Speaker: Dr. Michael Friendly,  York University
Department of Psychology

Title:  General Models and Graphs for Log Odds and Log Odds Ratios

Abstract: The analysis and interpretation of loglinear models for multi-way contingency tables is considerably enhanced by associated visualization methods including mosaic displays, doubledecker plots, association plots, sieve diagrams and fourfold displays, all implemented comprehensively in the vcd package for R. These are all "full-table" plots  that show the frequencies in all table cells as areas, together with other visual attributes and annotations to indicate residuals or other aspects of goodness-of-fit.  As such, they  can be quite complicated for large tables with more than a few factors or with many levels.

This talk illustrates a different approach based on log odds and log odds ratios, which are  often familiar loglinear models recast in these terms. This approach gives rise to simple  linear models and simple graphs. In particular, I describe two general classes of models for log odds and log odds ratios in R x C tables, possibly stratified by one or more additional factors.

I show that these may be cast as general linear models of the form log (\theta) = C log ( n ) where \theta is a vector of log odds or log odds ratios, C is an appropriate contrast matrix, and n is the vector of table frequencies. Such models can be readily estimated by generalized least squares. Then, each log odds or log odds ratio plots as a point, and the structure of the data as well as the model may be visualized using simple line graphs. These methods are now also implemented in the vcd package. I illustrate with some examples from my new book, "Discrete Data Analysis with R."