Estimation of response probabilities when the missing data are not missing at random can be done by postulating a parametric model for the distribution of the outcomes under full response and a model for the response probabilities. The two models define a parametric model for the joint distribution of the outcome and the response indicator, and therefore the parameters of this model can be estimated by maximization of the likelihood corresponding to this distribution. Modeling the distribution of the outcomes under full response, however, can be problematic since no data are available from this distribution. Sverchkov (2008) proposed an approach that permits estimating the parameters of the model for the response probabilities without modelling the distribution of the outcomes under full response. The present paper extends the approach developed in Sverchkov (2008).