Abstract: The diagnostic method of Hinkley and Wang (1988) is extended for assessing the influence of a group of cases to the regression models in which both response and linear predictor are transformed. Both the double transformation model and the single transformation model are considered. Approximations for casesdeletion diagnostics are obtained by taking advantage of the constructed variable regression technique and using a mean outlier model. An example is presented for illustrating the influence on the estimator of the single parameter when two cases are deleted.