This is really flailing in the dark, but do you have any "pathological" data points?  Something in one of the classes that doesn't fit piecewise could do this.  The piecewise function doesn't have to be differentiable at the join point, but it does have to be continuous.  If for some level of one of the categorical variables, the continuous variable shifts dramatically, this collinearity could cause this jump.  It sounds almost like a quasi-separation problem in logistic regression, for some reason. Setve Denham ... View more