Analysis of Incomplete Multivariate DataCRC Press, 1 aug 1997 - 448 pagina's The last two decades have seen enormous developments in statistical methods for incomplete data. The EM algorithm and its extensions, multiple imputation, and Markov Chain Monte Carlo provide a set of flexible and reliable tools from inference in large classes of missing-data problems. Yet, in practical terms, those developments have had surprisingly little impact on the way most data analysts handle missing values on a routine basis. Analysis of Incomplete Multivariate Data helps bridge the gap between theory and practice, making these missing-data tools accessible to a broad audience. It presents a unified, Bayesian approach to the analysis of incomplete multivariate data, covering datasets in which the variables are continuous, categorical, or both. The focus is applied, where necessary, to help readers thoroughly understand the statistical properties of those methods, and the behavior of the accompanying algorithms. All techniques are illustrated with real data examples, with extended discussion and practical advice. All of the algorithms described in this book have been implemented by the author for general use in the statistical languages S and S Plus. The software is available free of charge on the Internet. |
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algorithm analysis applied approximately asymptotic Bayesian inference Bayesian IPF calculated categorical variables cell probabilities chain Monte Carlo coefficients columns complete-data posterior computational conditional distribution contingency table correlation corresponding covariance matrix data matrix dataset denote density Dirichlet distribution elements EM algorithm error example fraction of missing Gibbs sampling given hyperparameters I-step imputation model incomplete independent interval estimates iterations likelihood function likelihood-ratio likelihood-ratio test linear loglinear model marginal distribution Markov chain Markov chain Monte methods missing data missing information missing values missing-data missingness patterns ML estimate monotone data augmentation multinomial multiple imputation multivariate normal normal model observed data observed-data likelihood observed-data loglikelihood observed-data posterior obtained odds ratios p-value P(Ymis parameter space posterior distribution posterior mode prior distribution problems quantiles random Rao-Blackwellized rates of missing regression rows Rubin sample saturated model Section starting value stationary sufficient statistics tion variance vector Ymis Yobs zero