have used multiple methods in their settings to achieve their desired goals.
As such, He et al. [S18] compared DTB with other famous approaches in the CPDP such as TNB, NN-filtering, and mixed data approach.
More specifically, the general trend seems to be the recall based nature of the data approaches.

5.5 CPDP vs. WPDP (RQ5)

The authors performed three sets of analysis for benchmarking the performance of CPDP models against that of WPDP as no general conclusion could be made by just considering individual studies.
Herbold [S23] observed that the CPDP performs better with recall, but it lacks the precision of WPDP models.
Zhang et al. [S40] observed that there are clear differences in the performance between the universal model and WPDP models with all performance measures except AUC.
Finally, despite having similar medium effect sizes, the fixed and random effect models do not agree on significance for AUC.

6 GUIDELINES AND RECOMMENDATIONS FOR FUTURE RESEARCH

The vast history of defect prediction has lead to proposal of many theories, approaches, and models.
Hall et al. [1] performed a comprehensive systematic review on the subject.
Many of the proposed ideas have been adapted and applied by CPDP branch despite its recent history.

6.2 On performance measures

Regarding the predictive performance, it is important to report multiple performance measures to fully grasp the nature and capabilities of the proposed models [1], especially with regard to compound measures such as f-measure.
Therefore, the choice of evaluation measure should be thought out carefully.
Ideally, defect prediction models are decision support systems for the developer or QA personnel, raising flags for potentially defective cases.
Herzig and Nagappan argue that practitioners prefer precision over recall in their workflow [93].

6.3 On the use of statistical tests and effect sizes

Performing appropriate statistical tests and computing and reporting relevant effect sizes would help in demonstrating the validity of the conclusions.
The less powerful non-parametric tests could show lack of significance due to their weaker power in comparison with parametric tests, however, parametric tests require more assumptions, some of which are violated in many experiments.
Different types of tests have been proposed and employed in software engineering, some of which are described in [56].
While discussing the subject, one must notice the possible disadvantages of using particular tests despite their occasional usefulness.

6.4 On the lack of search based and multi-objective methods for CPDP

Very few studies have focused on search based approaches in CPDP.
The authors observed that manipulating data can potentially improve the performance as described earlier in the 0098-5589 (c) 2017 IEEE.
Specifically, the authors observed only one study [S11] with a multiobjective approach.
There is a research gap on search-based and multiobjective methods for CPDP.

6.5 On the use of metric sets as features

The authors observe that feature extraction is seldom used in CPDP studies.
Adapting and applying state of the art techniques in feature extraction and applying the knowledge learnt from the body of work on lower-dimensional manifolds, spectral learning, and random projections may prove to be more useful in building predictors [57]–[59].
Only a few studies [52], [S3], [S15], [S37], [S40] (very limited in some) have considered the feature and metric manipulation by means of feature selection and obviously more research in the area is required.
Moreover, the feature manipulation approaches can be used in multi-objective methods as one of the data manipulation approaches as discussed earlier.
Most studies utilise software metrics without preprocessing, e.g., feature selection/extraction, even though the complex CPDP algorithms prevent reasoning based on these metrics.

6.6 On tuning hyper-parameters of learners

The authors observed that almost all studies use the default options set by the learning environments for setting the hyperparameters of learning techniques.
A recent study [53] asserted that the majority of the most commonly used classifiers require the setting of at least one parameter.
Similar observations are also presented in [1], [54], [55], raising concerns regarding the usage of default parameter values, which, if tuned properly, often lead to better performance.
The authors recommend that hyper-parameter tuning for existing and proposed approaches in CPDP research should not be considered optional, but rather necessary.

6.7 On the lack of CPDP studies on commercial/closed source systems

There are very few examples that demonstrate the applicability of CPDP approaches in industrial settings.
This lack of demonstration of practical applications lead to concerns regarding the actual value of CPDP.
Applying the techniques proposed in the literature to modern day software systems especially on the proprietary and closed source software could lead to further progresses in the field.
The majority of the studies have focused on open source data, which, despite their great value, might not be representative enough for the software industry as a whole.
While most of their recommendations target the rigour of further studies, this one specifically calls for the need for relevance in CPDP studies that are performed in real settings.

