Identification of Confirmatory Factor Analysis Models of Different Levels of Invariance for Ordered Categorical Outcomes
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This article considers the identification conditions of confirmatory factor analysis (CFA) models for ordered categorical outcomes with invariance of different types of parameters across groups. The current practice of invariance testing is to first identify a model with only configural invariance and then test the invariance of parameters based on this identified baseline model. This approach is not optimal because different identification conditions on this baseline model identify the scales of latent continuous responses in different ways. Once an invariance condition is imposed on a parameter, these identification conditions may become restrictions and define statistically non-equivalent models, leading to different conclusions. By analyzing the transformation that leaves the model-implied probabilities of response patterns unchanged, we give identification conditions for models with invariance of different types of parameters without referring to a specific parametrization of the baseline model. Tests based on this approach have the advantage that they do not depend on the specific identification condition chosen for the baseline model.
Keywordsordered categorical data invariance testing model identification
Work on this research by the second author was partially supported by the National Institute of Drug Abuse research education program R25DA026-119 (Director: Michael C. Neale) and by grant R01 AG18436 (20112016, Director: Daniel K. Mroczek) from National Institute on Aging, National Institute on Mental Health.
- Baker, F. B. (1992). Item response theory parameter estimation techniques. New York: Marcel Dekker.Google Scholar
- Davies, R. B. (1987). Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika, 74, 33–43.Google Scholar
- Estabrook, R. (2012). Factorial invariance: Tools and concepts for strengthening research. In G. Tenenbaum, R. Eklund, & A. Kamata (Eds.), Measurement in sport and exercise psychology. Champaign, IL: Human Kinetics.Google Scholar
- Meredith, W. (1964b). Rotation to achieve factorial invariance. Psychometrika, 29, 186–206.Google Scholar
- Millsap, R. E., & Meredith, W. (2007). Factorial invariance: Historical perspectives and new problems. In R. Cudeck & R. C. MacCallum (Eds.), Factor analysis at 100: Historical developments and future directions (pp. 131–152). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
- Muthén, B. O., & Kaplan, D. (1985). A comparison of some methodologies for the factor analysis of non-normal Likert variables. British Journal of Mathematical and Statistical Psychology, 38, 171–189.Google Scholar
- Muthén, L. K., & Muthén, B. O. (1998–2012). Mplus Users Guide (7th ed.). Los Angeles, CA: Muthén & Muthén.Google Scholar
- R Development Core Team. (2013). R: A language and environment for statistical computing. http://www.R-project.org.
- Rensvold, R. B., & Cheung, G. W. (2001). Testing for metric invariance using structural equation models, solving the standardization problem. Research in Management, 1, 25–50.Google Scholar
- Strom, D. O., & Lee, J. W. (1994). Variance components testing in the longitudinal mixed effects model. Biometrics, 50, 1171–1177 (Corrected in. Biometrics, 51, 1196.)Google Scholar
- van der Linden, W. J. and Barrett, M. D. (2015). Linking item response model parameters. Psychometrika. doi: 10.1007/s11336-015-9469-6.
- Widaman, K. F., & Reise, S. P. (1997). Exploring the measurement invariance of psychological instruments: Applications in the substance use domain. In K. J. Bryant, M. Windle, & S. G. West (Eds.), The science of prevention: Methodological advances from alcohol and substance abuse research (pp. 281–324). Washington, DC: American Psychological Association.CrossRefGoogle Scholar
- Wu, H. (accepted) A note on the identifiability of fixed effect 3PL models. Psychometrika.Google Scholar