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Generalized Measurement Invariance Tests with Application to Factor Analysis

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  • Edgar C. Merkle
  • Achim Zeileis

Abstract

The issue of measurement invariance commonly arises in factor-analytic contexts, with methods for assessment including likelihood ratio tests, Lagrange multiplier tests, and Wald tests. These tests all require advance definition of the number of groups, group membership, and offending model parameters. In this paper, we construct tests of measurement invariance based on stochastic processes of casewise derivatives of the likelihood function. These tests can be viewed as generalizations of the Lagrange multiplier test, and they are especially useful for: (1) isolating specific parameters affected by measurement invariance violations, and (2) identifying subgroups of individuals that violated measurement invariance based on a continuous auxiliary variable. The tests are presented and illustrated in detail, along with simulations examining the tests' abilities in controlled conditions.

Suggested Citation

  • Edgar C. Merkle & Achim Zeileis, 2011. "Generalized Measurement Invariance Tests with Application to Factor Analysis," Working Papers 2011-09, Faculty of Economics and Statistics, Universität Innsbruck.
    • Handle: RePEc:inn:wpaper:2011-09
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    References listed on IDEAS

    as
    1. Zeileis, Achim & Leisch, Friedrich & Hornik, Kurt & Kleiber, Christian, 2002. "strucchange: An R Package for Testing for Structural Change in Linear Regression Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 7(i02).
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    3. Achim Zeileis & Kurt Hornik, 2007. "Generalized M‐fluctuation tests for parameter instability," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 488-508, November.
    4. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-285, March.
    5. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    6. Steven Boker & Michael Neale & Hermine Maes & Michael Wilde & Michael Spiegel & Timothy Brick & Jeffrey Spies & Ryne Estabrook & Sarah Kenny & Timothy Bates & Paras Mehta & John Fox, 2011. "OpenMx: An Open Source Extended Structural Equation Modeling Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 306-317, April.
    7. Carolin Strobl & Julia Kopf & Achim Zeileis, 2011. "A new method for detecting differential item functioning in the Rasch model," Working Papers 2011-01, Faculty of Economics and Statistics, Universität Innsbruck.
    8. Hansen, Bruce E., 1992. "Testing for parameter instability in linear models," Journal of Policy Modeling, Elsevier, vol. 14(4), pages 517-533, August.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    measurement invariance; parameter stability; factor analysis; structural equation models;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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