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I use functions in R as context for the question, but it is more generally about the meaning of two terms used to describe weights applied to cases in regression models.

In lm, the "weights" argument triggers WLS fitting to minimize the sum of the weighted squared residuals. These are called typically called "sampling weights", "probability weights", or "inverse probability weights", as in Horvitz-Thompson estimation.

In nnet, the documentation for the "weights" argument notes that it expects a (case) weight for each example. I'm wondering what this means, precisely, and how case weights differ from the usual probability weights, if at all.

It may be that the emphasis on the word case here is simply used to distinguish the "weights" argument in nnet from the "Wts" argument, which is used to specify starting values for the regression coefficients between hidden and observed nodes.

Any insight about "(case) weights" would be very helpful.

bsbk
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  • The weights in lm are _not_ sampling weights. Although WLS is used to fit the model, the standard errors are not computed under the assumption that they are probability weights – Tim May 12 '16 at 04:17
  • @Tim Thanks for your comment. One could pass sampling weights to lm's weights argument and get an unbiased estimate of an effect (as in inverse propensity score weighting) though, I agree, in order to get correct SEs you would have to bootstrap (or use the survey package, etc). My main question is about the naming conventions used for different types of weights and, in this case, how they are called out in R. Are weights different from case weights? – bsbk May 12 '16 at 13:16
  • Don't know. My guess is that they will be treated in the same way, as that is the case in all the statistics packages I have used, but the documentation in nnet is pretty sparse. – Tim May 12 '16 at 23:44

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