Modeling Interactions Between Latent and Observed Continuous Variables Using Maximum-Likelihood Estimation In Mplus

Modeling with random slopes is used in random coefficient regression, multilevel regression, and growth modeling. Random slopes can be seen as continuous latent variables. Recently, a flexible modeling framework has been implemented in the Mplus program to do modeling with such latent variables combined with modeling of psychometric constructs, typically referred to as factors, measured by multiple indicators. This note shows how such a framework can handle interactions between latent continuous and observed continuous indicators. Three examples are given: a Monte Carlo simulation to estimate power to detect the interaction; a psychological example; and a growth modeling example. Mplus input, output, and data are available at the Mplus web site, www.statmodel.com/mplus/examples/webnote.html.