PLACE:  321 Snedecor

SPEAKER:
Heike Hofmann
Augsburg University, Augsburg, Germany

TITLE:
Generalised Odds Ratios for Visual Modeling

ABSTRACT:

Key Words: Odds Ratios, Mosaic Plot, Model Selection, Visual Modeling, Interaction Effects

The problem of displaying interaction effects graphically has been studied for a long time.  We show how Mosaic Plots can be applied to visualise interaction effects in categorical data.  This idea leads us to a graphical approach for model selection based on a classical backward selection. Visualising interaction effects is the goal of several graphical displays, such as Fourfold Displays (Friendly, 1994) or a special form of Stem-And-Leaf Plots (Hoaglin et al., 1991). These approaches could not easily be extended to higher dimensions, whether in the number of categories or in the number of variables.  We want to introduce in this paper how Mosaic Plots (Hartigan and Kleiner, 1981; Friendly, 1992) enable us to visualise even high-dimensional interaction effects, in an approach, which is based on a strict mathematical foundation.  The procedure for this is as follows:  in section 2 of the paper we give an extension of the well-known concept of odds-ratios to higher dimensions, which, together with alternative constraints for interaction effects in log-linear models, helps us to formulate a collapsibility condition that can be checked graphically and applied directly to the data.  In parallel we develop at the beginning of section 3 a method of visualising and comparing two-dimensional conditional odds ratios using Mosaic Plots.  In the second part of section 3 we combine these two approaches and show in the detailed example of the Cancer Knowledge Data visual modeling of categorical data based on the classical backward selection.

COFFEE: 3:45 p.m., 104 Snedecor