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Area of Science:

  • Psychometrics
  • Statistical Modeling

Background:

  • Measurement invariance is crucial for comparing latent constructs across populations.
  • Traditional methods have limitations in handling complex invariance assessments.
  • Moderated nonlinear factor analysis (MNLFA) has emerged as a promising approach.

Purpose of the Study:

  • To introduce and demonstrate the application of MNLFA for assessing measurement invariance.
  • To provide an accessible method for researchers using open-source software.
  • To highlight the advantages of MNLFA in handling multiple background variables and heteroskedasticity.

Main Methods:

  • Utilizing moderated nonlinear factor analysis (MNLFA).
  • Implementing MNLFA within a single-group confirmatory factor analysis framework via parameter moderation.
  • Applying the open-source R package OpenMx for statistical analysis.

Main Results:

  • MNLFA effectively assesses measurement invariance across multiple continuous and categorical background variables.
  • MNLFA accounts for heteroskedasticity by modeling factor and residual variances as functions of background variables.
  • The OpenMx package provides a viable, accessible platform for conducting MNLFA.

Conclusions:

  • MNLFA is a powerful tool for robust measurement invariance testing.
  • Open-source software like OpenMx democratizes advanced psychometric methods.
  • This approach enhances the validity of cross-group comparisons in latent construct measurement.