Estimating latent baseline-by-treatment interactions in statistical mediation analysis

Statistical mediation analysis is used to uncover intermediate variables, known as mediators [ $$ ], that explain how a treatment [ $$ ] changes an outcome [ $$ ]. Often, researchers examine whether baseline levels of $$ and $$ moderate the effect of $$ on posttest $$ or $$ . However, there is limited guidance on how to estimate baseline-by-treatment interaction (BTI) effects when $$ and $$ 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 Mplus syntax are provided to facilitate the implementation of these approaches.