Covariance Decompositions for Accurate Computation in Bayesian Scale-Usage Models

References

• Albert, J., and Chib, S. (1993), “Bayesian Analysis of Binary and Polychotomous Response Data,” Journal of the American Statistical Association, 88, 669–679.
   Web of Science ®Google Scholar
• Bradlow, E.T., and Zaslavsky, A.M. (1999), “A Hierarchical Latent Variable Model for Ordinal Data From a Customer Satisfaction Survey With ‘No Answer’ Responses,” Journal of the American Statistical Association, 94, 43–52.
   Web of Science ®Google Scholar
• Chen, M.-H., and Dey, D. (2000), “Bayesian Analysis for Correlated Ordinal Data Models,” in Generalized Linear Models: A Bayesian Perspective, eds. D. K. Dey, S. K. Ghosh, and B. K. Mallick, New York: Marcel Dekker, pp. 135–162.
   Google Scholar
• Chib, S., and Greenberg, E. (1998), “Analysis of Multivariate Probit Models,” Biometrika, 85, 347–361.
   Web of Science ®Google Scholar
• Chib, S., and Jeliazkov, I. (2006), “Inference in Semiparametric Dynamic Models for Binary Longitudinal Data,” Journal of the American Statistical Association, 101, 685–700.
   Web of Science ®Google Scholar
• Cowles, M.K. (1996), “Accelerating Monte Carlo Markov Chain Convergence for Cumulative-Link Generalized Linear Models,” Statistics and Computing, 6, 101–111.
   Web of Science ®Google Scholar
• Damien, P., and Walker, S. (2001), “Sampling Truncated Normal, Beta, and Gamma Densities,” Journal of Computational and Graphical Statistics, 10, 206–215.
   Web of Science ®Google Scholar
• Genz, A. (1992), “Numerical Computation of Multivariate Normal Probabilities,” Journal of Computational and Graphical Statistics, 1, 141–149.
   Google Scholar
• Geweke, J. (1991), “Efficient Simulation From the Multivariate Normal and Student-t Distributions Subject to Linear Constraints and the Evaluation of Constraint Probabilities,” Computing Science and Statistics: Proceedings of the Twenty-Third Symposium on the Interface, 23, 571–578.
   Google Scholar
• Hajivassiliou, V., McFadden, D., and Ruud, P. (1996), “Simulation of Multivariate Normal Rectangle Probabilities and Their Derivatives: Theoretical and Computational Results,” Journal of Econometrics, 72, 85–134.
   Web of Science ®Google Scholar
• Hsu, J.C. (1992), “The Factor Analytic Approach to Simultaneous Inference in the General Linear Model,” Journal of Computational and Graphical Statistics, 1, 151–168.
   Google Scholar
• Javaras, K., and Ripley, B. (2007), “An ‘Unfolding’ Latent Variable Model for Likert Attitude Data: Drawing Inferences Adjusted for Response Style,” Journal of the American Statistical Association, 102, 454–463.
   Web of Science ®Google Scholar
• Jeliazkov, I., Graves, J., and Kutzbach, M. (2008), “Fitting and Comparison of Models for Multivariate Ordinal Outcomes,” in Bayesian Econometrics,Vol. 23 of Advances in Econometrics, eds. S. Chib, W. Griffiths, G. Koop, and D. Terrell, Bingley: Emerald Group Publishing Ltd., pp. 115–156.
   Google Scholar
• Johnson, V.E., and Albert, J.H. (1999), Ordinal Data Modeling, New York: Springer–Verlag.
   Google Scholar
• Keane, M. (1994), “A Computationally Practical Simulation Estimator for Panel Data,” Econometrica, 62, 95–116.
   Web of Science ®Google Scholar
• Kottas, A., Müller, P., and Quintana, F. (2005), “Nonparametric Bayesian Modeling for Multivariate Ordinal Data,” Journal of Computational and Graphical Statistics, 14, 610–625.
   Web of Science ®Google Scholar
• Liechty, M.W., and Lu, J. (2010), “Multivariate Normal Slice Sampling,” Journal of Computational and Graphical Statistics, 19, 281–294.
   Web of Science ®Google Scholar
• Liu, J.S., Wong, W.H., and Kong, A. (1994), “Covariance Structure of the Gibbs Sampler With Applications to Comparisons of Estimators and Augmentation Schemes,” Biometrika, 81, 27–40.
   Web of Science ®Google Scholar
• MacEachern, S.N. (1994), “Estimating Normal Means With a Conjugate Style Dirichlet Process Prior,” Communications in Statistics, B, 23, 727–741.
   Google Scholar
• MacEachern, S.N., and Müller, P. (1998), “Estimating Mixtures of Dirichlet Process Models,” Journal of Computational Statistics, 7, 223–238.
   Web of Science ®Google Scholar
• McCulloch, R., and Rossi, P. (1994), “An Exact Likelihood Analysis of the Multinomial Probit Model,” Journal of Econometrics, 64, 207–240.
   Web of Science ®Google Scholar
• McCulloch, R.E., Polson, N.G., and Rossi, P.E. (2000), “A Bayesian Analysis of the Multinomial Probit Model With Fully Identified Parameters,” Journal of Econometrics, 99, 173–193.
   Web of Science ®Google Scholar
• Nandram, B., and Chen, M.-H. (1996), “Reparameterizing the Generalized Linear Model to Accelerate Gibbs Sampler Convergence,” Journal of Statistical Computation and Simulation, 54, 129–144.
   Web of Science ®Google Scholar
• Roberts, G.O., Sahu, S.K. (1997), “Updating Schemes, Correlation Structure, Blocking and Parameterisation for the Gibbs Sampler,” Journal of the Royal Statistical Society, Series B, 59, 291–317.
   Google Scholar
• Rossi, P., and McCulloch, R. (2008), Bayesm: Bayesian Inference for Marketing/Micro-economics, R package version 2.2-2 [online]. Available at http://cran.r-project.org/web/packages/bayesm/index.html.
   Google Scholar
• Rossi, P.E., Allenby, G.M., and McCulloch, R. (2005), Bayesian Statistics and Marketing, Chichester: Wiley.
   Google Scholar
• Rossi, P.E., Gilula, Z., and Allenby, G.M. (2001), “Overcoming Scale Usage Heterogeneity: A Bayesian Hierarchical Approach,” Journal of the American Statistical Association, 96, 20–31.
   Web of Science ®Google Scholar
• Stern, S. (1992), “A Method for Smoothing Simulated Moments of Discrete Probabilities in Multinomial Probit Models,” Econometrica, 60, 943–952.
   Web of Science ®Google Scholar
• ——— (1997), “Simulation-Based Estimation,” Journal of Economic Literature, 35, 2006–2039.
   Web of Science ®Google Scholar
• van Dyk, D.A., and Meng, X.-L. (2001), “The Art of Data Augmentation,” Journal of Computational and Graphical Statistics, 10, 1–50.
   Web of Science ®Google Scholar
• van Dyk, D.A., and Park, T. (2008), “Partially Collapsed Gibbs Samplers: Theory and Methods,” Journal of the American Statistical Association, 103, 790–796.
   Web of Science ®Google Scholar
• Webb, E.L., and Forster, J.J. (2008), “Bayesian Model Determination for Multivariate Ordinal and Binary Data,” Computational Statistics and Data Analysis, 52, 2632–2649.
   Web of Science ®Google Scholar