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Testing Measurement Invariance with Ordinal Missing Data: A Comparison of Estimators and Missing Data Techniques.

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This study evaluated methods for handling ordinal missing data in measurement equivalence/invariance (ME/I) testing. Probit and logit link functions with full information maximum likelihood estimation (FIML) provided the most accurate parameter estimates for ME/I analysis.

Keywords:
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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Social Sciences Research Methods

Background:

  • Ordinal missing data frequently occur in measurement equivalence/invariance (ME/I) testing.
  • Existing guidance on handling ordinal missing data in ME/I studies is limited.
  • Accurate ME/I testing is crucial for cross-group comparisons and model validation.

Purpose of the Study:

  • To evaluate the performance of five methods for addressing ordinal missing data in ME/I testing.
  • To compare the accuracy of parameter estimates and the validity of chi-square difference tests ([Formula: see text]) across methods.
  • To provide recommendations for researchers on selecting appropriate methods for ME/I analyses with ordinal missing data.

Main Methods:

  • Simulation study comparing five methods: continuous full information maximum likelihood estimation (FIML), continuous robust FIML (rFIML), FIML with probit links (pFIML), FIML with logit links (lFIML), and mean and variance adjusted weight least squares estimation with pairwise deletion (WLSMV_PD).
  • Assessment of type I error rates for chi-square difference tests ([Formula: see text]).
  • Evaluation of the accuracy of parameter estimates, including factor loadings and standard errors.

Main Results:

  • All methods except WLSMV_PD demonstrated acceptable control over type I error rates for [Formula: see text] tests.
  • Most methods maintained sufficient power to detect noninvariance under various conditions.
  • Only pFIML and lFIML consistently produced accurate factor loading estimates and standard errors across all simulated conditions.

Conclusions:

  • pFIML and lFIML are recommended for ME/I testing with ordinal missing data due to their superior performance in parameter estimation.
  • Researchers should carefully consider the choice of method for handling missing data to ensure valid ME/I results.
  • The study provides empirical evidence to guide the selection of appropriate statistical techniques in complex psychometric analyses.