In order toTo prove that this is equivalent to the previous model, we start by recognizing the above model is overspecified, in that <math>\Pr(Y_i=0)</math> and <math>\Pr(Y_i=1)</math> cannot be independently specified: rather <math>\Pr(Y_i=0) + \Pr(Y_i=1) = 1</math> so knowing one automatically determines the other. As a result, the model is [[nonidentifiable]], in that multiple combinations of '''''β'''''<submath>\beta_{0}</submath> and '''''β'''''<submath>\beta_{1}</submath> will produce the same probabilities for all possible explanatory variables. In fact, it can be seen that adding any constant vector to both of them will produce the same probabilities:
