I am more than 'a little disappointed' that you expect a detailed
explanation of the problems with your 'bug' report, especially as you did
not provide any explanation yourself as to your reasoning (nor did you
provide any credentials nor references).
Note that
1) Your report did not make clear that this was only relevant to
prediction intervals, which are not commonly used.
2) Only in some rather special circumstances do weights enter into
prediction intervals, and definitely not necessarily the weights used for
fitting. Indeed, it seems that to label the variances that do enter as
inverse weights would be rather misleading.
3) In a later message you referenced Brown's book, which is dealing with a
different model.
The model fitted by lm is
y = x\beta + \epsilon, \epsilon \sim N(0, \sigma^2)
(Row vector x, column vector \beta.)
If the observations are from the model, OLS is appropriate, but weighting
is used in several scenarios, including:
(a) case weights: w_i = 3 means `I have three observations like (y, x)'
(b) inverse-variance weights, most often an indication that w_i = 1/3
means that y_i is actually the average of 3 observations at x_i.
(c) multiple imputation, where a case with missing values in x is split
into say 5 parts, with case weights less than and summing to one.
(d) Heteroscedasticity, where the model is rather
y = x\beta + \epsilon, \epsilon \sim N(0, \sigma^2(x))
And there may well be other scenarios, but those are the most common (in
decreasing order) in my experience.
Now, consider prediction intervals. It would be perverse to consider
these to be for other than a single future observation at x. In scenarios
(a) to (c), R's current behaviour is what is commonly accepted to be
correct (and you provide no arguments otherwise). If a future observation
has missing values, predict.lm would only be a starting point for multiple
imputation.
Even if 'newdata' is not supplied, prediction intervals must apply to new
observations, not the existing ones (or the formula used is wrong: perhaps
to avoid your confusion they should not be allowed in that case).
Only in case (d), which is a different model, is it appropriate to supply
error variances (not weights) for prediction intervals. This is why I
marked it for the wishlist. Equally, one might want to specify
\sigma^2 for all future observations as being different from the model
fitting, as the training data may include other components of variance in
their error variances.
On Sat, 20 May 2006, jranke at uni-bremen.de wrote:
Dear R developers, I am a little disappointed that my bug report only made it to the wishlist, with the argument: Well, it does not say it has. Only relevant to prediction intervals. predict.lm does calculate prediction intervals for linear models from weighted regression, so they should be correct, right? As far as I can see they are bound to be wrong in almost all cases, if no weights for newdata can be given. So the point is that predict.lm needs such an argument in order to give correct prediction intervals for models from weighted linear regression. Also, it strikes me that in the absence of a "newdata" argument, the weights from the "lm" object need to be taken into account for constructing prediction intervals.
Where are the references and arguments?
My updated proposal fixing both points as well as the help file can be found at: http://www.uft.uni-bremen.de/chemie/ranke/r-patches/lm.predict.patch
Not found.
and I wrote up a small demonstration of the problem and my proposed solution: http://www.uft.uni-bremen.de/chemie/ranke/r-patches/lm.predict.pdf
That example is not a valid use of WLS, as you have the weights depending on the data you are fitting.
Kind regards, Johannes Ranke
Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595