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I am smoothing the relationship between a binary variable y and a continuous variable x. For this I've looked into both GAM and LOESS, but I cannot find a good comparison of the pros and cons of the two methods. Could someone explain when to use one over the other?

I will not be using the smoothing for any predictive modeling, but only as a way of visualizing the relationship. I would of course prefer to find the most interesting aspects of the relationship between the two variables. I am not that interested in this question related to any particular dataset, but more in the general case of when to use one model over the other. That is why I haven't posted any plots or data.

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  • $\begingroup$ have you tried fitting a simple logistic regression to it and visualizing the sigmoid? $\endgroup$
    – metjush
    Commented Nov 7, 2015 at 14:24
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    $\begingroup$ Yeah, I've tried logistic regression, LOESS and GAM. The logistic regression doesn't capture the relationship very well. However, I'm more interested in the general case than for my data specifically, which is why I haven't posted plots and data. $\endgroup$
    – pir
    Commented Nov 7, 2015 at 15:05
  • $\begingroup$ It would be helpful if you posted at least one plot along with a comment describing the issues, as you see them, with the method that you're illustrating. $\endgroup$
    – Creosote
    Commented Nov 13, 2015 at 7:55
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    $\begingroup$ There aren't any issues in particular. The two methods can just produce quite different lines and confidence intervals. I will see if I can find a good example. $\endgroup$
    – pir
    Commented Nov 15, 2015 at 21:15
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    $\begingroup$ @metjush simple logistic regression invokes a specific functional form on the relationship between the DV and a linear combination of the IVs. The point of nonparametric smoothing regressions, such as GAMs and LOWESS, is to make no assumptions about the functional form(s) of the relationship(s) between the DV and IVs. $\endgroup$
    – Alexis
    Commented Feb 14, 2016 at 20:52

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