Assessing Factorial Invariance in Ordered-Categorical Measures

Anderson, T. W. & Rubin, H. (1956). Statistical inference in factor analysis. In J. Neyman (Ed.), Proceedings of the third Berkeley symposium on mathematical statistics and probability, (pp. 111-150). Berkeley, CA: University of California Press.

Babakus E., 1987, Journal of Marketing Research, 37, 72

Bartholomew D. J., 1980, Series B, 42, 293

Bartholomew D. J., 1984, Series B, 46, 120

Bartholomew, D. J. (1987). Latent variable models and factor analysis. London: Charles Griffin & Company.

10.1037//0033-2909.105.3.467

Bock R. D., 1981, Psychometrika, 46, 443, 10.1007/BF02293801

Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.

Bollen K. A., 1985, Sociological Methods and Research, 14, 155, 10.1177/0049124185014002003

Boomsma, A. & Hoogland, J. J. (2001). The robustness of LISREL modeling revisited. In R. Cudeck, S. Du Toit & D. Sorbom (Eds.), Structural equation modeling: Present and future. (pp. 139-168). Lincolnwood, IL: Scientific Software Inc.

Browne, M. W. & Arminger, G. (1995). Specification and estimation of mean and covariance structure models. In G. Arminger, C. C. Clogg, & M. E. Sobel (Eds.), Handbook of statistical modeling for the social and behavioral sciences (pp. 185-249). New York: Plenum.

Browne, M. W. & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 136-162). Newbury Park, CA: Sage.

Christoffersson A., 1975, Psychometrika, 40, 5, 10.1007/BF02291477

Joreskog, K. G. (1979). A general approach to confirmatory factor analysis with addendum. In K. G. Joreskog, D. Sorbom, & J. Magidson (Eds.), Advances in factor analysis and structural equation models (pp. 21-43). New York: Abt Associates.

10.1007/BF00152012

Joreskog, K. G. (1993). Latent variable modeling with ordinal variables. In K. Haagen, D. J. Bartholomew, & M.Deistler (Eds.), Statistical modeling and latent variables (pp. 163-171). Amsterdam: North-Holland.

10.1207/S15327906347-387

Joreskog, K. G. & Sorbom, D. (1996). LISREL 8 User's Reference Guide. Chicago: Scientific Software International.

Lee S. Y., 1989, Psychometrika, 54, 63, 10.1007/BF02294449

Lord, F. M. & Novick, M. E. (1968). Statistical theories of mental test scores. Reading: Addison-Wesley.

Mathsoft (1999). S-Plus 2000 user's guide. Seattle: Mathsoft Inc.

McDonald, R. P. (1999). Test theory: A unified treatment. Mahwah, NJ: Lawrence Erlbaum Associates.

10.1016/0883-0355(89)90002-5

Meredith W., 1993, Psychometrika, 58, 525, 10.1007/BF02294825

Meredith W., 1992, Psychometrika, 57, 289, 10.1007/BF02294510

10.1207/S15328007SEM0801_1

Mislevy R. J., 1986, Journal of Educational Statistics, 11, 3, 10.3102/10769986011001003

Muthen B. O., 1978, Psychometrika, 43, 551, 10.1007/BF02293813

Muthen B. O., 1984, Psychometrika, 49, 115, 10.1007/BF02294210

Muthen, B. O. & Asparouhov, T. (2002). Latent variable analysis with categorical outcomes: Multiple-group and growth modeling in Mplus.Mplus Web Note No. 4, at http:// www.statmodel.com/mplus/examples/webnote.html.

Muthen B. O., 1981, Psychometrika, 46, 407, 10.1007/BF02293798

Muthen B. O., 1985, British Journal of Mathematical and Statistical Psychology, 38, 171, 10.1111/j.2044-8317.1985.tb00832.x

Muthen B. O., 1985, Journal of Educational Statistics, 10, 133, 10.3102/10769986010002133

Muthen, L. K. & Muthen, B. O. (1998). Mplus user's guide. Los Angeles: Author.

Olsson U. H., 1979, Multivariate Behavioral Research, 14, 485, 10.1207/s15327906mbr1404_7

10.1016/0167-9473(90)90100-V

Rigdon E. E., 1991, Journal of Marketing Research, 28, 491, 10.1177/002224379102800412

Satorra, A. (1992). Asymptotic robust inferences in the analysis of mean and covariance structures. In P. V. Marsden (Ed.), Sociological methodology 1992 (pp. 249-278). Oxford: Blackwell Publishers.

Satorra, A. (1993a). Asymptotic robust inferences in multiple-group analysis of augmentedmoment structures. In C. M. Cuadras & C. R. Rao (Eds.), Multivariate analysis: Future directions 2 (pp. 211-229). Amsterdam: Elsevier.

Satorra, A. (1993b). Multi-sample analysis of moment structures: Asymptotic validity of inferences based on second-order moments. In K. Haagen, D. J. Bartholomew, & M. Deistler (Eds.), Statistical modeling and latent variables (pp. 283-298). Amsterdam: North-Holland.

Satorra, A. & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variable analysis: Applications to developmental research (pp. 399-419). Newbury Park: Sage.

Shapiro, A. (1985). Identifiability of factor analysis: Some results and open problems. Linear Algebra and its Applications, 70, 1-7.

Takane Y., 1987, Psychometrika, 52, 393, 10.1007/BF02294363

Accepted October, 2003.