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I wondered if anyone could help me figure out what a smoother was in regard to Generalized Mixed Linear Models or point me in direction of some relevant litterature.


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You might get a better response from the statistics sister site, Cross Validated. Try there – kjetil b halvorsen Sep 22 '12 at 22:43

A "smoother" is todays often something like spline approximation or lowess. In general, you can see a (linear) smoother as a specific linear map. They are often compared to projections, like least square fits. A projection can be represented as a square, idempotent symmetric matrix. Such a matrix has eigenvalues 0 or 1. In the directions with zero eigenvalue, we are "zeroing out", in the directions with eigenvalue 1 we are doing nothing (that is, acting as an identity in Those directions). A smoother then typically will have a matrix representation with eigenvalues between zero and one, corresponding to some intermediate action between "zeroeing out" and "doing nothing". A nice book discussing smoothers from this perspective (with many examples) is "Generalized additive models" (Chapman & Hall) by Hastie and Tibshirani.

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