A Note on Estimating the Joreskog-Yang Model for Latent Variable Interaction Using LISREL 8.3

Kenny and Judd (1984) developed a latent variable interaction model for observed variables centered around their population means. They estimated the model by using a covariance matrix calculated from sample-mean-centered variables and products of these variables. Subsequently, Joreskog and Yang (1996) identified the need to include intercepts for the measurement and structural equations and estimated the model by using a covariance matrix calculated from noncentered observed variables and products of these variables, and means of the observed variables and the products of noncentered variables. Evidence is presented that the Joreskog-Yang procedure for estimating the Kenny-Judd interaction model is subject to severe convergence problems when implemented in LISREL8.3 and means for the indicators of the latent exogenous variables are nonzero. An alternative procedure is presented that solves the convergence problem and provides consistent estimators of the parameters.