RC Association Model Research Articles

Taxicab Correspondence Analysis and Taxicab Logratio Analysis: A Comparison on Contingency Tables and Compositional Data

In this paper, we attempt to see further by relating theory with practice: First, we review the principles on which three interrelated well developed methods for the analysis and visualization of contingency tables and compositional data are erected: Correspondence analysis based on Benzécri’s principle of distributional equivalence, Goodman’s RC association model based on Yule’s principle of scale invariance, and compositional data analysis based on Aitchison’s principle of subcompositional coherence. Second, we introduce a novel index named intrinsic measure of the quality of the signs of the residuals for the choice of the method. The criterion is based on taxicab singular value decomposition, on which the package TaxicabCA in R is developed. We present a minimal R script thatcan be executed to obtain the numerical results and the maps in this paper. Third, we introduce a flexible method based on the novel index for the choice of the constant to be added to contingency tables with zero counts so that logratio methods can be applied.

The Rescale Application of the RC Association Models in Logistic Regression

The aim of the research is to apply the row (R) and column (C) association model from Clogg and Shihadeh [1] to rescale the parents' education variable that is two ordinal variables to be transformed a continuous variable. The study also compares the results of β in logistic regression among using parents' education as years, ordinal variables and RC association model. The results indicate the β is maximized as the RC model is conducted, which can explain more variance for parent's education variable. The contribution of this study confirms that the results will be more significant when a proper statistical analysis, such as the RC model, is considered involving parent's education variable for related studies.

Bayesian test on equality of score parameters in the order restricted RC association model

In the RC association model for a two-way contingency table, it is often natural to impose order constraints on the score parameters of the row and column variables. In this article, a simple and efficient Bayesian model selection procedure is proposed that simultaneously compares all possible combinations of (in)equalities of successive score parameters in the order restricted RC association model. The method introduces normal latent variables into the model and uses a simple and accurate approximation to the likelihood function so that the full conditional posterior distributions of elements of the parameter are given as truncated normal distributions. The Gibbs sampling algorithm of Gelfand and Smith (1990) is employed to generate samples from the full model in which all the scores are strictly ordered, and posterior probabilities of all possible models are estimated by using the Gibbs output from the full model. A simulation study shows that the proposed method performs well in detecting the true model. Two real data sets are analyzed using the proposed method.

Asymptotic distribution of inequality-restricted canonical correlation with application to tests for independence in ordered contingency tables

For two-way ordered categorical data, correspondence analysis and the RC association model (the row–column-effect association model) with order-restricted scores have been proposed mainly for descriptive purposes. In this paper, tests for independence in two-way ordered contingency tables based on these models are developed in a general framework of inequality-restricted canonical correlation analysis. The limiting null distributions are characterized as the maxima of Gaussian random fields and asymptotic expansions of their tail probabilities are derived by the tube method, an integral geometric approach. Some numerical techniques for fitting order-restricted models are discussed. An example of data analysis is given to demonstrate the practical usefulness of the proposed method.

Diagnostics in Categorical Data Analysis

SUMMARY Diagnostics as measures of model deviations and of the influence of particular data sets are used extensively in modern regression analysis. For contingency tables, and more generally for the parametric multinomial distribution, it is not the influence of individual observations which is of interest, but rather the contribution to a lack of model fit or to the values of the parameter estimates from a single cell in the table, which must be evaluated. Hence diagnostics for contingency tables take somewhat different forms. In this paper such diagnostics are discussed and their applicability is illustrated with data sets analysed by the Goodman RC association model.