A two-step smoothing procedure for the analysis of sparse contingency tables with ordered categories

Abstract

Assessing the multivariate structure of data is often the aim of the statistical analysis of economical, demographic and social phenomena. In many situations in the analysis of categorical data it may happen that the number of cells can be close to, or even greater than, the number of observations at hand resulting in very small or even zero cell counts. In this case a contingency table is usually referred to as a sparse table. In this sort of situation the optimal properties of the usual statistical procedures may break down. Several authors investigated the use of smoothing methods for sparse count data but a little was done to evaluate if these methods can be helpful in discovering the multivariate structure of the data. This paper shows as the joint use of smoothing techniques and information measures may improve the analysis in a multivariate sparse context.