A semiparametric Bayesian approach for structural equation models

Biometrical Journal

Volumn 52, Issue 3, 2010, Pages 314-332

  Song, Xin Yuan ^a   Pan, Jun Hao ^b   Kwok, Timothy ^c   Vandenput, Liesbeth ^d   Ohlsson, Claes ^d   Leung, Ping Chung ^c  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b SUN YAT SEN UNIVERSITY   (China)

^c CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^d SAHLGRENSKA UNIVERSITY HOSPITAL   (Sweden)

Author keywords

Dirichlet process; Non normal data; Stick breaking prior; Structural equation models

Indexed keywords

BAYESIAN NETWORKS; STRUCTURAL ANALYSIS;

BAYESIAN APPROACHES; BREAKINGS; DIRICHLET PROCESS; LATENT VARIABLE; NON-NORMAL DATA; NON-NORMALITY; SEMIPARAMETRIC; STICK-BREAKING PRIOR; STRUCTURAL EQUATION MODELS; VARIABLE DISTRIBUTION;

NORMAL DISTRIBUTION;

ANDROGEN; SEX HORMONE;

AGED; BAYES THEOREM; BIOLOGICAL MODEL; BLOOD; BONE DENSITY; COHORT ANALYSIS; COMPLICATION; FRACTURES, BONE; HUMAN; MALE; METABOLISM; MULTICENTER STUDY (TOPIC); OSTEOPOROSIS; PATHOPHYSIOLOGY; REGRESSION ANALYSIS; RISK FACTOR; STATISTICAL MODEL;

AGED; ANDROGENS; BAYES THEOREM; BONE DENSITY; COHORT STUDIES; FRACTURES, BONE; GONADAL STEROID HORMONES; HUMANS; MALE; MODELS, BIOLOGICAL; MODELS, STATISTICAL; MULTICENTER STUDIES AS TOPIC; OSTEOPOROSIS; REGRESSION ANALYSIS; RISK FACTORS;

EID: 77954519426     PISSN: 03233847     EISSN: 15214036     Source Type: Journal    
DOI: 10.1002/bimj.200900135     Document Type: Article

References (41)

