Premium
A Unifying Framework for Marginalised Random‐Intercept Models of Correlated Binary Outcomes
Author(s) -
Swihart Bruce J.,
Caffo Brian S.,
Crainiceanu Ciprian M.
Publication year - 2014
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12035
Subject(s) - copula (linguistics) , binary data , binary number , random effects model , mathematics , marginal distribution , random variable , maximum likelihood , correlation , statistics , latent variable , econometrics , computer science , meta analysis , medicine , geometry , arithmetic
Summary We demonstrate that many current approaches for marginal modelling of correlated binary outcomes produce likelihoods that are equivalent to the copula‐based models herein. These general copula models of underlying latent threshold random variables yield likelihood‐based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data with exchangeable correlation structures. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalised random‐intercept models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate concepts. Copyright © 2013 John Wiley & Sons, Ltd.