6.8 On unfair comparisons of CPDP vs. WPDP

The authors observe that most WPDP counterparts, which are benchmarked with CPDP methods, usually employ the simplest form of learners.
These sophisticated methods are generally not applied to the within project data as benchmarks.
This is justifiable in the sense that some of the approaches are specifically designed for CPDP and can not be applied to WPDP.
Further, it is of great value if the studies use up-to-date and state of the art benchmarks in CPDP for validation and demonstration of their proposed approaches.
If this is not possible, a state-of-the-art WPDP counterpart, e.g., Random Forests, with hyper-parameter tuning should be used.

6.9 On the lack of replication packages

There are very few replication packages available for CPDP.
The implementations may contain small tweaks and details which sometimes are impossible to extract from the proposed algorithms presented in the papers.
Different levels of granularity, other types of metrics, other methods of blaming (code and data flow), and datasets from different companies with different practices are highly required.
The authors recommend reusable scripts, and whenever possible, the data to be shared whenever a new CPDP approach is proposed.

6.10 On the lack of regression studies in CPDP

Very few studies have considered continuous models.
In their list of 30 primary studies which passed the quality assessment phase, only two perform regression analysis to predict for the number of defects in software units.
With regression studies, broader decisions on allocating QA resources can be taken.
There is a research gap on regression based methods for CPDP.
The authors recommend further research to exploit and fill this gap.

7 THREATS TO VALIDITY

It is important to clarify the possible threats that influence the outcomes of their research.
The following are the validity threats identified during this SLR.

7.2 Search Terms

Finding all relevant primary studies is always a challenge in any SLR.
Search string was constructed with different terms identified by checking titles and keywords from the relevant papers already known to the authors.
Alternative spellings and synonyms for search terms were then added by consulting an expert in the area.
In addition to the automated search in six electronic databases, additional search strategies, i.e., snowballing, was carried out to find other relevant studies that might have been excluded.
These procedures provided a high confidence that the majority of the key studies were identified.

7.3 Study Selection Bias

The study selection process was carried out in two phases.
In the first round, studies were excluded based on the title and abstract independently by two researchers.
Potential disagreements were resolved during the pilot study and inclusion/exclusion criteria were refined.
Inter-rater reliability was evaluated to mitigate the threat emerged from the researchers’ personal subjective judgment.
The selection process was repeated until a full agreement was achieved.

7.4 Quality Assessment and Data Extraction

Two researchers independently investigated the quality of each study.
Quality assessment criteria were piloted and modified based on the results from the pilot study.
Inputs from an expert were taken in the cases where the researchers could not come to an agreement on a particular study.
Aforementioned actions mitigated the risk of missing any relevant study.
For data extraction, the studies were divided between two researchers; each researcher extracted the data from the relevant studies and the extracted data were rechecked by the other researcher.

7.5 Violin Plots

The number of data points included in their violin plots to synthesise the primary studies varies and is limited to what is reported in primary studies.
The number of data rows were also varied in the plots that are used to compare performance in relation to various factors.
Hall et al. [1] argue that the performance of the models could be impacted by other sources , i.e., the combination of the involved factors in the models are more important than any one of them 0098-5589 (c) 2017 IEEE.
Having said these, the authors tried to consider methodological issues that are believed to have impact on the performance [1] by performing additional comparisons in two levels (aggregated and combinations) into the data approaches which are heavily targeted by the studies.

7.6 Meta-analysis and Forest Plots

Similar to the case for the violin plots, the data contributing to the forest plots are not just from the proposed approaches, but the benchmarks also contribute to the data.
As such, the data and its size from different cases may vary highly.
The authors have to note that the data for CPDP contains the best of its domain, while the best WP data is not usually presented when the comparisons are made.
The results of fixed and random effect models confirm one another in the majority of cases, which is expected with well-defined targets.
Inclusion of both models is a step toward demonstrating the validity of their conclusions.

