A Robust Bayesian approach for structural equation models with missing data

Psychometrika

Volumn 73, Issue 3, 2008, Pages 343-364

  Lee, Sik Yum ^a   Xia, Ye Mao ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Model comparison; Nonlinear structural equation models with covariates; Normal independent distributions; Robust Bayesian methods

Indexed keywords

EID: 52949118123     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11336-008-9060-5     Document Type: Article

References (48)

1. R.J. Anderson J. Critchley J.C.N. Chan C.S. Dockram Z.S. Lee G.N. Thomas B.T. Tomlinson 2001 Factor analysis of the metabolic syndrome: Obesity vs insulin resistance as central abnormality International Journal of Obesity 25 1782 1788
2. D.F. Andrews C.L. Mallows 1974 Scale mixtures of normal distribution Journal of the Royal Statistical Society, Series B 36 99 102
3. A. Ansari K. Jedidi 2000 Bayesian factor analysis for multilevel binary observations Psychometrika 64 475 496
4. Bentler, P.M., & Wu, E.J.C. (2002). EQS 6 for windows user's guide. Encino: Multivariate Software.
5. M.W. Browne 1987 Robustness of statistical influence in factor analysis and related models Biometrika 74 375 384
6. M.W. Browne A. Shapiro 1988 Robustness of normal theory methods in the analysis of linear latent variable models British Journal of Mathematical and Statistical Psychology 41 193 208
7. M.H. Chen J.G. Ibrahim D. Sinha 2004 A new joint model for longitudinal and survival data with a cure fraction Journal of Multivariate Analysis 91 18 34
8. A.P. Dempster N.M. Laird D.B. Rubin 1977 Maximum likelihood from incomplete data via the EM algorithm (with discussion) Journal of the Royal Statistical Society, Series B 39 1 38
9. D.B. Dunson 2000 Bayesian latent variable models for clustered mixed outcomes Journal of the Royal Statistical Society, Series B 62 355 366
10. D.B. Dunson S.D. Perreault 2001 Factor analytic models of clustered multivariate data with informative censoring Biometrics 57 302 308
11. S. Geisser W. Eddy 1979 A predictive approach to model selection Journal of the American Statistical Association 74 153 160
12. A.E. Gelfand A.F.M. Smith T.M. Lee 1992 Bayesian analysis of constrained parameters and truncated data problem using Gibbs sampling Journal of the American Statistical Association 87 523 532
13. A. Gelman X.L. Meng 1998 Simulating normalizing constants: From importance sampling to bridge sampling to path sampling Statistical Science 13 163 185
14. S. Geman D. Geman 1984 Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images IEEE Transactions on Pattern Analysis and Machine Intelligence 6 721 741
15. W.K. Hastings 1970 Monter Carlo sampling methods using Markov chains and their applications Biometrika 57 97 109
16. J.P. Hobert G. Casella 1996 The effect of improper priors on Gibbs sampling in hierarchical linear mixed models Journal of the American Statistical Association 91 1461 1473
17. Ibrahim, J.G., Chen, M.H., & Sinha, D. (2001). Bayesian survival analysis. New York: Springer.
18. Jöreskog, K.G., & Sörbom, D. (1996). LISREL 8: Structural equation modelling with the SIMPLIS command language. Hove: Scientific Software International.
19. Y. Kano 1994 Consistency property of elliptical probability density function Journal of Multivariate Analysis 51 139 147
20. Y. Kano M. Berkane P.M. Bentler 1993 Statistical inference based on pseudomaximum likelihood estimators in elliptical populations Journal of the American Statistical Association 88 135 143
21. R.E. Kass A.E. Raftery 1995 Bayes factor Journal of the American Statistical Association 90 773 795
22. K.L. Lange J.S. Sinsheimer 1993 Normal/independent distributions and their applications in robust regression Journal of Computational and Graphical Statistics 2 175 198
23. K.L. Lange R.J.A. Little J.M.G. Taylor 1989 Robust statistical modelling using the t-distribution Journal of the American Statistical Association 84 881 896
