Effects of Violating the Homogeneity Assumption on Mediation Inferences

Mediation models are useful tools for investigating how intervention programs achieve their effects on target outcomes through mediating variables.  They are guided by two theoretical mechanisms for program development and evaluation: 1) action theory - how the program (X) affects the mediator (M), and 2) conceptual theory - how the mediator (M) is related to the outcome (Y).  Understanding the mediating mechanisms by which prevention programs achieve effects is useful for the development of efficient programs and provides a test of the theoretical basis for prevention effects.  One-model structural equation modeling (SEM) is commonly applied to simultaneously examine the combined effects from X to M, and from M to Y based on these two theories (X to M to Y), especially with recent developments of complex mediation models, such as multiple-mediator models, longitudinal mediation models where mediators and/or outcomes are latent growth factors, multilevel mediation models, and combined mediation/moderation models. Under One-model SEM, it is assumed that the conceptual theory part of the model -- relations between mediators and outcomes -- is homogeneous across treatment conditions, even under complex models.  Specifically, it assumes that the variances and covariance of the M and Y variables are the same across treatment conditions; and for growth modeling, it assumes that the functional forms of growth are the same.  However, it is possible that the nature of the intervention changes not only the mean but also the distribution (e.g., smaller variance), the functional form of growth (from linear to exponential growth), and other features of M and/or Y for the experimental group. This study investigates how the violation of the homogeneity assumption affects estimation of mediation effects using One-model SEM.  We will compare results from the One-model SEM against those from the multi-group model (M to Y across X), an alternative method of testing mediation effects, where the effect of X to M is the difference of the means of M across the two groups  For the results from the multi-group model to be the same as from the One-model SEM, we need to constrain the variance/covariance, the effect of M to Y, etc. to be the same across groups, and these constraints may not always be realistic and may lead to incorrect inference.  The difference between the constrained model and non-constrained model provides indication of bias in estimation when the homogeneous assumption is violated. We will use simulated and empirical data (e.g., data from the preventive intervention research) to conduct the study.