A Comparison of Regularization, Alignment, and a Traditional Method for Estimating Structural Relationships Across...

Area of Science:

• Psychometrics
• Structural Equation Modeling
• Multivariate Statistics

Background:

• Establishing partial measurement invariance is essential for valid cross-group comparisons of latent variables.
• Traditional methods often rely on identifying noninvariant items before estimating structural relationships.
• Newer techniques, including regularization and alignment, estimate latent parameters without pre-specifying anchor items.

Purpose of the Study:

• To compare the performance of traditional sequential search (MGCFA) with alignment, lasso, elastic net, and ridge regression.
• To evaluate bias and efficiency in estimating latent variable correlations and means without anchor items.
• To provide guidance on selecting appropriate methods based on the level of measurement noninvariance.

Main Methods:

• A simulation study was conducted comparing multiple-group CFA (MGCFA) with alignment, lasso, elastic net, and ridge regression.
• Varied factors included percentage, magnitude, and pattern of noninvariance, sample size, number of indicators, and latent variable correlation.
• Evaluated bias and efficiency in recovering factor correlations, means, and item parameters for a two-group model.

Main Results:

• Elastic net demonstrated less bias and greater efficiency under higher proportions of measurement noninvariance.
• Alignment methods performed better when noninvariance was low to moderate.
• The choice of method impacts the accuracy of latent variable parameter recovery.

Conclusions:

• Elastic net is recommended for situations with substantial measurement noninvariance.
• Alignment is a suitable choice for models with limited or moderate noninvariance.
• Researchers should consider the expected level of noninvariance when selecting a method for estimating latent correlations and means across groups.