Estimating Latent Variable Interactions With Non-Normal Observed Data: A Comparison of Four Approaches

Area of Science:

• Psychometrics
• Statistical Modeling
• Quantitative Psychology

Background:

• Latent variable interaction modeling is crucial for understanding complex relationships.
• Assessing the robustness of different modeling approaches under non-normality is essential for reliable results.
• Existing methods may produce biased estimates when data deviates significantly from normality.

Purpose of the Study:

• To evaluate the performance of four latent variable interaction modeling techniques: Constrained Product Indicator (CPI), Generalized Appended Product Indicator (GAPI), Unconstrained Product Indicator (UPI), and Latent Moderated Structural Equations (LMS).
• To investigate the robustness of these methods under high degrees of non-normality in observed exogenous variables.
• To identify which methods provide accurate and efficient estimates of latent interaction effects in various normality conditions.

Main Methods:

• Monte Carlo simulation was employed to generate data with varying degrees of non-normality.
• Four latent variable interaction modeling approaches (CPI, GAPI, UPI, LMS) were tested.
• Maximum Likelihood (ML) estimation was used, and statistical power and Type-I error rates were examined.

Main Results:

• Constrained Product Indicator (CPI) and Latent Moderated Structural Equations (LMS) yielded biased interaction effect estimates under high non-normality.
• When non-normality was mild, LMS provided the most efficient estimates and highest statistical power.
• Generalized Appended Product Indicator (GAPI) and Unconstrained Product Indicator (UPI) with ML estimation produced unbiased estimates in highly non-normal conditions.
• GAPI and UPI demonstrated acceptable Type-I error rates for interaction effect tests at sample sizes of 500 or greater.

Conclusions:

• The choice of latent variable interaction modeling approach significantly impacts estimate accuracy under non-normality.
• GAPI and UPI are recommended for robust latent interaction analysis when exogenous variables exhibit substantial non-normality.
• Researchers should carefully consider data distributional properties when selecting a latent interaction modeling strategy.