Past methodological research on mediation analysis mainly focused on situations where all variables were complete and continuous. When issues of categorical data occur combined with missing data, more methodological considerations are involved. Specifically, appropriate decisions need to be made on estimation methods of the indirect effects and on confidence intervals for testing the indirect effects with accommodations of missing data. We compare strategies that address these issues based on a model with a dichotomous mediator, aiming to provide guidelines for researchers facing such challenges in practice.
{"title":"Testing indirect effect with a complete or incomplete dichotomous mediator","authors":"Fan Jia, Wei Wu, Po-Yi Chen","doi":"10.1111/bmsp.12313","DOIUrl":"10.1111/bmsp.12313","url":null,"abstract":"<p>Past methodological research on mediation analysis mainly focused on situations where all variables were complete and continuous. When issues of categorical data occur combined with missing data, more methodological considerations are involved. Specifically, appropriate decisions need to be made on estimation methods of the indirect effects and on confidence intervals for testing the indirect effects with accommodations of missing data. We compare strategies that address these issues based on a model with a dichotomous mediator, aiming to provide guidelines for researchers facing such challenges in practice.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10063422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Diagnostic classification models (DCMs) can be used to track the cognitive learning states of students across multiple time points or over repeated measurements. This study developed an effective variational Bayes (VB) inference method for hidden Markov longitudinal general DCMs. The simulations performed in this study verified the validity of the proposed algorithm for satisfactorily recovering true parameters. Simulation and applied data analyses were conducted to compare the proposed VB method to Markov chain Monte Carlo (MCMC) sampling. The results revealed that the parameter estimates provided by the VB method were consistent with the MCMC method with the additional benefit of a faster estimation time. The comparative simulation also indicated differences between the two methods in terms of posterior standard deviation and coverage of 95% credible intervals. Thus, with limited computational resources and time, the proposed VB method can output estimations comparable to that of MCMC.
{"title":"Variational Bayes inference for hidden Markov diagnostic classification models","authors":"Kazuhiro Yamaguchi, Alfonso J. Martinez","doi":"10.1111/bmsp.12308","DOIUrl":"10.1111/bmsp.12308","url":null,"abstract":"<p>Diagnostic classification models (DCMs) can be used to track the cognitive learning states of students across multiple time points or over repeated measurements. This study developed an effective variational Bayes (VB) inference method for hidden Markov longitudinal general DCMs. The simulations performed in this study verified the validity of the proposed algorithm for satisfactorily recovering true parameters. Simulation and applied data analyses were conducted to compare the proposed VB method to Markov chain Monte Carlo (MCMC) sampling. The results revealed that the parameter estimates provided by the VB method were consistent with the MCMC method with the additional benefit of a faster estimation time. The comparative simulation also indicated differences between the two methods in terms of posterior standard deviation and coverage of 95% credible intervals. Thus, with limited computational resources and time, the proposed VB method can output estimations comparable to that of MCMC.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9533717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Auburn Jimenez, James Joseph Balamuta, Steven Andrew Culpepper
Cognitive diagnostic models provide a framework for classifying individuals into latent proficiency classes, also known as attribute profiles. Recent research has examined the implementation of a Pólya-gamma data augmentation strategy binary response model using logistic item response functions within a Bayesian Gibbs sampling procedure. In this paper, we propose a sequential exploratory diagnostic model for ordinal response data using a logit-link parameterization at the category level and extend the Pólya-gamma data augmentation strategy to ordinal response processes. A Gibbs sampling procedure is presented for efficient Markov chain Monte Carlo (MCMC) estimation methods. We provide results from a Monte Carlo study for model performance and present an application of the model.
