Testing Latent Variable Interaction Effect: Dealing with Data Nonnormality and Model Misspecification

The book discusses the effects of data nonnormality, model misspecification, sample size, and effect size on testing latent variable interactions through an inspection of the Jöreskog and Yang's (1996) model. Mattson's (1997) method was used to generate nonnormal latent variables in this Monte Carlo study. One covariance parameter was deleted for investigating the influence of misspecified models. The simulation involved a balanced experimental design, with 3 × 2 × 3 × 3 = 54 combinations. Data analysis focused on bias of estimating parameters, standard errors, model fit indexes. Variance partition was conducted to further examine the unique and combined influence of the factors (i.e., data nonnormality, model specification, sample size, effect size). Results indicated that data nonnormality and model misspecification had large effects on fit indexes (e.g., SRMR, RMSEA). Also, severe nonnormality led to a large bias of estimating the interaction effect. Implications of and recommendations for testing latent variable interactions are discussed.