Analysis of nonlinear structural equation models with nonignorable missing covariates and ordered categorical data

Statistica Sinica

Volumn 16, Issue 4, 2006, Pages 1117-1141

  Lee, Sik Yum ^a   Tang, Nian Sheng ^b  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b YUNNAN UNIVERSITY   (China)

Author keywords

Bayes factor; Gibbs sampler; Metropolis Hastings algorithm; Nonignorable missing data; Path sampling; Sensitivity analysis

Indexed keywords

EID: 33846536077     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (42)

1. Bagozzi, R. P., Gopinath, M. and Nyer, P. U. (1999). The role of emotions in marketing. J. Academy of Marketing Science 27, 184-206.
2. Bayarri, M. J. and Berger, J. O. (2000). P values for composite null models. J. Amer. Statist. Assoc. 95, 1127-1142.
3. Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis. Springer-Verlag, New York.
4. Bollen, K. A. (1989). A new incremental fit index for general structural equation models. Social. Methods Res. 17, 303-316.
5. Chib, S. and Greenberg, E. (1998). Analysis of multivariate probit models. Biometrika 85, 347-361.
6. DiCiccio, T. J., Kass, R. E., Raftery, A. and Wasserman, L. (1997). Computing Bayes factors by combining simulation and asymptotic approximations. J. Amer. Statist. Assoc. 92, 903-915.
7. Dunson, D. B. (2000). Bayesian latent variable models for clustered mixed outcomes. J. Roy. Statist. Soc. Ser. B 62, 355-366.
8. Follmann, D. and Wu, M. (1995). An approximate generalized linear model with random effects for informative missing data. Biometrics 51, 151-168.
9. Gelman, A. and Meng, X. L. (1998). Simulating normalizing constants: From importance sampling to bridge sampling to path sampling. Statist. Sci. 13, 163-185.
10. Gelman, A., Roberts, G. O. and Gilks, W. R. (1995). Efficient Metropolis jumping rules. In Bayesian Statistics 5 (Edited by J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith), 599-607. Oxford University Press, Oxford.
11. Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6, 721-741.
12. Golob, T. F. (2003). Structural equation modeling for travel behavior research. Transportation Research Part B 37, 1-25.
13. Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their application. Biometrika 57, 97-109.
14. Ibrahim, J. G., Chen, M. H. and Lipsitz, S. R. (1999). Monte Carlo EM for missing covariates in parametric regression models. Biometrics 55, 591-596.
15. Ibrahim, J. G., Chen, M. H. and Lipsitz, S. R. (2001). Missing responses in generalised linear mixed models when the missing data mechanism is nonignorbale. Biometrika 88, 551-564.
16. Jöreskog, K. G. and Sörbom, D. (1996). LISREL 8: Structural Equation Modelling with the SIMPLIS Command Language. Scientific Software International, Hove and London.
17. Kass, R. E. and Raftery, A. E. (1995). Bayes factors. J. Amer. Statist. Assoc. 90, 773-795.
18. Laird, N. M. and Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics 38, 963-974.
19. Lee, S. Y. and Shi, J. Q. (2000). Bayesian analysis of structural equation model with fixed covariates. Struct. Equ. Model. 7, 411-430.
20. Lee, S. Y. and Song, X. Y. (2003a). Bayesian analysis of structural equation models with dichotomous variables. Statist. Medicine 22, 3073-3088.
21. Lee, S. Y. and Song, X. Y. (2003b). Model comparison of nonlinear structural equation models with fixed covariates. Psychometrika 68, 27-47.
22. Lee, S. Y. and Song, X. Y. (2004a). Maximum likelihood estimation and model comparison for mixtures of structural equation models with ignorable missing data. J. Classification 20, 221-225.
23. Lee, S. Y. and Song, X. Y. (2004b). Bayesian model comparison of nonlinear structural equation models with missing continuous and ordinal categorical data. British J. Math. Statist. Psych. 57, 131-150.
24. Lee, S. Y. and Song, X. Y. (2004c). Evaluation of Bayesian and maximum likelihood approaches in analyzing structural equation models with small sample sizes. Multivariate Behavioral Research 39, 653-686.
25. Lee, S. Y. and Song, X. Y. (2004d). Maximum likelihood analysis of a general latent variable model with hierarchically mixed data. Biometrics 60, 624-636.
26. Lee, S. Y., Song, X. Y., Skevington, S. and Hao, Y. T. (2005). Application of structural equation models to quality of life. Structural Equation Modeling- A Multidisciplinary Journal 12, 435-453.
27. Lee, S. Y. and Zhu, H. T. (2000). Statistical analysis of nonlinear structural equation models with continuous and polytomous data. British J. Math. Statist. Psych. 53, 209-232.
28. Lindley, D. V. and Smith, A. F. M. (1972). Bayes estimates for the linear model (with discussion). J. Roy. Statist. Soc. Ser. B 34, 1-42.
29. Little, R. J. A. and Rubin, D. B. (1987). Statistical Analysis with Missing Data. Wiley, New York.
30. Lipsitz, S. R., Ibrahim, J. G. and Zhao, L. P. (1999). A weighted estimating equation for missing covariate data with properties similar to maximum likelihood. J. Amer. Statist. Assoc. 94, 1147-1160.
31. Lipsitz, S. R. and Ibrahim, J. G. (1996). A conditional model for incomplete covariates in parametric regression models. Biometrika 83, 916-922.
32. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953). Equations of state calculations by fast computing machine. J. Chemical Physics 21, 1087-1091.
33. Meng, X. L. and Wong, Y. X. (1996). Simulating ratios of normalizing constants via a simple identity: a theoretical exploration. Statist. Sinica 6, 831-860.
34. Morisky, D. E., Tiglao, T. V., Sneed, C. D., Tempongko, S. B., Baltazar, J. C., Detels, R. and Stein, J. A. (1998). The effects of establishment practices, knowledge and attitudes on condom use among Filipina sex workers. AIDS Care 10, 213-320.
35. Parzen, M., Lipsitz, S. R., Ibrahim, J. G. and Lipshultz, S. (2002). A weighted estimating equation for linear regression with missing covariate data. Statist. Medicine 21, 2421-2436.
36. Rathouz, P. J., Satten, G. A. and Carroll, R. J. (2002). Semiparametric inference in matched case-control studies with missing covariate data. Biometrika 89, 905-916.
37. Sammel, M. D. and Ryan, L. M. (1996). Latent variable models with fixed effects. Biometrics 52, 650-663.
38. Scheines, R., Hoijtink, H. and Boomsma, A. (1999). Bayesian estimation and testing of structural equation models. Psychometrika 64, 37-52.
39. Shi, J. Q. and Lee, S. Y. (2000). Latent variable models with mixed continuous and polytomous data. J. Roy. Statist. Soc. Ser. B 62, 77-87.
40. Song, X. Y. and Lee, S. Y. (2002). Analysis of structural equation model with ignorable missing continuous and polytomous data. Psychometrika 67, 261-288.
41. Stubbendick, A. L. and Ibrahim, J. G. (2003). Maximum likelihood methods for nonignorable missing response and covariates in random effects models. Biometrics 59, 1140-1150.
42. Williams, L. J., Edwards, J. R. and Vandenberg, R. J. (2003). Recent advances in causal modeling methods for organizational and management research. J. Management 29, 903-936.