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BIVARIATE MODELLING OF CLUSTERED CONTINUOUS AND ORDERED CATEGORICAL OUTCOMES
Author(s) -
CATALANO PAUL J.
Publication year - 1997
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/(sici)1097-0258(19970430)16:8<883::aid-sim542>3.0.co;2-e
Subject(s) - categorical variable , bivariate analysis , joint probability distribution , statistics , econometrics , multivariate statistics , mathematics , latent variable , random effects model , multivariate normal distribution , multivariate probit model , multinomial probit , computer science , probit model , medicine , meta analysis
Simultaneous observation of continuous and ordered categorical outcomes for each subject is common in biomedical research but multivariate analysis of the data is complicated by the multiple data types. Here we construct a model for the joint distribution of bivariate continuous and ordinal outcomes by applying the concept of latent variables to a multivariate normal distribution. The approach is then extended to allow for clustering of the bivariate outcomes. The model can be parameterized in a way that allows writing the joint distribution as a product of a standard random effects model for the continuous variable and a correlated cumulative probit model for the ordinal outcome. This factorization suggests convenient parameter estimation using estimating equations. Foetal weight and malformation data from a developmental toxicity experiment illustrate the results. © 1997 by John Wiley & Sons, Ltd. Stat. Med., Vol. 16, 883–900 (1997).