JSM 2004 - Toronto

Abstract #301985

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Activity Number: 50
Type: Contributed
Date/Time: Sunday, August 8, 2004 : 4:00 PM to 5:50 PM
Sponsor: ENAR
Abstract - #301985
Title: Modeling Ordinal Categorical Data
Author(s): John L. Fresen*+
Companies: Medical University of Southern Africa
Address: Dept. of Mathematics and Statistics, Pretoria, 0204, Republic of South Africa
Keywords: modeling ; ordinal ; categorical ; data
Abstract:

Two approaches are commonly used for analyzing ordinal categorical data. The first method is to use a loglinear model for the expected cell frequencies. If the underlying data, before categorization, follow a normal distribution then the linear predictor that is commonly used seems inappropriate. This situation is analyzed by considering the case where the variables follow a joint normal distribution and the case where one of the variables is a response variable and the rest are predictors. The second method, for the case of an ordinal categorical response variable, is to model the cumulative logits of the cell probabilities in terms of a linear predictor. Again, the linear predictor that is commonly used seems inappropriate if the underlying data follow the normal distribution. Different predictors for both these methods are discussed. The estimation is achieved by maximizing an approximate likelihood. Similar arguments hold for other distributions in which the variables have a correlation or regression structure. Examples are presented.

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