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Statistical mediation analysis is used to uncover intermediate variables, known as mediators [M], that explain how a treatment [X] changes an outcome [Y]. Often, researchers examine whether baseline levels of M and Y moderate the effect of X on posttest M or Y. However, there is limited guidance on how to estimate baseline-by-treatment interaction (BTI) effects when M and Y are latent variables, which entails the estimation of latent interaction effects. In this paper, we discuss two general approaches for estimating latent BTI effects in mediation analysis: using structural models or scoring latent variables prior to estimating observed BTIs and correcting for unreliability. We present simulation results describing bias, power, type 1 error rates, and interval coverage of the latent BTIs and mediated effects estimated using these approaches. These methods are also illustrated with an applied example. R and M plus  syntax are provided to facilitate the implementation of these approaches.

Estimating Latent Baseline-by-Treatment Interactions in Statistical Mediation Analysis