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I'm working with a dataset of >100k rows that includes 4 columns:

['Person','x_value','y_value','binary_response']

My goal is to able to run tests to evaluate differences with regard to which coordinates are 1 vs 0 and also how the coordinates for each 'Person' differ from the coordinates as a whole.

Based on the research I've done the best way of moving forward would be by use of a generalized additive model. Does anyone have some insight as to whether this sounds like the right approach and/or the best route to take within Python? I've done a lot of searching but haven't seemed to find much of a comparison to what I'm looking to do. Any feedback would be greatly appreciated.

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If I'm reading the question correctly, it seems that you want to use logistic regression, which a form of generalized linear model. You could of course still use a logistic GAM to incorporate non-linear effects in the x_value and y_value. pyGAM is one package you could try, or you could call R which has more mature packages available. You may also want to treat Person as a random effect.

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