A multiple imputation method for incomplete correlated ordinal data using multivariate probit models

References

• Albert, J. H., Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association 88:669–679.
   Google Scholar
• Ashford, J., Snowden, R. (1970). Multivariate probit analysis. Biometrics 26:535–546.
   Google Scholar
• Bernaards, C. A., Belin, T. R., and Schafer, J. L. (2005). Robustness of a multivariate normal approximation for imputation of incomplete binary data. Statistics in Medicine 26:1368–1382.
   Google Scholar
• Boscardin, W. J., Zhang, X., Belin, T. R. (2008). Modeling a mixture of ordinal and continuous repeated measures. Journal of Statistical Computation and Simulation 78 (10):873–886.
   Google Scholar
• Buuren, S. V. (2007). Multiple imputation of discrete and continuous data by fully conditional specification. Statistical Methods in Medical Research 16:219–242.
   Google Scholar
• Buuren, S. V., Brand, J. P. L., Groothuis-Oudshoorn, C. G. M., Rubin, D. B. (2006). Fully conditional specification in multivariate imputation. Journal of Statistical Computation and Simulation 76:1049–1064.
   Google Scholar
• Chen, M-H., Dey, D. K. (2000). A unified Bayesian approach for analyzing correlated ordinal response data. Brazilian Journal of Probability and Statistics 14:87–111.
   Google Scholar
• Chib, S., Greenberg, E. (1998). Analysis of Multivariate Probit Models. Biometrika 85: 347–361.
   Google Scholar
• Cropsey, K. L., Clark, C. B., Zhang, X., Hendricks, P. S., Jardin, B. F., Lahti, A. C. (2015). Race and medication compliance moderate smoking cessation outcomes in criminal justice smokers: results of a randomized clinical trial. American Journal of Preventive Medicine 49(3): 335–344.
   Google Scholar
• Demirtas, H. (2006). A method for multivariate ordinal data generation given marginal distributions and correlations. Journal of Statistical Computation and Simulation 76 (11):1017–1025.
   Google Scholar
• Dempster, A. P., Laird, N. M., Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39:1–38.
   Google Scholar
• Diggle, P., Kenward, M. G. (1994). Informative drop-out in longitudinal data analysis. Applied Statistics 43:49–93.
   Google Scholar
• Dunson, D. B. (2000). Bayesian latent variable models for clustered mixed outcomes. Journal of the Royal Statistical Society, Series B 62:355–366.
   Google Scholar
• Fagerstrom, K. O., Schneider, N. G. (1989). Measuring nicotine dependance: A review of the Fagerstrom tolerance questionnaire. Journal of Behavioral Medicine 12:159–182.
   Google Scholar
• Fitzmaurice, G. M., Laird, N. M. (2000). Generalized linear mixture models for handling non-ignorable dropouts in longitudinal studies. Biostatistics 1:141–156.
   Google Scholar
• Gelfand, A. E., Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85:398–409.
   Google Scholar
• Gelman, A., Carlin, J. B., Stern, H. S., Rubin, D. B. (2000). Bayesian Data Analysis. 2nd ed. Boca Raton, Florida: Chapman & Hall/CRC.
   Google Scholar
• Haukoos, J., Newgard, C. (2007). Advanced statistics: missing data in clinical research-part 1: an introduction and conceptual framework. Academic Emergency Medicine 14:662–668.
   Google Scholar
• Heatherton, T. F., Kozlowski, L. T., Frecker, R. C., Fagerstrom, K. O. (1991). The Fagerstrom test for nicotine dependence: a revision of the Fagerstrom tolerance questionnaire. British Journal of Addiction 86:1119–1127.
   Google Scholar
• He, R., Belin, T. (2012). Multiple imputation for high-dimensional mixed incomplete data using a factor model. Joint Statistical Meeting Proceedings - Biometrics Section on Statistical Learning and Data 20–33.
   Google Scholar
• Hedeker, D., Gibbons, R. D. (2006). Longitudinal Data Analysis. Hoboken, New Jersey:John Wiley and Sons, Inc.
   Google Scholar
• Horton, N. J., Lipsitz, S. R., Parzen, M. (2003). A potential for bias when rounding in multiple imputation. The American Statistician 57:229–232.
   Google Scholar
• Kenward, M. G. (1998). Selection models for repeated measurements with non-random dropout: an illustration of sensitivity. Statistics in Medicine 17:2723–2732.
   Google Scholar
• Kenward, M. G., Molenberghs, G. (1998). Likelihood based frequentist inference when data are missing at random. Statistical Science 13:236–247.
