Interaction effects in growth modeling: A full model

In substantively important research, Li, Duncan, and Acock (2000) and Duncan, Duncan, Strycker, Li, and Alpert (1999) extended Joreskog and Yang's (1996) structural equation model of latent interactions to latent growth modeling. We address 2 concerns with their approach: (a) Parameter constraints specified in their models were apparently inappropriate, and (b) they did not specify a full interaction model. Here we present more appropriate constraints and demonstrate a full interaction model for latent growth modeling that simultaneously estimates (a) the interaction between rates of change (slopes) of 2 predictors on the rate of change (slope) of the outcome and (b) the interaction between initial levels of growth (intercepts) of 2 predictors on the initial level (intercept) of outcome. Based on mathematical derivation and a comparison of alternative models fitted to simulated data, we show that our model is more appropriate and that their models can result in seriously biased parameter estimates.