A model for a multivariate binary response with covariates based on compatible conditionally specified logistic regressions

A model for a multivariate binary response vector with covariates is obtained. The conditional distribution of each binary response given the other binary responses and the covariates is equivalent to a logistic regression. A simple condition on the regression parameters is necessary and sufficient for the conditional distributions to be compatible, that is, yield a multivariate distribution for the binary response vector. The multivariate model has a wide range of dependence structure for the binary response variables, so it is more generally applicable compared with previous conditional models. The model is applied to a data set from cardiac surgery.