Log-linear models for ordinal multidimensional categorical data

Abstract

This study emphasised on methods for analysis of categorical data having ordered categories for the multidimensional case and the paper discusses some of the specialized models which efficiently use the information on the ordering, unlike standard methods for nominal categorical data, for multidimensional variables In order to illustrate the methodology, three dimensional data from a shopping survey in Oxford was used The Standard nominal model fitted, represented the associations between the life cycle level, car availability and the agreement with the statement I find getting to grocery shops very tiring, with 16 degrees of freedom The model selected taking the ordinal nature of variables into account also represented the same associations with 27 degrees of freedom, thus with lesser number of parameters The standard log-linear model requires describing interactions using a number of parameters where as when ordinal nature of the variables is considered, interactions can be represented by a few parameters Based on the model which takes into consideration the ordinal nature of the variables the odds ratios to illustrate the association between the life cycle and agreement, disagreement, tendency to disagree, in-between, and tendency to agree with statement are 0 8, 0 4, 0 9 and 0 9 respectively The odds ratio that describes the association of the car availability and the agreement with the statement is 0 91 It is established that ordering of categories utilizes the information reflected from data where as nominal models do not use the information in the ordered categories Also the suggested models have less parameters and are thus simpler and more parsimonious