Premium
Parameterization of Multivariate Random Effects Models for Categorical Data
Author(s) -
RabeHesketh S.,
Skrondal A.
Publication year - 2001
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2001.1256_1.x
Subject(s) - multivariate statistics , multivariate probit model , probit model , econometrics , logit , mathematics , categorical variable , statistics , identification (biology) , context (archaeology) , probit , ordered probit , geography , botany , archaeology , biology
Summary. Alternative parameterizations and problems of identification and estimation of multivariate random effects models for categorical responses are investigated. The issues are illustrated in the context of the multivariate binomial logit‐normal (BLN) model introduced by Coull and Agresti (2000, Biometrics 56 , 73–80). We demonstrate that the BLN model is poorly identified unless proper restrictions are imposed on the parameters. Moreover, estimation of BLN models is unduly computationally complex. In the first application considered by Coull and Agresti, an identification problem results in highly unstable, highly correlated parameter estimates and large standard errors. A probit‐normal version of the specified BLN model is demonstrated to be underidentified, whereas the BLN model is empirically underidentified. Identification can be achieved by constraining one of the parameters. We show that a one‐factor probit model is equivalent to the probit version of the specified BLN model and that a one‐factor logit model is empirically equivalent to the BLN model. Estimation is greatly simplified by using a factor model.