Detecting mixtures from structural model differences using latent variable mixture modeling: A comparison of relative model fit statistics

Structural Equation Modeling

Volumn 14, Issue 2, 2007, Pages 202-226

  Henson, James M ^a   Reise, Steven P ^b   Kim, Kevin H ^c  

^a OLD DOMINION UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CLASSIFICATION (OF INFORMATION); ENTROPY; MIXTURES; MULTIVARIANT ANALYSIS; STATISTICAL TESTS;

AKAIKE'S INFORMATION CRITERIONS; BAYESIAN INFORMATION; INTEGRATED CLASSIFICATION; LIKELIHOOD INFORMATION; LIKELIHOOD RATIO TESTS; NUMBER OF COMPONENTS; STRUCTURAL MODEL PARAMETERS; STRUCTURAL PARAMETER;

STATISTICS;

EID: 34247529815     PISSN: 10705511     EISSN: None     Source Type: Journal    
DOI: 10.1080/10705510709336744     Document Type: Article

References (47)

1. Akaike, H. (1974). A new look at statistical model identification. IEEE Transactions on Automatic Control, 6, 716-723.
2. Arminger, G., Stein, P., & Wittenberg, J. (1999). Mixtures of conditional mean- and covariance-structure models. Psychometrika, 64, 475-494.
3. Bauer, D. J., & Curran, P. J. (2003). Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes. Psychological Methods, 8, 338-363.
4. Bentler, P. M. (2004). EQS structural equations program manual. Encino, CA: Multivariate Software.
5. Biemacki, C., Celeux, G., & Govaert, G. (1998). Assessing a mixture model for clustering with the integrated classification likelihood (Tech. Rep. No. 3521). Rhône-Alpes, France: INRIA.
6. Biernacki, C., Celeux, G., & Govaert, G. (1999). An improvement of the NEC criterion for assessing the number of clusters in a mixture model. Pattern Recognition Letters, 20, 267-272.
7. Biernacki, C., & Govaert, G. (1997). Using the classification likelihood to choose the number of clusters. Computing Science and Statistics, 29, 451-457.
8. Bozdogan, H. (1987). Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52, 345-370.
9. Celeux, G., & Soromenho, G. (1996). An entropy criterion for assessing the number of clusters in a mixture model. Journal of Classification, 13, 195-212.
10. Colder, C. R., Mehta, P., Balanda, K., Campbell, R. T., Mayhew, K. P., Stanton, W. R., et al. (2001). Identifying trajectories of adolescent smoking: An application of latent growth mixture modeling. Health Psychology, 20, 127-135.
11. Cutler, A., & Windham, M. P. (1993). Information-based validty functionals for mixture analysis. In H. Bozdogan (Ed.), Proceedings of the first U.S.-Japan conference on the Frontiers of Statistical Modeling (pp. 149-170). Amsterdam, The Netherlands: Kluwer.
12. Dolan, C. V., & Van Der Maas, H. L. J. (1998). Fitting multivariate normal finite mixtures subject to structural equation modeling. Psychometrika, 63, 227-253.
13. Everitt, B. S. (1981). A Monte Carlo investigation of the likelihood ratio test for the number of components in a mixture of normal distributions. Multivariate Behavioral Research, 16, 171-180.
14. Fleishman, A. I. (1978). A method for simulating non-normal distributions. Psychometrika, 43, 521-532.
15. Hays, W. L. (1994). Statistics. Fort Worth, TX: Harcourt Brace.
16. Jedidi, K., Jagpal, H. S., & DeSaibo, W. S. (1997a). Finite-mixture structural equation models for response-based segmentation and unobserved heterogeneity. Marketing Science, 16(1), 39-59.
17. Jedidi, K., Jagpal, H. S., & DeSarbo, W. S. (1997b). STEMM: A general finite mixture structural equation model. Journal of Classification, 14, 23-50.
18. Jeffries, N. O. (2003). A note on "Testing the number of components in a normal mixture." Biometrika, 90, 991-994.
19. Joreskog, K. G. (1971). Simultaneous factor analysis in several populations. Psychometrika, 36, 409-426.
20. Kullback, S., & Leibler, R. A. (1951). On information and sufficiency. Annals of Mathematical Statistics. 22, 79-86.
