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How to decide, based on data exploration and data visualisation, between a GAM and a GLM.
Linear Models (LM) assume that the relationship between the response and the predictor are linear. Generalized Linear Models (GLM) assume linearity on the link scale, which means we can work with non-linear relationship between the response and the predictor, but this relationship still needs to be monotonic (i.e. either going upwards on downwards). Generalized Additive Models (GAM) do not assume any particular relationship, which means this relationship can go up and down (i.e. it is curved or wiggly). I hope I correctly summarized it up to here.
The issue of difference between GLM and GAM, or when to use GAMs as opposed to GLMs has been covered elsewhere (e.g. here) - this is not what my question is about.
My primary question is what kind of data exploration or data visualisation tools would you typically use in order to determine if GAMs are an appropriate tool as opposed to GLM. What would be a good guidelines to follow for a typical practice on deciding that.
1) If the response is continuous, I suppose you could just do a scatterplot for the response and each of the predictors, which should likely give you a hint. Correct?
2a) But if the response is presence/absence (1/0), you would need a binomial model, whether GLM or GAM. How would you decide (based on data exploration and visualisation) on which one to use?
2b) If data are presence/absence, would it make sense to run simple GAMs for the response and each of the potential predictors in turn, plot them to see the relationships, and then either use GAMs if the relationships are curvy, or a GLM if they are not? Would this be considered a good practice to guide your analytical decisions?