A multivariate probit model for correlated binary responses given the predictors of interest has been considered. Some of the responses are subject to classification errors and hence are not directly observable. Also measurements on some of the predictors are not available; instead the measurements on its surrogate are available. However, the conditional distribution of the unobservable predictors given the surrogate is completely specified. Models are proposed taking into account either or both of these sources of errors. Likelihood-based methodologies are proposed to fit these models. To ascertain the effect of ignoring classification errors and/or measurement error on the estimates of the regression and correlation parameters, a sensitivity study is carried out through simulation. Finally, the proposed methodology is illustrated through an example.
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