Meta-analytic Structural Equation Modeling (MASEM) refers to fitting structural equation models (such as path models or factor models) to meta-analytic data. Currently, fitting MASEMs may be challenging for researchers that are not accustomed to working with R software and packages. Therefore, we developed webMASEM; a web application for MASEM. This app implements the one-stage MASEM approach, and allows users to apply MASEM in a user-friendly way. The aim of this article is to provide a tutorial on one-stage MASEM and a practical guide to webMASEM. We will pay specific attention to how the data should be structured and prepared for webMASEM, because mistakes in this step may lead to faulty results without receiving an error message. The use of webMASEM is illustrated with an analysis of a meta-analytic path model in which the path coefficients are moderated by a study-level variable, and a meta-analytic factor model in which the factor loadings are moderated by a study-level variable. All used datafiles and R-codes are available online.

Restricted factor analysis (RFA) is a powerful method to test for uniform differential item functioning (DIF), but it may require empirically selecting anchor items to prevent inflated Type I error rates. We conducted a simulation study to compare two empirical anchor-selection strategies: a one-step rank-based strategy and an iterative selection procedure. Unlike the iterative procedure, the rank-based strategy had a low risk and degree of contamination within the empirically selected anchor set, even with small samples. To detect nonuniform DIF, RFA requires an interaction effect with the latent factor. The latent moderated structural equations (LMS) method has been applied to RFA and has revealed inflated Type I error rates. We propose using product indicators (PI) as a more widely available alternative to measure the latent interaction. A simulation study, involving several sample-size conditions and magnitudes of uniform and nonuniform DIF, revealed that PI obtained similar power but lower Type I error rates, as compared to LMS.

This study compared two single-group approaches for assessing measurement invariance across an observed background variable: restricted factor analysis (RFA) and moderated nonlinear factor analysis (MNLFA). In MNLFA models, heteroskedasticity can be accounted for by allowing the common-factor variance and the residual variances to differ as a function of the background variable. In contrast, RFA models assume homoskedasticity of both the common factor and the residuals. We conducted a simulation study to examine the performance of RFA and MNLFA under common-factor and residual homoskedasticity and heteroskedasticity. Results suggest that MNLFA and RFA with product indicators outperform RFA with latent moderated structural equations in conditions with heteroskedastic common-factors, and MNLFA outperforms RFA in conditions with residual heteroskedasticity. We provide an explanation for the robustness of RFA with product indicators to violations of common-factor homoskedasticity.

Meta-analytic Structural Equation Modeling (MASEM) refers to fitting structural equation models (such as path models or factor models) to meta-analytic data. Currently, fitting MASEMs may be challenging for researchers that are not accustomed to working with R software and packages. Therefore, we developed webMASEM; a web application for MASEM. This app implements the one-stage MASEM approach, and allows users to apply MASEM in a user-friendly way. The aim of this article is to provide a tutorial on one-stage MASEM and a practical guide to webMASEM. We will pay specific attention to how the data should be structured and prepared for webMASEM, because mistakes in this step may lead to faulty results without receiving an error message. The use of webMASEM is illustrated with an analysis of a meta-analytic path model in which the path coefficients are moderated by a study-level variable, and a meta-analytic factor model in which the factor loadings are moderated by a study-level variable. All used datafiles and R-codes are available online.

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