Multilevel Heterogeneous Factor Analysis and Application to Ecological Momentary Assessment.

Area of Science:

• Psychometrics
• Statistical Modeling
• Multilevel Analysis

Background:

• Multilevel heterogeneous models in confirmatory factor analysis (CFA) analyze repeated measurements on individuals.
• Existing models by Ansari et al. assume invariant factor structure but allow individual variation in means and factor loadings.
• A key restriction is the assumption of diagonal residual covariance matrices, implying independence of residuals.

Purpose of the Study:

• To relax the diagonality assumption of the residual covariance matrix in multilevel heterogeneous CFA.
• To introduce a formal Bayesian Lasso method for estimating correlated individual-level residuals.
• To improve model goodness of fit and avoid heuristic modifications of the covariance matrix.

Main Methods:

• Application of a multilevel heterogeneous model for confirmatory factor analysis.
• Relaxation of the diagonality assumption for the individual-level residual covariance matrix.
• Estimation of the residual covariance matrix using a formal Bayesian Lasso method.

Main Results:

• The proposed method, by allowing correlated residuals, alleviates the restriction of configural invariance.
• The Bayesian Lasso approach provides a principled way to estimate the residual covariance matrix.
• Improved goodness of fit was observed compared to models with diagonal residual covariance assumptions.

Conclusions:

• Estimating correlated individual-level residuals using Bayesian Lasso enhances multilevel CFA.
• This approach offers a statistically rigorous alternative to ad hoc modifications for improving model fit.
• The method is effective for analyzing complex repeated measures data, as demonstrated with simulations and ecological momentary assessment data.