Power of the Likelihood Ratio Test in Multiple Group Confirmatory Factor Analysis under Partial Measurement Invariance

Abstract

The power of the likelihood ratio test in multiple group confirmatory factor analysis under partial measurement invariance is studied. A six-variable, two-factor model is considered where a specification error exists for one group. The size of the specification error as well as the size of the free parameters are varied. Power is obtained via the method of Satorra and Saris (1985). Results show that the power of the test is dependent on the size of the misspecified parameter, the size of the free loadings, as well as the correlation between the misspecified parameter and the parameter held invariant. Bias is also observed for estimates of the invariant parameters. Results are discussed in terms of strategies of multiple group modeling.

Get full access to this article

View all access options for this article.

References

Bentler, P. B. (1985). Theory and implementation of EQS, a structural equation program. Los Angeles: BMDP Statistical Software.

Box, G. E. P. (1949). A general distribution theory for a class of likelihood criteria. Biometrika, 36, 317-346.

Byrne, B. M. and Shavelson, R. J. (1986). Adolescent self-concept: Testing the assumption of equivalent structure across gender. American Educational Research Journal, 24, 365-385.

Byrne, B. M. , Shavelson, R. J. , and Muthen, B. (in press). Testing for the equivalence of factor covariance and mean structures: The issue of partial measurement invariance. Psychological Bulletin.

Joreskog, K. G. (1971). Simultaneous factor analysis in several populations. Psychometrika 36, 409-426.

Joreskog, K. G. and Sorbom, D. (1985). LISREL VI: Analysis of linear structural relationships by the method of maximum like-lihood. Mooresville, IN: Scientific Software.

Kaplan, D. (1988). The impact of specification error on the estimation, testing, and improvement of structural equation models. Multivariate Behavioral Research, 23, 69-86.

Kaplan, D. (1989). A study of the sampling variability and z-values of parameter estimates from misspecified structural equation models. Multivariate Behavioral Research, 24, 41-57.

Kaplan, D. (in press). Model modification in covariance structure analysis: Application of the expected parameter change statistic. Multivariate Behavioral Research.

10.

Luijben, T. , Boomsma, A. , and Molenaar, I. W. (1987). Modification of factor analysis models in covariance structure analysis: A Monte Carlo study. Heymans Bulletins Psychologische Instituten, University of Groningen.

11.

MacCallum, R. (1986). Specification searches in covariance structure modeling. Psychological Bulletin, 100, 107-120.

12.

McGaw, B. and Joreskog, K. G. (1971). Factorial invariance of ability measures in groups differing in intelligence and socioeconomic status. British Journal of Mathematical and Statistical Psychology, 24, 154-168.

13.

Muthen, B. (1987). LISCOMP: Analysis of linear structural relations using a comprehensive measurement model. Mooresville, IN: Scientific Software, Inc.

14.

Muthen, B. and Christoffersson, A. (1981). Simultaneous factor analysis of dichotomous variables in several groups. Psychometrika, 46, 407-419.

15.

Saris, W. E. , Satorra, A. , and Sorbom, D. (1987). The detection and correction of specification errors in structural equation models. In C. C. Clogg (ed.), Sociological Methodology, 1987. San Francisco: Jossey-Bass.

16.

Saris, W. E. , and Stronkhorst, H. (1984). Causal modelling in nonexperimental research. Amsterdam: Sociometric Research Foundation.

17.

Satorra, A. (1989). Alternative test criteria in covariance structure analysis: A unified approach. Psychometrika, 54, 131-151.

18.

Satorra, A. and Saris, W. E. (1985). Power of the likelihood ratio test in covariance structure analysis. Psychometrika, 50, 83-90.

19.

Wolfle, L. M. and Robertshaw, D. (1983). Racial differences in measurement error in educational achievement models. Journal of Educational Measurement, 20, 39-49.