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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.