7.7 Data Quality

In their study, the authors did not consider the low quality nature of NASA datasets.
The authors also skipped the maturity test for them as a large portion of the studies have used them in their experiments and their effectiveness has been investigated extensively.
Hall et al. [1] excluded the models built on NASA datasets as no maturity information is available for them.

8 CONCLUSION

The main objective of this SLR was to summarize and synthesize the existing CPDP studies in order to identify what kind of independent variables, modeling techniques, performance evaluation criteria, and approaches are used in building CPDP models.
Moreover, this study aimed to explore the predictive performance of cross project defect prediction models compared with that of within project models.
NN, SVM, and DTree are the modeling techniques with the highest median f-measure performance values in CPDP.
Ensembles show a different behaviour with fmeasure and AUC, where they perform below average for the former and best for the latter.

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Related Papers (5)

Frequently asked questions (10), q1. what contributions have the authors mentioned in the paper "a systematic literature review and meta-analysis on cross project defect prediction" .

Further, the authors aim to assess the performance of CPDP vs. within project DP models. The authors conducted a systematic literature review. The authors provide guidelines for further research.

Q2. What are the future works mentioned in the paper "A systematic literature review and meta-analysis on cross project defect prediction" ?

Below is a list of the suggestions for future research.

Q3. What are the independent variables used in the categorical studies?

The independent variables used in the categorical studies can be mainly categorized as traditional metrics (size and complexity metrics), process metrics (code delta, code churn), and Object-Oriented metrics.

Q4. What are the two approaches to tackle strongly correlated features?

Dimensionality reduction and PCA [66] (Principal Component Analysis) in particular are other approaches to tackle strongly correlated features.

Q5. What other techniques are used to build prediction models?

Other base learners such as Decision Tree (DTree), Support Vector Machine (SVM), and Random Forests (RF) are also used to build prediction models in a considerable number of cases.

Q6. What are the main methods used to compare CPDP and WPDP studies?

Meta-analysis and, specifically, both fixed and random effect models are considered to compare the results of CPDP and WPDP studies.

Q7. What is the source for the huge variance in the stability of different learning techniques?

One of the sources for the huge variance in the stability of different learning techniques, data approaches, etc. is probably the use of different sets of datasets that are utilized for building prediction models in different studies.

Q8. What are the common issues addressed in categorical studies?

The majority of the categorical studies have addressed different data related issues such as data heterogeneity, class imbalance, highly skewed data, etc. as a part of their proposed approach.

Q9. How many datasets were selected to train the Universal model?

Of this huge set of datasets, 1385 were selected to train the Universal model as many of these datasets were either trivial or did not contain adequate data to be considered for defect prediction.

Q10. What level of granularity do some of the studies perform for the prediction of a?

some of the studies [S13], [S37] perform predictions at multiple levels of granularity such as function/class/file levels.

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PDF arXiv:1907.12027v4 [cs.SE] 19 Feb 2020
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1 Introduction

2 Systematic review

2.1 Bibliometric analysis

2.2 Overview of major results

3 The inter-connectivity of papers

3.1 Bibliographic coupling and citation-based approaches

3.2 Community detection

4 Meta-analysis

4.1 Meta-regression tests of publication selection bias

4.2 Multiple meta-regression analysis: econometric results and discussion

5 Conclusions

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JEL Classification

A Systematic Literature Review and Meta-Analysis on Cross Project Defect Prediction

1.1 Prior Research

1.2 Research Goals

1.3 Contributions

2 RESEARCH METHODOLOGY

2.1 Selection of Primary Studies

2.2 Inclusion and Exclusion Criteria

2.3 Selection Results

2.4 Quality Assessment

2.5 Data Extraction

2.6 Data Analysis

2.6.1 Performance Indicators

2.6.2 Modelling Techniques

2.6.3 CPDP Approaches

2.6.4 Meta-analysis and Forest Plots

3.1 Theme: Independent Variables

3.1.1 Performance in relation to independent variables

3.2 Theme: Modelling Techniques

3.2.1 Performance in relation to modelling techniques

3.3 Theme: Performance Evaluation Criteria

3.4 Theme: CPDP Approaches