## Bayesian Models for Categorical DataThe use of Bayesian methods for the analysis of data has grown substantially in areas as diverse as applied statistics, psychology, economics and medical science. Bayesian Methods for Categorical Data sets out to demystify modern Bayesian methods, making them accessible to students and researchers alike. Emphasizing the use of statistical computing and applied data analysis, this book provides a comprehensive introduction to Bayesian methods of categorical outcomes. * Reviews recent Bayesian methodology for categorical outcomes (binary, count and multinomial data). * Considers missing data models techniques and non-standard models (ZIP and negative binomial). * Evaluates time series and spatio-temporal models for discrete data. * Features discussion of univariate and multivariate techniques. * Provides a set of downloadable worked examples with documented WinBUGS code, available from an ftp site. The author's previous 2 bestselling titles provided a comprehensive introduction to the theory and application of Bayesian models. Bayesian Models for Categorical Data continues to build upon this foundation by developing their application to categorical, or discrete data - one of the most common types of data available. The author's clear and logical approach makes the book accessible to a wide range of students and practitioners, including those dealing with categorical data in medicine, sociology, psychology and epidemiology. |

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### Contents

1 | |

Chapter 2 Model Comparison and Choice | 29 |

Chapter 3 Regression for Metric Outcomes | 55 |

Chapter 4 Models for Binary and Count Outcomes | 113 |

Chapter 5 Further Questions in Binomial and Count Regression | 155 |

Chapter 6 Random Effect and Latent Variable Models for Multicategory Outcomes | 197 |

Chapter 7 Ordinal Regression | 235 |

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### Common terms and phrases

000 iterations ¼ 0 þ ¼ 1Þ alternative American Statistical Association applied approach assess assumed average Bayes factor Bayesian analysis Bayesian model binary data binomial Carlin Categorical Data Chib clusters coefficients Congdon consider convergence correlation count data covariance cut points Data Analysis data augmentation deﬁned density deviance Dirichlet discrete mixture distribution error estimated example exponential family function gamma Gelfand Gelman Gibbs sampling identifiability ij ¼ ijÞ impact inference interaction intercept involves itÞ iÞ ¼ Journal latent linear models linear regression logð logit link logit model marginal likelihood Markov chain matrix MCMC methods missingness mixture models model probabilities multinomial multinomial probit multivariate normal observed obtained ordinal outcomes outliers overdispersion Poisson Poisson regression posterior mean predictive check predictors prior probit random effects regression model response Royal Statistical Society sampling selection smooth spatial Spiegelhalter spline two-chain run values variables variance yi ¼ zero