A bivariate logistic regression model based on latent variables. (17th July 2020)

• Record Type: Journal Article
• Authors: Kristensen, Simon Bang; Bibby, Bo Martin
• Is Part Of: Statistics in medicine. Volume 39:Number 22(2020)
• Page Start: 2962
• Page End: 2979
• Publication Date: 2020-07-17
• Subjects: correlated Bernoulli variables -- generalized linear mixed models -- joint mixed models; Medical statistics -- Periodicals; Statistique médicale -- Périodiques; Statistiques médicales -- Périodiques; 610.727
• DOI: 10.1002/sim.8587
• Languages: English
• ISSNs: 0277-6715

Abstract

Abstract: Bivariate observations of binary and ordinal data arise frequently and require a bivariate modeling approach in cases where one is interested in aspects of the marginal distributions as separate outcomes along with the association between the two. We consider methods for constructing such bivariate models based on latent variables with logistic marginals and propose a model based on the Ali‐Mikhail‐Haq bivariate logistic distribution. We motivate the model as an extension of that based on the Gumbel type 2 distribution as considered by other authors and as a bivariate extension of the logistic distribution, which preserves certain natural characteristics. Basic properties of the obtained model are studied and the proposed methods are illustrated through analysis of two data sets: a basic science cognitive experiment of visual recognition and awareness and a clinical data set describing assessments of walking disability among multiple sclerosis patients.