  In this note, conditions for the existence and uniqueness of the maximum
likelihood estimate for multidimensional predictor, binary response models are
introduced from a sensitivity testing point of view. The well known condition
of Silvapulle is translated to be an empirical likelihood maximization which,
with existing R code, mechanizes the process of assessing overlap status. The
translation shifts the meaning of overlap, defined by geometrical properties of
the two-predictor groups, from the intersection of their convex cones is
non-empty to the more understandable requirement that the convex hull of their
differences contains zero. The code is applied to reveal the character of
overlap by examining minimal overlapping structures and cataloging them in
dimensions fewer than four. Rules to generate minimal higher dimensional
structures which account for overlap are provided. Supplementary materials are
available online.
