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Including quadratic effects in latent variable interaction models can reduce spurious interactions but may decrease power and accuracy. Researchers should prioritize theoretical grounding for higher-order effects models.

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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.