An alternative to post hoc model modification in confirmatory factor analysis: The Bayesian lasso.

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Confirmatory Factor Analysis (CFA) is widely used but has strict assumptions.
• Poor model fit to real data is a common issue in CFA.
• Post hoc modification indices can identify correlated residual errors but pose sequential modification challenges.

Purpose of the Study:

• To propose a novel Bayesian method for modeling correlated residual errors in CFA.
• To address limitations of post hoc modification index approaches.
• To achieve model parsimony and identifiability in measurement models.

Main Methods:

• Modeling the entire inverse residual covariance matrix as a sparse positive definite matrix.
• Utilizing a Lasso prior on the inverse covariance matrix.
• Analyzing both simulated and real data (n=175) from a 28-item emotion measure.

Main Results:

• The proposed Bayesian method effectively models correlated residual terms.
• It circumvents the sequential modification problem inherent in traditional approaches.
• The method ensures a positive definite covariance matrix for error terms.
• Lasso prior facilitates model parsimony and identifiability.

Conclusions:

• The novel Bayesian approach offers a robust and practical solution for handling correlated residual errors in CFA.
• This method enhances the validity and usefulness of measurement models.
• It provides a more parsimonious and identifiable alternative to post hoc modifications.