{"title":"A sequential exploratory diagnostic model using a Pólya-gamma data augmentation strategy","authors":"Auburn Jimenez, James Joseph Balamuta, Steven Andrew Culpepper","doi":"10.1111/bmsp.12307","DOIUrl":"10.1111/bmsp.12307","url":null,"abstract":"<p>Cognitive diagnostic models provide a framework for classifying individuals into latent proficiency classes, also known as attribute profiles. Recent research has examined the implementation of a Pólya-gamma data augmentation strategy binary response model using logistic item response functions within a Bayesian Gibbs sampling procedure. In this paper, we propose a sequential exploratory diagnostic model for ordinal response data using a logit-link parameterization at the category level and extend the Pólya-gamma data augmentation strategy to ordinal response processes. A Gibbs sampling procedure is presented for efficient Markov chain Monte Carlo (MCMC) estimation methods. We provide results from a Monte Carlo study for model performance and present an application of the model.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41170914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Causality and prediction in structural equation modeling: A commentary by Yutaka Kano on: “Which method delivers greater signal-to-noise ratio: Structural equation modeling or regression analysis with weighted composites?” by Yuan and Fang","authors":"Yutaka Kano","doi":"10.1111/bmsp.12306","DOIUrl":"10.1111/bmsp.12306","url":null,"abstract":"","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9439924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Changepoints are abrupt variations in a sequence of data in statistical inference. In educational and psychological assessments, it is essential to properly differentiate examinees' aberrant behaviours from solution behaviour to ensure test reliability and validity. In this paper, we propose a sequential Bayesian changepoint detection algorithm to monitor the locations of changepoints for response times in real time and, subsequently, further identify types of aberrant behaviours in conjunction with response patterns. Two simulation studies were conducted to investigate the efficiency and accuracy of the proposed detection procedure in terms of identifying one or multiple changepoints at different locations. In addition to manipulating the number and locations of changepoints, two types of aberrant behaviours were also considered: rapid guessing behaviour and cheating behaviour. Simulation results indicate that ability estimates could be improved after removing responses from aberrant behaviours identified by our approach. Two empirical examples were analysed to illustrate the application of the proposed sequential Bayesian changepoint detection procedure.
{"title":"A sequential Bayesian changepoint detection procedure for aberrant behaviours in computerized testing","authors":"Jing Lu, Chun Wang, Jiwei Zhang, Xue Wang","doi":"10.1111/bmsp.12305","DOIUrl":"10.1111/bmsp.12305","url":null,"abstract":"<p>Changepoints are abrupt variations in a sequence of data in statistical inference. In educational and psychological assessments, it is essential to properly differentiate examinees' aberrant behaviours from solution behaviour to ensure test reliability and validity. In this paper, we propose a sequential Bayesian changepoint detection algorithm to monitor the locations of changepoints for response times in real time and, subsequently, further identify types of aberrant behaviours in conjunction with response patterns. Two simulation studies were conducted to investigate the efficiency and accuracy of the proposed detection procedure in terms of identifying one or multiple changepoints at different locations. In addition to manipulating the number and locations of changepoints, two types of aberrant behaviours were also considered: rapid guessing behaviour and cheating behaviour. Simulation results indicate that ability estimates could be improved after removing responses from aberrant behaviours identified by our approach. Two empirical examples were analysed to illustrate the application of the proposed sequential Bayesian changepoint detection procedure.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9813812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Florian Schuberth, Tamara Schamberger, Mikko Rönkkö, Yide Liu, Jörg Henseler
In a recent article published in this journal, Yuan and Fang (British Journal of Mathematical and Statistical Psychology, 2023) suggest comparing structural equation modeling (SEM), also known as covariance-based SEM (CB-SEM), estimated by normal-distribution-based maximum likelihood (NML), to regression analysis with (weighted) composites estimated by least squares (LS) in terms of their signal-to-noise ratio (SNR). They summarize their findings in the statement that “[c]ontrary to the common belief that CB-SEM is the preferred method for the analysis of observational data, this article shows that regression analysis via weighted composites yields parameter estimates with much smaller standard errors, and thus corresponds to greater values of the [SNR].” In our commentary, we show that Yuan and Fang have made several incorrect assumptions and claims. Consequently, we recommend that empirical researchers not base their methodological choice regarding CB-SEM and regression analysis with composites on the findings of Yuan and Fang as these findings are premature and require further research.
