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Are the estimators unbiased efficient and consistent? Or is GAM better for classification and prediction than non additive models? Interaction terms aren’t allowed in GAM.

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Yes, they are perfectly suitable, after all GAMs are linear in their parameters, i.e. they will be have like "usual" GLMs. And we can have interactions terms when using GAMs (e.g. in R using s( ..., by=var_x) and/or in the form of tensor products t(var_1, var_2)).

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