This paper considers the regression analysis of categorical variables when the response variable is incompletely observed and the non-response mechanism is assumed to be non-ignorable. Maximum likelihood estimation of the model parameters can lead to substantively implausible boundary solutions where the estimated proportion of non-respondents taking certain values of the response variable is zero. A geometric explanation of why boundary solutions occur was given in a previous paper for a simple model. By extending this explanation, it is possible to define the sub-class of non-ignorable models whose parameters are identified, and to show all models not in this sub-class are non-identified. The conditions under which a model is a member of this class are easily established.