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Logistic regression fits a model that predicts a binary variable whilst performing a logit transformation of the linear combination (LC) of predictors: 1/1 + exp(-LC).

I have a working machine learning algorithm which does the same but fits a non linear combination of predictors by maximising the log likelihood. I would like to apply this algorithm to presence only data as suggested here:

Presence-only data and the em algorithm

Could I just use formula (4) (its log likelihood version)? How do I use the resulting fitted model to perform predictions if I do not know the value of z but just the predictors/co-variates? I also do not understand the difference between observed and full likelihood? Any clarification would be very much appreciated.

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It turns out that I can use formula 4 but have to use the standard logit link function for predictions.

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