A comparison of methods for estimating quadratic effects in nonlinear structural equation models

Area of Science:

• Psychometrics
• Statistical Modeling
• Quantitative Psychology

Background:

• Latent variable regression models are crucial for analyzing complex relationships.
• Accurate estimation of quadratic effects is essential for understanding non-linear associations.
• Existing methods for quadratic effects in latent variable models vary in performance.

Purpose of the Study:

• To compare five distinct methods for estimating and testing quadratic effects in latent variable regression.
• To evaluate the performance of these methods using Monte Carlo simulations.
• To provide recommendations for the most effective estimation techniques.

Main Methods:

• Monte Carlo simulations were used to assess estimation and hypothesis testing.
• Five methods were compared: 2-stage moderated regression, unconstrained product indicator, latent moderated structural equations, Bayesian approach, and marginal maximum likelihood estimation.
• The latent quadratic model was applied to educational reading data for comparison.

Main Results:

• Maximum likelihood estimation and Bayesian approaches generally performed best across multiple criteria.
• Performance was evaluated based on bias, root-mean-square error, standard error ratios, power, and Type I error control.
• Key differences and similarities among the five methods were identified.

Conclusions:

• Maximum likelihood estimation and Bayesian methods are recommended for estimating quadratic effects in latent variable models.
• The study highlights the strengths and weaknesses of different statistical approaches.
• Findings inform best practices in quantitative research and statistical analysis.