Maximum Likelihood Estimation of Multilevel Structural Equation Models with Random Slopes for Latent Covariates

Area of Science:

• Psychometrics
• Statistics
• Multilevel Modeling

Background:

• Maximum likelihood estimation (MLE) is crucial for structural equation models (SEMs).
• Two-level SEMs with random slopes for latent covariates present computational challenges due to complex likelihood functions.
• Numerical integration is often required but can be computationally intensive.

Purpose of the Study:

• To present a novel MLE routine for two-level SEMs with random slopes for latent covariates.
• To address the computational burden associated with numerical integration in these models.
• To improve the efficiency of parameter estimation in complex multilevel SEMs.

Main Methods:

• The routine employs a reformulation of the likelihood function, as proposed by du Toit and Cudeck (2009).
• This reformulation allows for analytical integration of a significant subset of random effects.
• The method reduces the need for high-dimensional numerical integration, thereby decreasing computational cost.

Main Results:

• The proposed routine effectively handles two-level SEMs with random slopes for latent covariates.
• Analytical integration of random effects significantly reduces the computational burden compared to full numerical integration.
• The method's performance was validated through a simulation study and an empirical example.

Conclusions:

• The presented MLE routine offers a computationally efficient solution for complex two-level SEMs.
• This approach facilitates more accessible and practical analysis of multilevel data with latent variables and random slopes.
• The findings contribute to advancements in statistical modeling for complex data structures.