{"title":"Exploration of the MCMC Wald test with linear regression.","authors":"Michael P Woller, Craig K Enders","doi":"10.3758/s13428-024-02426-z","DOIUrl":null,"url":null,"abstract":"<p><p>Recently, Asparouhov and Muthén Structural Equation Modeling: A Multidisciplinary Journal, 28, 1-14, (2021a, 2021b) proposed a variant of the Wald test that uses Markov chain Monte Carlo machinery to generate a chi-square test statistic for frequentist inference. Because the test's composition does not rely on analytic expressions for sampling variation and covariation, it potentially provides a way to get honest significance tests in cases where the likelihood-based test statistic's assumptions break down (e.g., in small samples). The goal of this study is to use simulation to compare the new MCM Wald test to its maximum likelihood counterparts, with respect to both their type I error rate and power. Our simulation examined the test statistics across different levels of sample size, effect size, and degrees of freedom (test complexity). An additional goal was to assess the robustness of the MCMC Wald test with nonnormal data. The simulation results uniformly demonstrated that the MCMC Wald test was superior to the maximum likelihood test statistic, especially with small samples (e.g., sample sizes less than 150) and complex models (e.g., models with five or more predictors). This conclusion held for nonnormal data as well. Lastly, we provide a brief application to a real data example.</p>","PeriodicalId":8717,"journal":{"name":"Behavior Research Methods","volume":" ","pages":"7391-7409"},"PeriodicalIF":4.6000,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Behavior Research Methods","FirstCategoryId":"102","ListUrlMain":"https://doi.org/10.3758/s13428-024-02426-z","RegionNum":2,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/6/17 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"PSYCHOLOGY, EXPERIMENTAL","Score":null,"Total":0}
引用次数: 0
Abstract
Recently, Asparouhov and Muthén Structural Equation Modeling: A Multidisciplinary Journal, 28, 1-14, (2021a, 2021b) proposed a variant of the Wald test that uses Markov chain Monte Carlo machinery to generate a chi-square test statistic for frequentist inference. Because the test's composition does not rely on analytic expressions for sampling variation and covariation, it potentially provides a way to get honest significance tests in cases where the likelihood-based test statistic's assumptions break down (e.g., in small samples). The goal of this study is to use simulation to compare the new MCM Wald test to its maximum likelihood counterparts, with respect to both their type I error rate and power. Our simulation examined the test statistics across different levels of sample size, effect size, and degrees of freedom (test complexity). An additional goal was to assess the robustness of the MCMC Wald test with nonnormal data. The simulation results uniformly demonstrated that the MCMC Wald test was superior to the maximum likelihood test statistic, especially with small samples (e.g., sample sizes less than 150) and complex models (e.g., models with five or more predictors). This conclusion held for nonnormal data as well. Lastly, we provide a brief application to a real data example.
期刊介绍:
Behavior Research Methods publishes articles concerned with the methods, techniques, and instrumentation of research in experimental psychology. The journal focuses particularly on the use of computer technology in psychological research. An annual special issue is devoted to this field.