Effects of Latent Variable Nonnormality and Model Misspecification on Testing Structural Equation Modeling Interactions

Abstract

Interest in testing interaction terms within the latent variable modeling framework has been on the rise in recent years. However, little is known about the influence of nonnormality and model misspecification on such models that involve latent variable interactions. The authors used Mattson's data generation method to control for latent variable distributional properties, and they examined how data nonnormality and model misspecification affected latent variable interaction models in relation to varying sample sizes and different magnitudes of incorrectly constrained model parameters. The authors conducted 600 replications for each of the 54 configurations of the 4-factor completely crossed balanced deign. In general, results were suggestive of less bias under conditions of latent variable normality, large sample sizes, correctly specified models, and smaller parameters that were incorrectly constrained (i.e., misspecified). Similarly, these conditions were also found to produce better fitting models as gauged by several popular measures of model fit.

Keywords:

• latent variable interaction
• model fit
• model misspecification
• nonnormality
• parameter estimate
• structural equation model

Notes

Indicator reliability is readily available as: r_xx = [1 − (error variance)/(total variance)]. The error variance is the θ_i value of each indicator as specified under “Model for Simulation.” The total variances of the four indicators are specified in Equation 3 (four diagonal elements in the middle). For example, for X₁, its error variance θ₁ is 0.51, and its total variance is (φ₁₁ + θ₁) = (0.49 + 0.51), and its reliability r_xx = 1 − [0.51/(0.49 + 0.51)] = 0.49.