The plausibility and feasibility of remedies for evaluating structural fit

Various structural fit indices (SFIs) have been proposed to evaluate the structural component of a structural equation model (SEM). Decomposed SFIs treat estimated latent (co)variances from an unrestricted confirmatory factor analysis (CFA) as input data for a path model, from which standard global fit indices are calculated. Conflated SFIs fit a SEM with both measurement and structural components, comparing its fit to orthogonal and unrestricted CFAs. Sensitivity of conflated SFIs to the same structural misspecification depends on standardized factor loadings, but decomposed SFIs have inflated Type-I error rates when compared to rule-of-thumb cutoffs, due to treating estimates as data. We explored whether two alternative approaches avoid either shortcoming by separating the measurement and structural model components while accounting for uncertainty of factor-covariance estimates: (a) plausible values and (b) the Structural-After-Measurement (SAM) approach. We conduct population analyses by varying levels of construct reliability and numbers of indicators per factor, under populations with simple and complex measurement models. Results show SAM is as promising as existing decomposed SFIs. Plausible values provide less accurate estimates, but future research should investigate whether its pooled test statistic has nominal Type I error rates

Power analysis for conditional indirect effects: A tutorial for conducting Monte Carlo simulations with categorical exogenous variables

Conceptual and statistical models that include conditional indirect effects (i.e., so-called “moderated mediation” models) are increasingly popular in the behavioral sciences. Although there is ample guidance in the literature for how to specify and test such models, there is scant advice regarding how to best design studies for such purposes, and this especially includes techniques for sample size planning (i.e., “power analysis”). In this paper, we discuss challenges in sample size planning for moderated mediation models and offer a tutorial for conducting Monte Carlo simulations in the specific case where one has categorical exogenous variables. Such a scenario is commonly faced when one is considering testing conditional indirect effects in experimental research, wherein the (assumed) predictor and moderator variables are manipulated factors and the (assumed) mediator and outcome variables are observed/measured variables. To support this effort, we offer example data and reproducible R code that constitutes a “toolkit” to make up for limitations in other software and aid researchers in the design of research to test moderated mediation models