21. Leroux, B. G. (1992). Consistent estimation of a mixing distribution. Annals of Statistics, 20, 1350-1360.
22. Li, F., Duncan, T. E., & Hops, H. (2001). Examining developmental trajectories in adolescent alcohol use using piecewise growth mixture modeling analysis. Journal of Studies on Alcohol, 62, 199-222.
23. Lo, Y., Mendell, N. R., & Rubin, D. B. (2001). Testing the number of components in a normal mixture. Biometrika, 88, 767-778.
24. Lubke, G. H., Dolan, C. V., Kelderman, H., & Mellenbergh, G. J. (2003a). On the relationship between sources of within- and between-group differences and measurement invariance in the common factor model. Intelligence, 31, 543-566.
25. Lubke, G. H., Dolan, C. V., Kelderman, H., & Mellenbergh, G. J. (2003b). Weak measurement invariance with respect to unmeasured variables: An implication of strict factorial invariance. British Journal of Mathematical and Statistical Psychology, 56, 231-248.
26. Lubke, G. H., & Muthén, B. O. (2005). Investigating population heterogeneity with factor mixture models. Psychological Methods, 10, 21-39.
27. Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, 519-530.
28. Mardia, K. V. (1974). Applications of some measures of multivariate skewness and kurtosis. Sankhya, B36, 115-128.
29. McDonald, R. P. (1999). Test theory: A unified treatment. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
30. McLachlan, G. J. (1987). On bootstrapping the likelihood ratio test statistic for the number of components in a normal mixture. Applied Statistics, 36, 318-324.
31. McLachlan, G. J., & Basford, K. E. (1988). Mixture models: Inference and applications to clustering. New York: Marcel Dekker.
32. McLachlan, G. J., & Peel, D. (2000). Finite mixture models. New York: Wiley.
33. Muthén, B. O. (1989). Latent variable modeling in heterogeneous populations. Psychometrika, 54, 557-585.
34. Muthén, B. O. (2003). Statistical and substantive checking in growth mixture modeling: Comment on Bauer and Curran (2003). Psychological Methods, 8, 369-377.
35. Muthén, B. O., & Muthén, L. K. (2000). Integrating person-centered and variable-centered analyses: Growth mixture modeling with latent trajectory classes. Alcoholism: Clinical and Experimental Research, 24, 882-891.
36. Muthén, L. K., & Muthén, B. O. (2001). Mplus user's guide (2nd ed.). Los Angeles: Muthén & Muthén.
37. Ramaswamy, V., DeSarbo, W. S., Reibstein, D. J., & Robinson, W. T. (1997). An empirical pooling approach for estimating marketing mix elasticities with PIMS data. Marketing Science, 12(1), 103-124.
38. Rissanen, J. (1978). Modeling by shortest data description. Automatica, 14, 465-471.
39. Rost, J. (1990). Rasch models in latent classes: An integration of two approaches to item analysis. Applied Psychological Measurement, 14, 271-283.
40. Rost, J. (1991). A logistic mixture distribution model for polychotomous item responses. British Journal of Mathematical and Statistical Psychology, 44, 75-92.
41. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461-464.
42. Sclove, L. S. (1987). Application of model-selection criteria to some problems in multivariate analysis. Psychometrics, 52, 333-343.
43. Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. London: Oxford University Press.
44. Sörborn, D. (1974). A general method for studying differences in factor means and factor structures between groups. British Journal of Mathematical and Statistical Psychology, 27, 229-239.
45. Titterington, D. M., Smith, A. F. M., & Makov, U. E. (1985). Statistical analysis of finite mixture distributions. New York: Wiley.
46. Vale, C. D., & Maurelli, V. A. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48, 465-471.
47. Vuong, Q. H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. Econometrics, 57, 307-333.