   Google Scholar
• Lawrence, E., Bingham, D., Liu, C., Nair, V. N. (2008). Bayesian inference for multivariate ordinal data using parameter expansion. Technometrics 50:182–191.
   Google Scholar
• Li, Y., Schafer, D. W. (2008). Likelihood analysis of the multivariate ordinal probit regression model for repeated ordinal responses. Computational Statistics and Data Analysis 52:3474–3492.
   Google Scholar
• Little, R. J. A., Rubin, D. B. (2002). Statistical Analysis with Missing Data. 2nd ed. Wiley: New York.
   Google Scholar
• Liu, C. (2001). Bayesian analysis of the multivariate probit model: discussion of ‘The art of data augmentation’ by Van Dyk and Meng. Journal of Computational and Graphical Statistics 10:75–81.
   Google Scholar
• MacEachern, S. N. (2007). Comment on article by Jain and Neal. Bayesian Analysis 2:483–494.
   Google Scholar
• Markov Chain Monte Carlo in Practice. (1996). Edited by Gilks, W. R., Richardson, S., and Spiegelhalter, D. J. Boca Raton, Florida: Chapman & Hall.
   Google Scholar
• McCullagh, P. (1980). Regression models for ordinal data. Journal of Royal Statistical Society B 42:109–142.
   Google Scholar
• Nandram, B., Chen, M.-H. (1994). Accelerating Gibbs sampler convergence in the generalized linear models via a reparameterization. Journal of Statistical Computation and Simulation 81:27–40.
   Google Scholar
• Pearson, K. (1900). Mathematical Contributions to the Theory of Evolution. VII. On the correlation of characters not quantitatively measureable. Philosophical Transactions of the Royal Society of London. Series A 195:1–47.
   Google Scholar
• Raghunathan, T. E., Lepkowski, J. M., Hoewyk, J. V., Solenberger, P. (2001). A multivariate technique for multiply imputing missing values using a sequence of regression models. Survey Methodology 27:85–95.
   Google Scholar
• Robert, C. P., Casella, G. (1999). Monte Carlo Statistical Methods. New York: Springer.
   Google Scholar
• Rubin, D. B. (1976). Inference and missing data. Biometrika 63:581–592.
   Google Scholar
• Rubin, D. B. (1978). Multiple imputation in sample surveys – a phenomenological Bayesian approach to nonresponse. Proceedings of the Survey Research Methods Section In Proceedings of the Survey Q9 Research Methods Section 20–28.
   Google Scholar
• Rubin, D. B. (1987). Multiple Imputation for Nonresponse in Surveys. Wiley: New York.
   Google Scholar
• Schafer, J. L. (1997). Analysis of Incomplete Multivariate Data. Chapman & Hall: London.
   Google Scholar
• Siddique, J., Harel, O., Crespi, C. M., Hedeker, D. (2014). Binary variable multiple-model multiple imputation to address missing data mechanism uncertainty: application to a smoking cessation trial. Statistics in Medicine 33(17):3013–3028.
   Google Scholar
• Smith, S. F. M., Roberts, G. O. (1993). Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. Journal of Royal Statistical Society B 55:3–23.
   Google Scholar
• Tanner, M. A., Wong, W. H. (1987). The calculation of posterior distributions by data augmentation (with discussion). Journal of the American Statistical Association 82:528–550.
   Google Scholar
• Tierney, L. (1994). Markov chains for exploring posterior distributions. The Annals of Statistics 4:1701–1962.
   Google Scholar
• Touloumis, A., Agresti, A., Kateri, M. (2013). GEE for multinomial responses using a local odds ratios parameters. Biometrics 69:633–640.
   Google Scholar
• White, I. R., Royston, P., Wood, A. M. (2011). Multiple imputation using chained equations: Issues and guidance for practice. Statistics in Medicine 30:377–399.
   Google Scholar
• Yang, X., Li, J., Shoptaw, S. (2008). Imputation-based strategies for clinical trial longitudinal data with nonignorable missing values. Statistics in Medicine 27:2826–2849.
   Google Scholar
• Yucel, R. M., Yulei, He, and Zaslavsky, A. M. (2008). Using calibration to improve rounding in multiple imputation. The American Statistician 62(2):125–129.
   Google Scholar
• Zhang, X., Boscardin, W. J., Belin, T. R. (2006). Sampling correlation matrices in Bayesian models with correlated latent variables. Journal of Computational and Graphical Statistics 15:880–896.
   Google Scholar