The choice of product indicators in latent variable interaction models: post hoc analyses

Area of Science:

• * Social Psychology
• * Quantitative Psychology

Background:

• * The product indicator (PI) approach is widely used for modeling nonlinear effects in latent variables.
• * This method involves practitioner-selected PIs, introducing potential arbitrariness.
• * Previous research primarily used Monte Carlo studies, lacking real-world case evaluations.

Purpose of the Study:

• * To evaluate the impact of PI configuration choices on modeling nonlinear effects using a real-world social psychology case.
• * To compare the performance of matched-pair PI configurations against an all-pairs PI configuration.
• * To assess the all-pairs PI approach's suitability for small sample sizes and compare it with latent moderated structural equations.

Main Methods:

• * Three post hoc analyses were conducted on a social psychology dataset with 2 latent variables and 3-4 indicators each.
• * Estimated interaction effects across over 4,000 PI configurations, including 60 recommended matched-pair configurations.
• * Performed a post hoc Monte Carlo study varying sample sizes and data distributions to examine convergence, bias, Type I error, and power.

Main Results:

• * The selection of PIs substantially affected estimated interaction effects, even among matched-pair configurations.
• * Variation in estimates across matched-pair configurations was considerable.
• * The all-pairs PI configuration demonstrated better overall performance, improved convergence, and more stable interaction test outcomes compared to matched-pair configurations.

Conclusions:

• * The choice of product indicator configuration critically influences the modeling of nonlinear effects among latent variables.
• * The all-pairs PI configuration is recommended over matched-pair configurations due to its superior performance and lack of ambiguity.
• * The all-pairs PI approach shows promise for small sample sizes and warrants comparison with alternative methods like latent moderated structural equations.