A Mixed Approach and a Distribution-Free Multiple Imputation Technique for the Estimation of a Multivariate Probit Model with Missing Values

Abstract

In the present paper a mixed generalized estimating/pseudo-score equations (GEPSE) approach together with a distribution-free multiple imputation technique is proposed for the estimation of regression and correlation structure parameters of multivariate probit models with missing values for an ordered categorical timeinvariant variable. Furthermore, a generalization of the squared trace correlation (R2T) for multivariate probit models, denoted by pseudo-R2T, is proposed. A simulation study was conducted, simulating a probit model with an equicorrelation structure in the errors of an underlying regression model and using two different missing mechanisms. For a low "true" correlation the difference between the GEPSE, a generalized estimating equations (GEE) and a maximum likelihood (ML) estimator were negligible. For a high "true" correlation the GEPSE estimator turned out to be more efficient than the GEE and very efficient relative to the ML estimator. Furthermore, the pseudo-R2T was close to R2T of the underlying linear model. The mixed approach is illustrated using a psychiatric data set of depressive in-patients. The results of this analysis suggest that the depression score at discharge from a psychiatric hospital and the occurrence of stressful life events seem to increase the probability of having an episode of major depression within a one-year interval after discharge. Furthermore, the correlation structure points to short-time effects on having or not having a depressive episode, not accounted for in the systematic part of the regression model.