Bayesian methods for categorical data under informative general censoring

Paulino, Carlos Daniel; Pereira, Carlos Alberto de Bragança

doi:10.1093/biomet/82.2.439

Cited by 23 publications

(27 citation statements)

References 10 publications

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“…They investigated a Bayesian method for selecting between nonignorable and ignorable nonresponse models, pointing out that the limited amount of information available makes standard model comparison methods inappropriate. Other works dealing with missing data for categorical responses include Basu and Pereira (1982), Albert and Gupta (1985), Kadane (1985), Dickey, Jiang, and Kadane (1987), Park and Brown (1994), Paulino and Pereira (1995), Park (1998), Bradlow and Zaslavsky (1999), and Soares and Paulino (2001). Viana (1994) and Prescott and Garthwaite (2002) studied misclassified multinomial and binary data, respectively, with applications to misclassified case-control data.…”

Section: Dealing With Nonresponsementioning

confidence: 99%

Bayesian inference for categorical data analysis

Agresti

Hitchcock

2005

JISS

133

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This article surveys Bayesian methods for categorical data analysis, with primary emphasis on contingency table analysis. Early innovations were proposed by Good (1953Good ( , 1956Good ( , 1965 for smoothing proportions in contingency tables and by Lindley (1964) for inference about odds ratios. These approaches primarily used conjugate beta and Dirichlet priors. Altham (1969Altham ( , 1971 presented Bayesian analogs of small-sample frequentist tests for 2×2 tables using such priors. An alternative approach using normal priors for logits received considerable attention in the 1970s by Leonard and others (e.g., Leonard 1972). Adopted usually in a hierarchical form, the logit-normal approach allows greater flexibility and scope for generalization. The 1970s also saw considerable interest in loglinear modeling. The advent of modern computational methods since the mid-1980s has led to a growing literature on fully Bayesian analyses with models for categorical data, with main emphasis on generalized linear models such as logistic regression for binary and multi-category response variables.

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Section: Dealing With Nonresponsementioning

confidence: 99%

Bayesian inference for categorical data analysis

Agresti

Hitchcock

2005

JISS

133

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“…Molenberghs and Kenward (2007) review some other possibilities of sensitivity analyses using the local influence approach of Cook (1986). A radically different strategy rests on Bayesian methods in the framework of unconstrained missingness models like those in Paulino (2001, 2007), based on the work of Paulino and Pereira (1995). In this case, careful attention should be given to prior distributions, because posterior summaries may exhibit some prior dependence, as Forster and Smith (1998) showed.…”

Section: Discussionmentioning

confidence: 99%

Missing data mechanisms and their implications on the analysis of categorical data

2009

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We review some issues related to the implications of different missing data mechanisms on statistical inference for contingency tables and consider simulation studies to compare the results obtained under such models to those where the units with missing data are disregarded. We confirm that although, in general, analyses under the correct missing at random and missing completely at random models are more efficient even for small sample sizes, there are exceptions where they may not improve the results obtained by ignoring the partially classified data. We show that under the missing not at random (MNAR) model, estimates on the boundary of the parameter space as well as lack of identifiability of the parameters of saturated models may be associated with undesirable asymptotic properties of maximum likelihood estimators and likelihood ratio tests; even in standard cases the bias of the estimators may be low only for very large samples. We also show that the probability of a boundary solution obtained under the correct MNAR model may be large even for large samples and that, consequently, we may not always conclude that a MNAR model is misspecified because the estimate is on the boundary of the parameter space.

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“…In order to overcome this problem, the censoring mechanism is typically assumed to be ignorable (noninformative) in that the unknown parameter of the distribution describing the censoring mechanism is unrelated to the parameter of interest (see [12] and the references therein). Paulino and Pereira [29] discuss Bayesian conjugate methods for categorical data under general, informative censoring. In particular, they are concerned with Bayesian estimation of the cell frequencies through posterior expectations.…”

Section: Nonidentifiabilitymentioning

confidence: 99%

Bayesian Methods for Categorical Data

Gutiérrez‐Peña¹

2005

Encyclopedia of Statistics in Behavioral Science

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The Bayesian approach to statistical inference is based on a subjective interpretation of probability. Given a prior distribution describing our prior beliefs concerning the value of an unknown quantity, Bayes' theorem allows us to update those beliefs in the light of observed data. The resulting posterior distribution then summarizes all the available information about the quantity of interest, conditional on the posited model. Bayesian methods for the analysis of categorical data use the same classes of models as the classical approach. However, Bayesian analyses can be more informative – the posterior distribution of the parameter contains more information than mere point estimates or test statistics – and may provide more natural solutions in certain situations such as those involving sparse or missing data, or unidentifiable parameters.

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Bayesian methods for categorical data under informative general censoring

Cited by 23 publications

References 10 publications

Bayesian inference for categorical data analysis

Bayesian inference for categorical data analysis

Missing data mechanisms and their implications on the analysis of categorical data

Bayesian Methods for Categorical Data

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