{"title":"Premature conclusions about the signal-to-noise ratio in structural equation modeling research: A commentary on Yuan and Fang (2023)","authors":"Florian Schuberth, Tamara Schamberger, Mikko Rönkkö, Yide Liu, Jörg Henseler","doi":"10.1111/bmsp.12304","DOIUrl":"10.1111/bmsp.12304","url":null,"abstract":"<p>In a recent article published in this journal, Yuan and Fang (<i>British Journal of Mathematical and Statistical Psychology</i>, 2023) suggest comparing structural equation modeling (SEM), also known as covariance-based SEM (CB-SEM), estimated by normal-distribution-based maximum likelihood (NML), to regression analysis with (weighted) composites estimated by least squares (LS) in terms of their signal-to-noise ratio (SNR). They summarize their findings in the statement that “[c]ontrary to the common belief that CB-SEM is the preferred method for the analysis of observational data, this article shows that regression analysis via weighted composites yields parameter estimates with much smaller standard errors, and thus corresponds to greater values of the [SNR].” In our commentary, we show that Yuan and Fang have made several incorrect assumptions and claims. Consequently, we recommend that empirical researchers not base their methodological choice regarding CB-SEM and regression analysis with composites on the findings of Yuan and Fang as these findings are premature and require further research.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12304","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9319019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The use of multidimensional forced-choice (MFC) items to assess non-cognitive traits such as personality, interests and values in psychological tests has a long history, because MFC items show strengths in preventing response bias. Recently, there has been a surge of interest in developing item response theory (IRT) models for MFC items. However, nearly all of the existing IRT models have been developed for MFC items with binary scores. Real tests use MFC items with more than two categories; such items are more informative than their binary counterparts. This study developed a new IRT model for polytomous MFC items based on the cognitive model of choice, which describes the cognitive processes underlying humans' preferential choice behaviours. The new model is unique in its ability to account for the ipsative nature of polytomous MFC items, to assess individual psychological differentiation in interests, values and emotions, and to compare the differentiation levels of latent traits between individuals. Simulation studies were conducted to examine the parameter recovery of the new model with existing computer programs. The results showed that both statement parameters and person parameters were well recovered when the sample size was sufficient. The more complete the linking of the statements was, the more accurate the parameter estimation was. This paper provides an empirical example of a career interest test using four-category MFC items. Although some aspects of the model (e.g., the nature of the person parameters) require additional validation, our approach appears promising.
{"title":"A dual process item response theory model for polytomous multidimensional forced-choice items","authors":"Xuelan Qiu, Jimmy de la Torre","doi":"10.1111/bmsp.12303","DOIUrl":"10.1111/bmsp.12303","url":null,"abstract":"<p>The use of multidimensional forced-choice (MFC) items to assess non-cognitive traits such as personality, interests and values in psychological tests has a long history, because MFC items show strengths in preventing response bias. Recently, there has been a surge of interest in developing item response theory (IRT) models for MFC items. However, nearly all of the existing IRT models have been developed for MFC items with binary scores. Real tests use MFC items with more than two categories; such items are more informative than their binary counterparts. This study developed a new IRT model for polytomous MFC items based on the cognitive model of choice, which describes the cognitive processes underlying humans' preferential choice behaviours. The new model is unique in its ability to account for the ipsative nature of polytomous MFC items, to assess individual psychological differentiation in interests, values and emotions, and to compare the differentiation levels of latent traits between individuals. Simulation studies were conducted to examine the parameter recovery of the new model with existing computer programs. The results showed that both statement parameters and person parameters were well recovered when the sample size was sufficient. The more complete the linking of the statements was, the more accurate the parameter estimation was. This paper provides an empirical example of a career interest test using four-category MFC items. Although some aspects of the model (e.g., the nature of the person parameters) require additional validation, our approach appears promising.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12303","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9229089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Christoph Koenig, Benjamin Becker, Esther Ulitzsch
Response time modelling is developing rapidly in the field of psychometrics, and its use is growing in psychology. In most applications, component models for response times are modelled jointly with component models for responses, thereby stabilizing estimation of item response theory model parameters and enabling research on a variety of novel substantive research questions. Bayesian estimation techniques facilitate estimation of response time models. Implementations of these models in standard statistical software, however, are still sparse. In this accessible tutorial, we discuss one of the most common response time models—the lognormal response time model—embedded in the hierarchical framework by van der Linden (2007). We provide detailed guidance on how to specify and estimate this model in a Bayesian hierarchical context. One of the strengths of the presented model is its flexibility, which makes it possible to adapt and extend the model according to researchers' needs and hypotheses on response behaviour. We illustrate this based on three recent model extensions: (a) application to non-cognitive data incorporating the distance-difficulty hypothesis, (b) modelling conditional dependencies between response times and responses, and (c) identifying differences in response behaviour via mixture modelling. This tutorial aims to provide a better understanding of the use and utility of response time models, showcases how these models can easily be adapted and extended, and contributes to a growing need for these models to answer novel substantive research questions in both non-cognitive and cognitive contexts.
