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What is the difference between LOESS and LOWESS? From Wikipedia I can only see that LOESS is a generalization of LOWESS. Do they have slightly different parameters?

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I think it is important to distinguish between methods and their implementations in software. The main difference with respect to the first is that lowess allows only one predictor, whereas loess can be used to smooth multivariate data into a kind of surface. It also gives you confidence intervals. In these senses, loess is a generalization. While the default for lowess is to use the tricube weighting, loess carries out an unweighted fit by default.

Now for the implementation. In some software, lowess uses a linear polynomial, while loess uses a quadratic polynomial (though you can alter that). The defaults and shortcuts that the algorithms use are often quite different, so that it is hard to get the univariate outputs to match exactly. On the other hand, I am not aware of a case where the choice between the two made a substantive difference.

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    $\begingroup$ Cleveland's 1979 LOWESS paper in JASA. has tricube weighting for this. It's explicitly mentioned in step 4 on p831 of "Robust Locally Weighted Regression and Smoothing Scatterplots," William S. Cleveland, Journal of the American Statistical Association, Vol. 74, No. 368. (Dec., 1979), pp. 829-836. If the Wikipedia article is accurate, LOESS didn't change that default -- they both do it. $\endgroup$ – Glen_b -Reinstate Monica Jul 12 '15 at 16:39
  • $\begingroup$ Maybe this is not standard usage after all. I guess lowess also typically uses a linear polynomial, while loess uses a quadratic polynomial. $\endgroup$ – Dimitriy V. Masterov Jul 12 '15 at 17:09
  • $\begingroup$ When is one preferred over the other? $\endgroup$ – pir Jul 12 '15 at 20:11
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    $\begingroup$ It may be difficult to track down differences precisely, since lowess evolved over time, and loess was simply what Bill Cleveland started calling it after some geoscientists he was talking to about lowess told him why it reminded them of loess. He adopted the new name at that point, and what was 'typical' loess continued to evolve (slightly) after that. There are more differences between options within the 1979 paper I point to above than there are between typical implementations of the two. We may need to take two specific points along that evolution to identify specific differences. $\endgroup$ – Glen_b -Reinstate Monica Jul 13 '15 at 1:58
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Specifically for R, the difference is small. There is a very detailed explanation here: https://support.bioconductor.org/p/2323/

But notice that lowess() in R outputs data list while loess() outputs the model which can be input into predict().

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    $\begingroup$ the discussion in the link is excellent. it tells you the exact relationship between the argument $\endgroup$ – cmo Feb 15 '19 at 18:50

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