Confidence intervals for a semiparametric approach to modeling nonlinear relations among latent variables

Structural Equation Modeling

Volumn 18, Issue 4, 2011, Pages 537-553

  Pek, Jolynn ^a   Losardo, Diane ^a   Bauer, Daniel J ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

Confidence interval; Delta method; Nonlinear; Parametric bootstrap; Structural equation mixture model

Indexed keywords

EID: 84855787409     PISSN: 10705511     EISSN: None     Source Type: Journal    
DOI: 10.1080/10705511.2011.607072     Document Type: Article

References (29)

1. Arminger, G., & Stein, P. (1997). Finite mixtures of covariance structure models with regressors. SociologicalMethods and Research, 26, 148-182.
2. Arminger, G., Stein, P., & Wittenberg, J. (1999). Mixtures of conditional mean and covariance structure models. Psychometrika, 64, 475-494.
3. Bauer, D. J. (2005). A semiparametric approach to modeling nonlinear relations among latent variables. Structural Equation Modeling, 12, 513-535.
4. Bauer, D. J., Baldasaro, R. E., & Gottfredson, N. C. (in press). Diagnostic procedures for detecting nonlinear relationships between latent variables. Structural Equation Modeling.
5. Bollen, K. A. (1989). Structural equation models with latent variables. New York, NY: Wiley.
6. Dolan, C. V., & van der Maas, H. L. J. (1998). Fitting multivariate normal finite mixtures subject to structural equation modeling. Psychometrika, 63, 227-253.
7. Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. New York, NY: Chapman & Hall.
8. Jaccard, J., & Wan, C. K. (1995). Measurement error in the analysis of interaction effects between continuous predictors using multiple regression: Multiple indicator and structural equation approaches. Psychological Bulletin, 117, 348-357.
9. Jedidi, K., Jagpal, H. S., & DeSarbo, W. S. (1997a). Finite-mixture structural equation models for response-based segmentation and unobserved heterogeneity. Marketing Science, 16, 39-59.
10. Jedidi, K., Jagpal, H. S., & DeSarbo, W. S. (1997b). STEMM: A general finite mixture structural equation model. Journal of Classification, 14, 23-50.
11. Jöreskog, K. G., & Yang, F. (1996). Nonlinear structural equation models: The Kenny-Judd model with interaction effects. In G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced structural equation modeling: Issues and techniques (pp. 57-88). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
12. Kelava, A., Moosbrugger, H., Dimitruk, P., & Schermelleh-Engel, K. (2008). Multicollinearity and missing constraints: A comparison of three approaches for the analysis of latent nonlinear effects. Methodology, 4, 51-66.
13. Kenny, D. A., & Judd, C. M. (1984). Estimating the non-linear and interactive effects of latent variables. Psychological Bulletin, 96, 201-210.
14. Klein, A. G., & Moosbrugger, H. (2000). Maximum likelihood estimation of latent interaction effects with the LMS method. Psychometrika, 65, 457-474.
15. Klein, A. G., & Muthén, B. O. (2007). Quasi maximum likelihood estimation of structural equation models with multiple interaction and quadratic effects. Multivariate Behavioral Research, 42, 647-673.
16. Lee, S. Y., & Zhu, H. T. (2000). Statistical analysis of nonlinear structural equation models with continuous and polytomous data. British Journal of Mathematical and Statistical Psychology, 53, 209-232.
17. Marsh, H. W., Wen, Z., & Hau, K. T. (2004). Structural equation models of latent interactions: Evaluation of alternative estimation strategies and indicator construction. Psychological Methods, 9, 275-300.
18. Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance. Psychometrika, 58, 525-543.
19. Mooijaart, A., & Bentler, R. (1986). Random polynomial factor analysis. In E. Diday, M. Jambu, L. Lebart, J. Pages, & R. Tomassone (Eds.), Data analysis and informatics, IV: Proceedings of the fourth international symposium on data analysis and informatics (pp. 241-250). North Holland, Amsterdam: Elsevier Science.
20. Muthén, B. O. (2001). Second-generation structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class/latent growth modeling. In A. Sayer & L. Collins (Eds.), New methods for the analysis of change (pp. 291-322). Washington, DC: American Psychological Association.
21. Muthén, B. O., & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55, 463-469.
22. Muthén, L. K., & Muthén, B. O. (2007). Mplus user's guide (5th ed.). Los Angeles, CA: Author.
23. Ping, R. A. (1996). Latent variable interaction and quadratic effect estimation: A two-step technique using structural equation analysis. Psychological Bulletin, 119, 166-175.
24. SAS Institute Inc. (2008). SAS® 9.2 Enhanced logging facilities. Cary, NC: Author.
25. Schumacker, R. E., & Marcoulides, G. A. (Eds.). (1998). Interaction and nonlinear effects in structural equation models. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
26. Steiger, J. H., Shapiro, A., & Browne, M. W. (1985). On the multivariate asymptotic distribution of sequential chisquare statistics. Psychometrika, 50, 253-264.
27. Stroud, T. W. (1972). Fixed alternatives and Wald's formulation of the noncentral asymptotic behavior of the likelihood ratio statistic. Annals of Mathematical Statistics, 43, 447-454.
28. Titterington, D. M., Smith, A. F. M., & Makov, U. E. (1985). Statistical analysis of finite mixture distributions. Chichester, UK: Wiley.
29. Wald, A. (1943). Tests of statistical hypotheses concerning several parameters when the number of observations is large. Transactions of the American Mathematical Society, 54, 426-482.