Multilevel factor mixture modeling (FMM) is a hybrid of multilevel confirmatory factor analysis (CFA) and multilevel latent class analysis (LCA). It allows researchers to examine population heterogeneity at the within level, between level, or both levels. This tutorial focuses on explicating the model specification of multilevel FMM that considers…

Currently, dynamic structural equation modeling (DSEM) and residual DSEM (RDSEM) are commonly used in testing intensive longitudinal data (ILD). Researchers are interested in ILD mediation models, but their analyses are challenging. The present paper mathematically derived, empirically compared, and step-by-step demonstrated three types (i.e.,…

In the past decade, moderated mediation analysis has been extensively and increasingly employed in social and behavioral sciences. With its widespread use, it is particularly important to ensure the moderated mediation analysis will not bring spurious results. Spurious effects have been studied in both mediation and moderation analysis, but this…

This article provides an overview of different computational options for inference following normal theory maximum likelihood (ML) estimation in structural equation modeling (SEM) with incomplete normal and nonnormal data. Complete data are covered as a special case. These computational options include whether the information matrix is observed or…

A multiple testing procedure for examining implications of the missing completely at random (MCAR) mechanism in incomplete data sets is discussed. The approach uses the false discovery rate concept and is concerned with testing group differences on a set of variables. The method can be used for ascertaining violations of MCAR and disproving this…

Fraction of missing information [lambda][subscript j] is a useful measure of the impact of missing data on the quality of estimation of a particular parameter. This measure can be computed for all parameters in the model, and it communicates the relative loss of efficiency in the estimation of a particular parameter due to missing data. It has…

Mixed-dyadic data, collected from distinguishable (nonexchangeable) or indistinguishable (exchangeable) dyads, require statistical analysis techniques that model the variation within dyads and between dyads appropriately. The purpose of this article is to provide a tutorial for performing structural equation modeling analyses of cross-sectional…

This article is concerned with the question of whether the missing data mechanism routinely referred to as missing completely at random (MCAR) is statistically examinable via a test for lack of distributional differences between groups with observed and missing data, and related consequences. A discussion is initially provided, from a formal logic…

Valuable methods have been developed for incorporating ordinal variables into structural equation models using a latent response variable formulation. However, some model parameters, such as the means and variances of latent factors, can be quite difficult to interpret because the latent response variables have an arbitrary metric. This limitation…

A well-known ad-hoc approach to conducting structural equation modeling with missing data is to obtain a saturated maximum likelihood (ML) estimate of the population covariance matrix and then to use this estimate in the complete data ML fitting function to obtain parameter estimates. This 2-stage (TS) approach is appealing because it minimizes a…

Two-level data sets are frequently encountered in social and behavioral science research. They arise when observations are drawn from a known hierarchical structure, such as when individuals are randomly drawn from groups that are randomly drawn from a target population. Although 2-level data analysis in the context of structural equation modeling…

Confirmatory factor analysis (CFA) is a statistical procedure frequently used to test the fit of data to measurement models. Published CFA studies typically report factor pattern coefficients. Few reports, however, also present factor structure coefficients, which can be essential for the accurate interpretation of CFA results. The interpretation…

To date, finite mixtures of structural equation models (SEMMs) have been developed and applied almost exclusively for the purpose of providing model-based cluster analyses. This type of analysis constitutes a direct application of the model wherein the estimated component distributions of the latent classes are thought to represent the…

A model with fixed relations between manifest and latent variables is presented for investigating choice reaction time data. The numbers for fixation originate from the polynomial function. Two options are considered: the component-based (1 latent variable for each component of the polynomial function) and composite-based options (1 latent…

Multilevel structural equation modeling (MSEM) has been proposed as an extension to structural equation modeling for analyzing data with nested structure. We have begun to see a few applications in cross-cultural research in which MSEM fits well as the statistical model. However, given that cross-cultural studies can only afford collecting data…