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A bivariate cumulative probit regression model for ordered categorical data
Author(s) -
Kim Kyungmann
Publication year - 1995
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4780141207
Subject(s) - categorical variable , bivariate analysis , covariate , multivariate probit model , statistics , probit model , mathematics , econometrics , regression analysis
This paper proposes a latent variable regression model for bivariate ordered categorical data and develops the necessary numerical procedure for parameter estimation. The proposed model is an extension of the standard bivariate probit model for dichotomous data to ordered categorical data with more than two categories for each margin. In addition, the proposed model allows for different covariates for the margins, which is characteristic of data from typical opthalmological studies. It utilizes the stochastic ordering implicit in the data and the correlation coefficient of the bivariate normal distribution in expressing intra‐subject dependency. Illustration of the proposed model uses data from the Wisconsin Epidemiologic Study of Diabetic Retinopathy for identifying risk factors for diabetic retinopathy among younger‐onset diabetics. The proposed regression model also applies to other clinical or epidemiological studies that involve paired organs.