LogitModelFit bias term when using design matrix

Question

I'm using the LogitModelFit function with a 32-columns design matrix and 0 or 1 output vector: LogitModelFit[{datax, datay}].

The fits seems to work, however the fit function has no bias term, unlike the other examples provided in the documentation.

For example, when I apply the fit function to the origin ConstantArray[0, 32], a value of 0.5 is returned.

The documentation specifies that for a design matrix m and response vector v, the model is $\hat{v}=1/(1+\exp(\mathbf m.\beta))$ (so no intercept term).

I don't understand how this is standard behaviour. How can I change it ?

Answer 1

Ok so the answer is simply to add an intercept column of 1s to the design matrix (here X):

X = ArrayFlatten[{{1,X}}];
fit = LogitModelFit[{X, y}];
results = MapThread[fit, Transpose[X]];

To test the hypothesis fit on a new datapoint however it's important to add 1 as its first parameter, ie. fit only works on the new feature space.