24. S.Y. Lee X.Y. Song 2003 Bayesian analysis of structural equation models with dichotomous variables Statistics in Medicine 22 3073 3088
25. S.Y. Lee X.Y. Song 2003 Model comparison of nonlinear structural equation models with fixed covariates Psychometrika 68 27 47
26. S.Y. Lee X.Y. Song 2004 Bayesian model comparison of nonlinear structural equation models with missing continuous and ordinal categorical data British Journal of Mathematical and Statistical Psychology 57 131 150
27. S.Y. Lee X.Y. Song 2004 Evaluation of the Bayesian and maximum likelihood approaches in analyzing structural equation models with small sample sizes Multivariate Behavioral Research 39 653 686
28. S.Y. Lee X.Y. Song 2004 Maximum likelihood analysis of a general latent variable with hierarchically mixed data Biometrics 60 624 636
29. S.Y. Lee X.Y. Song 2007 A unified maximum likelihood approach for analyzing structural equation models with missing non-standard data Sociological Methods & Research 35 352 381
30. S.Y. Lee Y.M. Xia 2006 Maximum likelihood methods in treating outliers and symmetrically heavy-tailed distributions for nonlinear structural equation models with missing data. Psychometrika 71 565 585
31. R.J.A. Little 1988 Robust estimation of mean and covariance matrix from data with missing values Applied Statistics 37 23 39
32. Little, R.J.A., & Rubin, D.B. (1987). Statistical analysis with missing data. New York: Wiley.
33. C.H. Liu 1995 Missing data imputation using the multivariate t-distribution Journal of Multivariate Analysis 46 198 206
34. C.H. Liu 1996 Bayesian robust multivariate linear regression with incomplete data Journal of the American Statistical Association 91 1219 1227
35. C.H. Liu D.B. Rubin 1994 The ECME algorithm: A simple extension of EM and ECM with Faster Monotone convergence Biometrika 81 633 648
36. N. Metropolis A.W. Rosenbluth M.N. Rosenbluth A.H. Teller E. Teller 1953 Equations of state calculations by fast computing machines Journal of Chemical Physics 21 1087 1092
37. L.I. Pettit K.D.S. Young 1990 Measuring the effect of observations on the Bayes factor Biometrika 77 455 466
38. A. Philippe 1997 Simulation of right and left truncated gamma distributions by mixtures Statistics and Computing 7 173 181
39. T. Raykov 2007 Longitudinal analysis with regression among random effects: A latent variable modeling approach Structural Equation Modeling: A Multidisciplinary Journal 14 146 169
40. C. Ritter M. Tanner 1992 Facilitating the Gibbs sampler: The Gibbs stopper and the Griddy-Gibbs sampler Journal of the American Statistical Association 87 861 868
41. R. Scheines H. Hoijtink A. Boomsma 1999 Bayesian estimation and testing of structural equation models Psychometrika 64 37 52
42. A. Shapiro M.W. Browne 1987 Analysis of covariance structural under elliptical distribution Journal of the American Statistical Association 82 1092 1097
43. X.Y. Song S.Y. Lee 2004 Bayesian analysis of two-level nonlinear structural equation models with continuous and polytomous data British Journal of Mathematical and Statistical Psychology 57 29 52
44. X.Y. Song S.Y. Lee 2006 Model comparison of generalized linear mixed models Statistics in Medicine 25 1685 1698
45. X.Y. Song S.Y. Lee 2007 Bayesian analysis of latent variable models with nonignorable missing outcomes from exponential family Statistics in Medicine 26 681 693
46. X.Y. Song S.Y. Lee M.C. Ng W.Y. So J.C.N. Chan 2007 Bayesian analysis of structural equation models with multinomial variables and an application to type 2 diabetic nephropathy Statistics in Medicine 26 2348 2369
47. J.J. Wang Q. Qiao M. Mietting J. Lappalainen G. Hu J. Tuomilehto 2004 The metabolic syndrome defined by factor analysis and incident type 2 diabetes in Chinese population with high postprandial glucose Diabetes Care 27 2429 2437
48. M. Willoughby N. Vandergift C. Blair D.A. Granger 2007 A structural equation modeling approach for the analysis of cortisol data collected using pre-post-post designs Structural Equation Modeling: A Multidisciplinary Journal 14 125 145