A mixed approach and a distribution free multiple imputation technique for the estimation of multivariate probit models with missing values

In the present paper a mixed generalized estimating/pseudo­score 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 time invariant variable. Furthermore, a generalization of the squared trace correlation (R_T^2) for multivariate probit models, denoted as pseudo R_T^2, 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 R_T^2 was close to R_T^2 of the underlying linear model. The mixed approach is illustrated using a psychiatric data set of depressive inpatients. The results of this analysis suggest, that the depression score at discharge from a psychiatric hospital and the occurence of stressful life events seem to increase the probability of having an episode of major depression within a one­year interval after discharge. Furthermore, the correlation structure points to short­time effects on having or not having a depressive episode, not accounted for in the systematic part of the regression model