The purpose of this simulation study was to assess the performance of latent variable models that take into account the complex sampling mechanism that often underlies data used in educational, psychological, and other social science research. Analyses were conducted using the multiple indicator multiple cause (MIMIC) model, which is a flexible…

Multigroup confirmatory factor analysis (MCFA) is a popular method for the examination of measurement invariance and specifically, factor invariance. Recent research has begun to focus on using MCFA to detect invariance for test items. MCFA requires certain parameters (e.g., factor loadings) to be constrained for model identification, which are…

Confirmatory factor analytic (CFA) procedures can be used to provide evidence of measurement invariance. However, empirical evaluation has not focused on the accuracy of common CFA steps used to detect a lack of invariance across groups. This investigation examined procedures for detection of test structure differences across groups under several…