Beyond ANOVA: An Introduction to Structural Equation Models for Experimental Designs. (July 2019) - Breitsohl, Heiko
Structural equation modeling (SEM) can offer useful features to researchers conducting experiments. Yet most researchers appear not to apply such models when analyzing their data, relying instead on more restrictive (and sometimes inappropriate) approaches, such as analysis of variance (ANOVA). This paper is aimed at introducing experimentalists to the modeling options available in SEM. I compare and contrast ANOVA with two SEM-based approaches, addressing general attributes; specific features, such as the relation to confirmatory factor analysis; and assumptions imposed under each approach. A corresponding decision tree offers additional guidance for selecting between approaches. I then describe a general procedure for building and testing models under the two SEM-based approaches, ranging from preparatory decisions to checking assumptions, to obtaining estimates and conducting hypothesis tests. In addition, I discuss options for latent variable scaling, reporting effect sizes disattenuated from measurement error, incorporating manipulation checks, and adjusting inferences for Type I error inflation. Finally, I offer an example based on a real study (with annotated code for Mplus and R), taking readers though the modeling process and illustrating some implications of modeling choices.