Abstract
The aim of this paper is to demonstrate the R package conting for the Bayesian analysis of complete and incomplete contingency tables using hierarchical log-linear models. This package allows a user to identify interactions between categorical factors (via complete contingency tables) and to estimate closed population sizes using capture-recapture studies (via incomplete contingency tables). The models are fitted using Markov chain Monte Carlo methods. In particular, implementations of the Metropolis-Hastings and reversible jump algorithms appropriate for log-linear models are employed. The conting package is demonstrated on four real examples.
Highlights
Contingency tables are formed when a population is cross-classified according to a series of categories
Each cell count of the contingency table gives the number of units observed under a particular cross-classification
Incomplete contingency tables formed from capture-recapture studies can be used to estimate closed populations (Fienberg 1972)
Summary
Contingency tables (see, e.g., Agresti 2007) are formed when a population is cross-classified according to a series of categories (or factors). Each cell count of the contingency table gives the number of units observed under a particular cross-classification. Cell counts corresponding to not being observed by any of the sources are missing (or unknown). They can be estimated by fitting a statistical model to the observed cell counts and predicting the missing cell counts. We can distinguish our concept of incomplete contingency tables from those where conting: Bayesian Analysis of Contingency Tables in R the cell counts are misclassified or are only partially observed due to non-response from units of the population, see, e.g., Gelman, Carlin, Stern, and Rubin (2004, Sections 21.5 and 21.6) and Tan, Tian, and Ng (2010, Chapter 4)
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