High-dimensional multivariate probit analysis

A computationally practical form of probit analysis for multiple response variables based on an assumed common factor model for the latent tolerances is proposed. Numerical integration over the factor space provides maximum likelihood estimation of the probit regression parameters and of the probabilities of response combinations under the model. The procedure is applied to five variables from the Pneumoconiosis Field Trial, two variables of which were previously analyzed by Ashford and Sonrden (1970, Biometrics 26, 535-546).