1. Belanger, C., Luu-The, V., Dupont, P. and Tchernof, A. (2002). Adipose tissue intracrinology: potential importance of local androgen/estrogen metabolism in the regulation of adiposity. Hormone and Metabolic Research 34, 737-745.
2. Bentler, P. M. (1983). Some contributions to efficient statistics in structural models: specification and estimation of moment structures. Psychometrika 48, 493-517.
3. Browne, M. W. (1984). Asymptotic distribution-free methods in the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology 37, 62-83.
4. Congdon, P. (2003). Applied Bayesian Modeling. Wiley, New York.
5. Dunson, D. B. (2005). Bayesian semiparametric isotonic regression for count data. Journal of the American Statistical Association 100, 618-627.
6. Escobar, M. D. and West, M. (1995). Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association 90, 577-588.
7. Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. The Annals of Statistics 1, 209-230.
8. Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 721-741.
9. Ghosh, J. and Dunson, D. B. (2009). Default prior distributions and efficient posterior computation in Bayesian factor analysis. Journal of Computational and Graphical Statistics 18, 306-320.
10. Hastings, W.K. (1970). Monte Carlo sampling methods using Markov chains and their application. Biometrika 57, 97-109.
11. Hu, L., Bentler, P. M. and Kano, Y. (1992). Can test statistics in covariance structure analysis be test? Psychological Bulletin 112, 357-362.
12. Ishwaran, H. and James, L. F. (2001). Gibbs sampling methods for stick-breaking priors. Journal of the American Statistical Association 96, 161-173.
13. Ishwaran, H. and Zarepour, M. (2000). Markov chain Monte Carlo in approximate Dirichlet and beta twoparameter process hierarchical models. Biometrika 87, 371-390.
14. Jöreskog, K. G. and Sörbom, D. (1996). LISREL 8: Structural Equation Modeling with the SIMPLIS Command Language. Scientific Software International, Chicago.
15. Kano, Y., Berkane, M. and Bentler, P. M. (1993). Statistical inference based on pseudo-maximum likelihood estimators in elliptical populations. Journal of the American Statistical Association 88, 135-143.
16. Kass, R. E. and Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association 90, 773-795.
17. Kleinman, K. and Ibrahim, J. (1998). A semiparametric Bayesian approach to the random effects model. Biometrics 54, 921-938.
18. Kottas, A. and Gelfand, A. E. (2001). Bayesian semiparametric median regression modeling. Journal of the American Statistical Association 96, 1458-1468.
19. Labrie, F., Luu-The, V., Lin, S. X., Simard, J., Labrie, C., El-Alfy, M., Pelletier, G. and Belanger, A. (2000). Intracrinology: role of the family of 17 beta-hydroxysteroid dehydrogenases in human physiology and disease. Journal of Molecular Endocrinology 25, 1-16.
20. Lau, E. M., Leung, P. C., Kwok, T., Woo, J., Lynn, H., Orwoll, E., Cummings, S. and Cauley, J. (2006). The determinants of bone mineral density in Chinese men-results from Mr. Os (Hong Kong), the first cohort study on osteoporosis in Asian men. Osteoporosis International 17, 297-303.
21. Lee, S. Y. (2007). Structural Equation Modeling - A Bayesian Approach. Wiley, New York.
22. Lee, S. Y., Lu, B. and Song, X. Y. (2008). Semiparametric Bayesian analysis of structural equation models with fixed covariates. Statistics in Medicine 27, 2341-2360.
23. Lee, S. Y. and Xia, Y. M. (2006). Maximum likelihood methods in treating outliers and symmetrically heavytailed distributions for nonlinear structural equation models with missing data. Psychometrika 71, 565-585.
24. Lopes, H. F., Müller, P. and Rosner, G. L. (2003). Bayesian meta-analysis for longitudinal data models using multivariate mixture priors. Biometrics 59, 66-75.
25. Maffei, L., Murata, Y., Rochira, V., Tubert, G., Aranda, C., Vazquez, M., Clyne, C. D., Davis, S., Simpson, E. R. and Carani, C. (2004). Dysmetabolic syndrome in a man with a novel mutation of the aromatase gene: effects of testosterone, alendronate, and estradiol treatment. Journal of Clinical Endocrinology & Metabolism 89, 61-70.
26. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953). Equations of state calculations by fast computing machine. Journal of Chemical Physics 21, 1087-1091.
27. Müller, P., Erkanli, A. and West, M. (1996). Bayesian curve fitting using multivariate normal mixtures. Biometrika 83, 67-79.
28. Muthén, L. K. and Muthén, B. O. (1998-2007). Mplus User's Guide (5th edn). Muthén & Muthén, Los Angeles, CA.
29. Papaspiliopoulos, O. (2008). A note on posterior sampling from Dirichlet mixture models. Technical Report.
30. Papaspiliopoulos, O. and Roberts, G. O. (2008). Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models. Biometrika 95, 169-186.
31. Roeder, C. and Wasserman, L. (1997). Practical Bayesian density estimation using mixtures of normals. Journal of the American Statictical Association 92, 894-902.
32. Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statistica Sinica 4, 639-650.
33. Shapiro, A. and Browne, M. W. (1987). Analysis of covariance structures under elliptical distributions. Journal of the American Statistical Association 82, 1092-1097.
34. Sobel, V., Schwartz, B., Zhu, Y.S., Cordero, J. J. and Imperato-McGinley, J. (2006). Bone mineral density in the complete androgen insensitivity and 5alpha-reductase-2 deficiency syndromes. Journal of Clinical Endocrinology and Metabolism 91, 3017-3023.
35. Spiegelhalter, D. J., Thomas, A., Best, N. G. and Lunn, D. (2003). WinBUGS User Manual. Version 1.4. MRC Biostatistics Unit, Cambridge, England.
36. Sturtz, S., Ligges, U. and Gelman, A. (2005). R2WinBUGS: a package for running WinBUGS from R. Journal of Statistical Software 12, 1-16.
37. Vandenput, L., Labrie, F., Mellstrom, D., Swanson, C., Knutsson, T., Peeker, R., Ljunggren, O., Orwoll, E., Eriksson, A. L., Damber, J. E. and Ohlsson, C. (2007). Serum levels of specific glucuronidated androgen metabolites predict BMD and prostate volume in elderly men. Journal of Bone and Mineral Research 22, 220-227.
38. Walker, S. G. (2007). Sampling the Dirichlet mixture model with slices. Communications in Statistics Simulation and Computation 36, 45-54.
39. West, S. G., Finch, J. F. and Curran, P. J. (1995). Structural equation models with nonnormal variables: problems and remedies. In: Hoyle, R. H. (Ed.), Structural Equation Modeling: Concepts, Issues and Applications. Sage, Newbary Park, CA, pp. 56-75.
40. Yang, M. and Dunson, D. B. (2008). Bayesian semiparametric structural equation models with latent variables. Psychometrika revised.
41. Yaturu, S., Humphrey, S., Landry, C. and Jain, S. K. (2009). Decreased bone mineral density in men with metabolic syndrome alone and with type 2 diabetes. Medical Science Monitor 15, CR5-CR9.