Heterogeneity among contingency tables diagnosed by hierarchicallog-linear models and their effect on Biplots

Abstract

The theory of singular value decomposition of matched matrices is used to verify the heterogeneity of rows, columns and between matched two-way tables. An exploratory analysis that can be visualized in biplots and through simulations studies with the hierarchical log-linear model using ordinary residuals and the components of residual deviance. The effect of heterogeneity was studied generating different sample sizes and their behavior was checked by adjusting Poisson’s model. We concluded that the model of ordinary residuals is the one that best reflects the degree of heterogeneity among the matched tables. Finally, an illustrative example is presented in order to guide the researcher to interpret the relationship between the results of the log-linear models with the biplots considering the effects between the sum and difference between the tables.