Interactions of Latent Variables in Structural Equation Models

Interactions of variables occur in a variety of statistical analyses. The best known procedures for models with interactions of latent variables are technically demanding. Not only does the potential user need to be familiar with structural equation modeling (SEM), but the researcher must be familiar with programming nonlinear and linear constraints and must be comfortable with fairly large and complicated models. This article provides a largely nontechnical description of an alternative two-stage least squares (2SLS) technique to include interactions of latent variables in SEM. The method requires the selection of instrumental variables and we give rules for their selection in the most common cases. We compare the 2SLS method to the alternatives. Some of the important advantages of the 2SLS are that it can handle nonnormal observed variables, is readily available in major statistical software packages, and has a known asymptotic distribution. In providing the comparisons, we reanalyze all the interaction examples from Kenny and Judd's (1984) article with the 2SLS method. We also give a new empirical example, and list SAS programs for all examples.