Assessing Spurious Interaction Effects in Structural Equation Modeling: A Cautionary Note

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Simultaneous estimation of interaction and quadratic effects is crucial in regression to avoid errors.
• Previous research focused on multiple regression, neglecting structural equation modeling (SEM) for latent variables.

Purpose of the Study:

• To investigate the necessity of including quadratic effects in latent variable interaction models using Monte Carlo simulation.
• To assess the impact of including quadratic effects on interaction detection and model estimation.

Main Methods:

• Monte Carlo simulation was employed to examine latent variable interaction models.
• The study compared models with and without latent variable quadratic effects.

Main Results:

• Including latent variable quadratic effects reduced spurious interactions but lowered power for true interactions.
• Inaccurate parameter and standard error estimates, along with reduced convergence rates, were observed.

Conclusions:

• Researchers should use latent variable interaction models for latent variable interactions, not interaction quadratic models.
• Including quadratic effects is viable for mitigating spurious interactions with large sample sizes (≥500) and high reliability, but theoretical justification is paramount.