Exploratory Approach and Maximum Likelihood Estimation of Models for Non Symmetrical Analysis of Two-Way Multiple Contingency Tables

Abstract

In non symmetrical analysis of two—way multiple contingency tables we are interested in the dependence between one response variable and two explicative variables. The exploratory approach based on multiple and partial non symmetrical correspondence analysis can be used complementary to asymmetrical association models, logit—linear models and latent budget analysis. In this paper, maximum likelihood estimation of these models is obtained by using alternatingly a multidimensional Newton algorithm. Model parameters are identified by a generalized singular value decomposition with the same metrics as used in non symmetrical correspondence analyses. This provides factorial representations of both the dependence effects among the variables and the residuals from independence.