反应时间模型在心理测量学领域发展迅速,在心理学中的应用也越来越广泛。在大多数应用中,反应时间的成分模型与反应的成分模型是联合建模的,从而稳定了项目反应理论模型参数的估计,并使研究各种新的实质性研究问题成为可能。贝叶斯估计技术有助于估计响应时间模型。然而,这些模型在标准统计软件中的实现仍然很少。在这个易于理解的教程中,我们将讨论最常见的响应时间模型之一——由van der Linden(2007)嵌入到分层框架中的对数正态响应时间模型。我们提供了关于如何在贝叶斯层次上下文中指定和估计该模型的详细指导。所提出的模型的优点之一是它的灵活性,这使得它可以根据研究人员的需求和对反应行为的假设来调整和扩展模型。我们通过三个最近的模型扩展来说明这一点:(a)应用于包含距离困难假设的非认知数据,(b)模拟反应时间和反应之间的条件依赖关系,以及(c)通过混合建模来识别反应行为的差异。本教程旨在更好地理解响应时间模型的使用和效用,展示如何轻松地调整和扩展这些模型,并有助于这些模型在非认知和认知上下文中回答新的实质性研究问题。
{"title":"Bayesian hierarchical response time modelling—A tutorial","authors":"Christoph Koenig, Benjamin Becker, Esther Ulitzsch","doi":"10.1111/bmsp.12302","DOIUrl":"10.1111/bmsp.12302","url":null,"abstract":"<p>Response time modelling is developing rapidly in the field of psychometrics, and its use is growing in psychology. In most applications, component models for response times are modelled jointly with component models for responses, thereby stabilizing estimation of item response theory model parameters and enabling research on a variety of novel substantive research questions. Bayesian estimation techniques facilitate estimation of response time models. Implementations of these models in standard statistical software, however, are still sparse. In this accessible tutorial, we discuss one of the most common response time models—the lognormal response time model—embedded in the hierarchical framework by van der Linden (2007). We provide detailed guidance on how to specify and estimate this model in a Bayesian hierarchical context. One of the strengths of the presented model is its flexibility, which makes it possible to adapt and extend the model according to researchers' needs and hypotheses on response behaviour. We illustrate this based on three recent model extensions: (a) application to non-cognitive data incorporating the distance-difficulty hypothesis, (b) modelling conditional dependencies between response times and responses, and (c) identifying differences in response behaviour via mixture modelling. This tutorial aims to provide a better understanding of the use and utility of response time models, showcases how these models can easily be adapted and extended, and contributes to a growing need for these models to answer novel substantive research questions in both non-cognitive and cognitive contexts.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12302","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10763975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Principal component regression (PCR) is a popular technique in data analysis and machine learning. However, the technique has two limitations. First, the principal components (PCs) with the largest variances may not be relevant to the outcome variables. Second, the lack of standard error estimates for the unstandardized regression coefficients makes it hard to interpret the results. To address these two limitations, we propose a model-based approach that includes two mean and covariance structure models defined for multivariate PCR. By estimating the defined models, we can obtain inferential information that will allow us to test the explanatory power of individual PCs and compute the standard error estimates for the unstandardized regression coefficients. A real example is used to illustrate our approach, and simulation studies under normality and nonnormality conditions are presented to validate the standard error estimates for the unstandardized regression coefficients. Finally, future research topics are discussed.
