Structural Equation Modeling for Mixed Designs

Abstract

A mixed-design study, also called a split-plot design, intends to evaluate the differences among multiple independent groups and multiple treatment conditions simultaneously, with repeated measurements of the same participants. Structural equation modeling (SEM), also referred to as path analysis, is a statistical technique used by researchers in many fields to verify or disprove hypothesized causal links among a predefined system of variables. The existing SEM methods for detecting differences in path strength among multiple datasets can accommodate comparisons of independent groups or repeated measures (e.g. with and without stimulus), but not both. Thus SEM is unable to perform a direct analysis of a mixed-design study. To fill this void, we have developed a cohesive two-level parametric modeling approach using the maximum likelihood method (MLE SEM) for detecting differences in pathways caused by multiple factors, both between and within groups, such as group membership and treatment condition. The method is illustrated through a brain functional pathway analysis. Further, developments of the mixed-design methodology for Latent Variable SEM and Partial Least Squares SEM (PLS SEM) are included, and guidelines for power and sample size are provided.