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I was looking at CrossValidate archives as well as r-archives and crantastic...for a package that has a robust approach to generalized additive models. I found two packages "robustgam" and "rgam" but their implemented functions cover only binomial and Poisson distributions (pls correct me if I am wrong).

I would greatly appreciate if anyone could share with us other R-packages or robust approaches of general additive modeling that might have a better performance with small data sets ($n<100$ records or 50 -100 records).

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  • $\begingroup$ Interesting thought...I am not sure but sounds that it might work! Did you have in mind a specific pacgage like mgcv, or robustgam or rgam? Thank you VERY MUCH for your immediate response. I sincerely appreciate it. $\endgroup$
    – user22478
    Commented Jun 2, 2013 at 23:43
  • $\begingroup$ no, that was wrong... $\endgroup$
    – user603
    Commented Jun 3, 2013 at 5:39
  • $\begingroup$ yes...thank you any new ideas? $\endgroup$
    – user22478
    Commented Jun 3, 2013 at 18:06

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The mgcv package contains a scaled-t family for the conditional distribution of the response, that, like the Gaussian, has support for the entire real line (is suitable for a response that is continuous and is bounded at -Inf and +Inf), but which has heavier tails than the Gaussian.

Estimating the model requires estimating another parameter of the distribution, the degrees of freedom, the smaller the degrees of freedom the heavier the tails of the conditional distribution of the response.

Because of the heavier tails in this distribution, the model is made more robust to more extreme observations as they have higher probability density until the scaled-t with suitable degrees of freedom than under the Gaussian, all else equal. As a result, the model doesn't need to move the fitted smoother towards these extreme values, to achieve a reasonable fit.

To use it, use family = scat() in the call the gam() or bam().

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    $\begingroup$ This was what I was thinking. Question, though: does this use the same error distribution for every input (akin to OLS having constant variance), or are the degrees of freedom allowed to change? $\endgroup$
    – Dave
    Commented Mar 20, 2020 at 22:25
  • $\begingroup$ @Dave The scat family in mgcv doesn't allow for a linear predictor (beyond an intercept) for $\nu$; in general though, one could have a model for $\nu$. The VGAM, gamlss packages allow for this as do more general packages like brms*/*Stan etc $\endgroup$
    – Gavin Simpson
    Commented Mar 20, 2020 at 22:54
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    $\begingroup$ But see stats.stackexchange.com/questions/45784/…, MASS (the book) advices against trying to estimate $\nu$, it looses robustness. $\endgroup$
    – kjetil b halvorsen ♦
    Commented Mar 21, 2020 at 0:50
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    $\begingroup$ @kjetilbhalvorsen Yep; good point. The gamlss package at least parameterises the its t distribution using mu, sigma and nu. Not sure how this changes things with respect to your Answer & the stuff in MASS? $\endgroup$
    – Gavin Simpson
    Commented Mar 21, 2020 at 3:36

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