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.