Summary
Binary responses are correlated when the sampling units are clustered or when repeated binary responses are taken on the same experiment unit. In this paper we present a Bayesian analysis of logistic regression models for correlated binary data with random effects. We assume that the random effects, namely αi, i = 1, …, n are draw from a mixture of normal distributions. This assumption gives a great flexibility of fit by correlated binary data. Considering Gibbs sampling with Metropolis-Hastings algorithms, we obtain Monte Carlo estimates for the posterior quantities of interest
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Albert, L; Jais, J.P. (1998). Gibbs Sampler For The Logistic Model in the Analysis of Longitudinal Binary Data. Statistics in Medicine, 17, 2905–2921.
Barnhart, H.X.; Williamson, J.M. (1998). Goodness-of-fit Tests for GEE Modeling with Binary Data. Biometrics, 54, 720–729.
Chib, S.; Greenberg, E. (1998). Analysis of Multivariate Probit Models. Biometrika, 85, 347–361.
Dey, D.K.; Chen, M.H (1996). Bayesian Analysis of Correlated Binary Data Models. Technical Report, Dep. of Statistics, University of Connecticut, U.S.A.
Gelfand, A.E. (1995). Model Determination Using Sampling-Based Methods. In Markov Chain Monte Carlo in Practice (eds W.R. Gilks, S. Richardson and D.J. Spiegelhalter. London: Chapaman & Hall, 145–161.
Gelfand, A.E.; Smith, A.F.M. (1990). Sampling-Based Approaches to Calculating Marginal Densities. Journal of the American Statistical Association, 85, 398–409.
Gelman, A.; Rubin, B.D. (1992). Inference from Iterative Simulation Using Multiple Sequences. Statistical Science, 4, 457–511.
Gilks, W.R.; Best, N.G.; Tan, K.K.C. (1995). Adaptive Rejection Metropolis Sampling Within Gibbs Sampling. Applied Statistics, 44, 455–472.
Horton, N.J.; Bebchuk, J.D.; Jones, C.L.; Lipsitz, S.R.; Catalano, P.J.; Zahner, G.E.P.; Fitzmaurice, G.M. (1999). Gooddness-of-fit for GEE: an Example with Mental Helth Service Utilization. Statistics im Medicine, 18, 213–222.
Huggins, R.M. (1991). Some Practical Aspects of a Conditional Likelihood Approach to Capture Experiments. Biometrics, 47, 725–732.
Kass, R.E.; Wasserman, L. (1995). A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion. Journal of the American Statistical Association, 90, 928–934.
Maddala, G.S. (1983). Limited-dependent and Variables in Econometrics, Econometric Society monographs in quantitative economics, Cambridge University Press, Cambridge.
Ochi, Y. e Prentice, R.L. (1984). Likelihood Inference in a Correlated Probit Regression Model. Biometrics, 71, 531–543.
Prentice, R.L. (1988). Correlated Binary Regression with Covariate Specific to each Binary Observation. Biometrics, 44, 1033–1048.
Schwarz, G. (1978). Estimating the Dimension of a Model. Annals of Statistics, 6, 461–464.
Smith, A.F.M.; Robert, G. O. (1993). Bayesian Computation via the Gibbs Sampler and Related MCMC Methods. Journal of the Royal Statistical Society, series B, 55, 3–24.
Tanner, M.; Wong, W. (1987). The Calculation of Posterior Distributions by Data Augmentation. Journal of the American Statistical Association, 82, 528–550.
Acknowledgements
The authors are thankful to the referees for some useful suggestions which improved the paper.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Achcar, J.A., Janeiro, V. & Mazucheli, J. Regression Models for Correlated Biliary Data with Random Effects Assuming a Mixture of Normal Distributions. Computational Statistics 18, 39–55 (2003). https://doi.org/10.1007/s001800300131
Published:
Issue Date:
DOI: https://doi.org/10.1007/s001800300131