{"title":"A model-based approach to multivariate principal component regression: Selecting principal components and estimating standard errors for unstandardized regression coefficients","authors":"Fei Gu, Mike W.-L. Cheung","doi":"10.1111/bmsp.12301","DOIUrl":"10.1111/bmsp.12301","url":null,"abstract":"<p>Principal component regression (PCR) is a popular technique in data analysis and machine learning. However, the technique has two limitations. First, the principal components (PCs) with the largest variances may not be relevant to the outcome variables. Second, the lack of standard error estimates for the unstandardized regression coefficients makes it hard to interpret the results. To address these two limitations, we propose a model-based approach that includes two mean and covariance structure models defined for multivariate PCR. By estimating the defined models, we can obtain inferential information that will allow us to test the explanatory power of individual PCs and compute the standard error estimates for the unstandardized regression coefficients. A real example is used to illustrate our approach, and simulation studies under normality and nonnormality conditions are presented to validate the standard error estimates for the unstandardized regression coefficients. Finally, future research topics are discussed.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10653240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Josue E. Rodriguez, Donald R. Williams, Paul-Christian Bürkner
Categorical moderators are often included in mixed-effects meta-analysis to explain heterogeneity in effect sizes. An assumption in tests of categorical moderator effects is that of a constant between-study variance across all levels of the moderator. Although it rarely receives serious thought, there can be statistical ramifications to upholding this assumption. We propose that researchers should instead default to assuming unequal between-study variances when analysing categorical moderators. To achieve this, we suggest using a mixed-effects location-scale model (MELSM) to allow group-specific estimates for the between-study variance. In two extensive simulation studies, we show that in terms of Type I error and statistical power, little is lost by using the MELSM for moderator tests, but there can be serious costs when an equal variance mixed-effects model (MEM) is used. Most notably, in scenarios with balanced sample sizes or equal between-study variance, the Type I error and power rates are nearly identical between the MEM and the MELSM. On the other hand, with imbalanced sample sizes and unequal variances, the Type I error rate under the MEM can be grossly inflated or overly conservative, whereas the MELSM does comparatively well in controlling the Type I error across the majority of cases. A notable exception where the MELSM did not clearly outperform the MEM was in the case of few studies (e.g., 5). With respect to power, the MELSM had similar or higher power than the MEM in conditions where the latter produced non-inflated Type 1 error rates. Together, our results support the idea that assuming unequal between-study variances is preferred as a default strategy when testing categorical moderators.
{"title":"Heterogeneous heterogeneity by default: Testing categorical moderators in mixed-effects meta-analysis","authors":"Josue E. Rodriguez, Donald R. Williams, Paul-Christian Bürkner","doi":"10.1111/bmsp.12299","DOIUrl":"10.1111/bmsp.12299","url":null,"abstract":"<p>Categorical moderators are often included in mixed-effects meta-analysis to explain heterogeneity in effect sizes. An assumption in tests of categorical moderator effects is that of a constant between-study variance across all levels of the moderator. Although it rarely receives serious thought, there can be statistical ramifications to upholding this assumption. We propose that researchers should instead default to assuming <i>unequal</i> between-study variances when analysing categorical moderators. To achieve this, we suggest using a mixed-effects location-scale model (MELSM) to allow group-specific estimates for the between-study variance. In two extensive simulation studies, we show that in terms of Type I error and statistical power, little is lost by using the MELSM for moderator tests, but there can be serious costs when an equal variance mixed-effects model (MEM) is used. Most notably, in scenarios with balanced sample sizes or equal between-study variance, the Type I error and power rates are nearly identical between the MEM and the MELSM. On the other hand, with imbalanced sample sizes and unequal variances, the Type I error rate under the MEM can be grossly inflated or overly conservative, whereas the MELSM does comparatively well in controlling the Type I error across the majority of cases. A notable exception where the MELSM did not clearly outperform the MEM was in the case of few studies (e.g., 5). With respect to power, the MELSM had similar or higher power than the MEM in conditions where the latter produced non-inflated Type 1 error rates. Together, our results support the idea that assuming unequal between-study variances is preferred as a default strategy when testing categorical moderators.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9255143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}