Bayesian semiparametric analysis of structural equation models with mixed continuous and unordered categorical variables

Statistics in Medicine

Volumn 28, Issue 17, 2009, Pages 2253-2276

  Song, Xin Yuan ^a   Xia, Ye Mao ^a   Lee, Sik Yum ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Blocked Gibbs sampler; Model selection; Modified truncated Dirichlet process; Phenotype and genotype latent variables; Structural equation models

Indexed keywords

ARTICLE; BAYESIAN LEARNING; BAYESIAN SEMIPARAMETRIC ANALYSIS; DIABETIC NEPHROPATHY; GENOTYPE; GLYCEMIC CONTROL; HUMAN; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MEDICAL RESEARCH; METHODOLOGY; NON INSULIN DEPENDENT DIABETES MELLITUS; PHENOTYPE; PROBABILITY; SAMPLE SIZE; SIMULATION; STRUCTURAL EQUATION MODELING;

BAYES THEOREM; BIOMETRY; DIABETIC NEPHROPATHIES; GENOTYPE; HUMANS; LIKELIHOOD FUNCTIONS; MODELS, STATISTICAL; PHENOTYPE;

EID: 69949095876     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.3612     Document Type: Article

References (38)

1. Bollen KA. Structural Equations with Latent Variables. Wiley: New York, 1989.
2. Jöreskog KG, Sörbom D. LISREL 8: Structural Equation Modelling with the SIMPLIS Command Language. Scientific Software International: Hove and London, 1996.
3. Bentler PM, Stein JA. Structural equation models in medical research. Statistical Methods in Medical Research 1992; 1:159-181.
4. Seaqist ER, Goetz FC, Rich S, Barbosa J. Familial clustering of diabetic kidney disease: evidence for genetic susceptibility to diabetic nephropathy. New England Journal of Medicine 1989; 320:1161-1165.
5. Ravid M, Brosh D, Ravid-Safran D, Levy Z, Rachmani R. Main risk factors for nephropathy in type 2 diabetes mellitus are plasma cholesterol levels, mean blood pressure and hyperglycaemia. Archives of Internal Medicine 1998; 158:998-1004.
6. Fioretto P, Steffes MW, Sutherland DE, Goetz FC, Mauer M. Reversal of lesions of diabetics nephropathy after pancreas transplantation. New England Journal of Medicine 1998; 339:69-75.
7. Parving HH, Tarnow L, Rossing P. Genetics of diabetic nephropathy. Journal of American Society of Nephrology 1996; 7:2509-2517.
8. Carlsson M, Orho-Melander M, Hedenbro J, Groop LC. Common variants in the beta2-(Gln27Glu) and beta3-(Trp64Arg)-adrenoceptor genes are associated with elevated serum NEFA concentrations and type II diabetics. Diabetologia 2001; 44:629-636.
9. Song XY, Lee SY, Ng MCY, So WY, Chan JCN. A Bayesian latent variable model for analyzing phenotype and genotype variables with an application to type 2 diabetic nephropathy. Statistics in Medicine 2006; 26:2348-2369.
10. Hu L, Bentler PM, Kano Y. Can test statistics in covariance structure analysis be trusted? Psychological Bulletin 1992; 112:351-362.
11. West SG, Finch JF, Curran PJ. Structural equation models with nonnormal variables: problems and remedies. In Structural Equation Modeling: Concepts, Issues and Applications, Hoyle RH (ed.). Sage Publications: Thousand Oaks, 1995; 56-75.
12. Shapiro A, Browne MW. Analysis of covariance structural under elliptical distribution. Journal of the American Statistical Association 1987; 82:1092-1097.
13. Kano Y, Berkane M, Bentler PM. Statistical inference based on pseudo-maximum likelihood estimators in elliptical populations. Journal of the American Statistical Association 1993; 88:135-143.
14. Ferguson TS. A Bayesian analysis of some nonparametric problems. The Annals of Statistics 1973; 1:209-230.
15. Kleinman KP, Ibrahim JG. A semiparametric Bayesian approach to the random effects model. Biometrics 1998; 54:921-938.
16. Müller P, Rosner G. A Bayesian population model with hierarchical mixture priors applied to blood count data. Journal of the American Statistical Association 1997; 92:1279-1292.
17. Dunson DB, Yang M, Baird D. Semiparametric Bayes hierarchical models with mean and variance constraints. Discussion Paper, Department of Statistics, Duke University, 2007.
18. Lee SY, Lu B, Song XY. Semiparametric Bayesian analysis of structural equation models with fixed covariates. Statistics in Medicine 2008; 27:2341-2360.
19. Kass RE, Raftery AE. Bayes factors. Journal of the American Statistical Association 1995; 90:773-795.
20. Lee SY. Structural Equation Modeling: A Bayesian Approach. Wiley: New Jersey, 2007.
21. Gelman A, Meng XL. Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Statistical Science 1998; 13:163-185.
22. Wang Y, Ng MCY, So WY, Tong PCY, Ma RCW, Chow CC, Cockram CS, Chan JCN. Prognostic effect of insertion/deletion polymorphism of ACE gene on renal and cardiovascular clinal outcomes in Chinese patients with type 2 diabetes. Diabetes Care 2005; 28:348-354.
23. Imai K, van Dyk DA. A Bayesian analysis of the multinomial probit model using marginal data augmentation. Journal of Econometrics 2005; 124:311-334.
24. Ishwaran H, James LF. Gibbs sampling methods for stick-breaking priors. Journal of the American Statistical Association 2001; 96:161-173.
25. Sethuraman J. A constructive definition of the Dirichlet priors. Statistica Sinica 1994; 4:639-650.
26. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E. Equations of state calculations by fast computing machines. Journal of Chemical Physics 1953; 21:1087-1092.
27. Hastings WK. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 1970; 57:97-100.
28. Ishwaran H, James LF, Sun JY. Bayesian model selection in finite mixtures by marginal density decompositions. Journal of the American Statistical Association 2001; 96:1316-1332.
29. Basu S, Chib S. Marginal likelihood and Bayes factors for Dirichlet process mixture models. Journal of the American Statistical Association 2003; 98:224-235.
30. Ibrahim JG, Land PW. A predictive approach to the analysis of designed experiments. Journal of the American Statistical Association 1994; 89:309-319.
31. Laud PW, Ibrahim JG. Predictive model selection. Journal of the Royal Statistical Society, Series B 1995; 57:247-262.
32. Chen MH, Dey DK, Ibrahim JG. Bayesian criterion based model assessment for categorical data. Biometrika 2004; 91:45-63.
33. Ibrahim JG, Chen MH, Sinha D. Criterion based methods for Bayesian model assessment. Statistica Sinica 2001; 11:419-443.
34. Lee SY, Song XY. Maximum likelihood analysis of a general latent variable model with hierarchy mixed data. Biometrics 2004; 60:624-636.
35. Rabe-Hesketh S, Skrondal A, Pickles A. A generalized multilevel structural equation modeling. Psychometrika 2004; 69:167-190.
36. Song XY, Lee SY, Hser YI. A two-level structural equation model approach for analyzing multivariate longitudinal responses. Statistics in Medicine 2008; 27:3017-3041.
37. Doss H. Bayesian nonparametric estimation of the median; part I: computation of the estimates. The Annals of Statistics 1985; 13:1432-1444.
38. Kottas A, Gelfand AE. Bayesian semiparametric median regress modeling. Journal of the American Statistical Association 2001; 96:1458-1468.