Bayesian analysis of contingency tables: a simulation and graphics-based approach

Vounatsou, Penelope; Smith, A. F. M.

doi:10.1007/bf00140872

Cited by 1 publication

(2 citation statements)

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“…Forster and Skene (1994) applied Gibbs sampling with adaptive rejection sampling to the Knuiman and Speed (1988) formulation of multivariate normal priors for loglinear model parameters. Other examples include George and Robert (1992), Chib (1993), Forster (1994), Albert (1996), Chipman and Hamada (1996), Vounatsou and Smith (1996), Albert (1999), andMcCulloch, Polson, andRossi (2000).…”

Section: Bayesian Computationmentioning

confidence: 97%

“…As mentioned previously, Albert and Gupta (1982) had used a hierarchical Dirichlet approach to smoothing toward a prior belief of symmetry. Vounatsou and Smith (1996) analyzed certain structured contingency tables, including symmetry, quasi-symmetry and quasi-independence models for square tables and for triangular tables that result when the category corresponding to the (i, j) cell is indistinguishable from that of the (j, i) cell (a case also studied by Altham 1975). They assessed goodness of fit using distance measures and by comparing sample predictive distributions of counts to corresponding observed values.…”

Section: Estimating Loglinear Model Parameters In Two-way Tablesmentioning

confidence: 99%

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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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