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Modeling a Categorical Variable Allowing Arbitrarily Many Category Choices

Alan Agresti and I-Ming Liu
Biometrics
Vol. 55, No. 3 (Sep., 1999), pp. 936-943
Stable URL: http://www.jstor.org/stable/2533629
Page Count: 8
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Modeling a Categorical Variable Allowing Arbitrarily Many Category Choices
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Abstract

This article discusses the modeling of a categorical variable for which subjects can select any number of categories. For c categories, the response variable consists of a cross-classification of c binary components, one pertaining to each category. Using data from a survey (Loughin, T. M. and Scherer, P. N., 1998, Biometrics, 54, 630-637) in which Kansas farmers indicated their primary sources of veterinary information, we discuss simultaneous logit modeling of the binary components of the multivariate response. The use of maximum likelihood or quasi-likelihood fitting provides chi-squared tests with degrees of freedom df = c(r - 1) for testing the independence between each of the c response components and an explanatory variable with r categories. These tests are alternatives to the weighted chi-squared test and the bootstrap test proposed by Loughin and Scherer for this hypothesis.

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