(PR#8877) predict.lm does not have a weights argument for
On Wed, 24 May 2006, Peter Dalgaard wrote:
ripley at stats.ox.ac.uk writes:
(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.
I'd have (d) higher on the list, but never mind. There's also
I find that if you detect heteroscedasticity, then one of the following applies: - a transformation of y would be beneficial - a non-normal model, e.g. a Poisson regression, is more appropriate - the error variance really depends on y or Ey not x, as in most measurement-error scenarios (and the example in ?nls and the example in the addendum to the bug report). - in analytical chemistry as in the example on the addendum to the bug report, there are errors in both y and x to consider, and a functional relationship model is better. So I very rarely actually get as far as predicting from a heteroscedastic regression model.
(e) Inverse probability weights: Knowing that part of the population is undersampled and wanting results that are compatible with what you would have gotten in a balanced sample. Prototypically: You sample X, taking only a third of those with X > c; find population mean of X, (or univariate regression on some other variable, which is only recorded in the subsample).
I would call this an example of case weights (you are just weighting cases and saying `I have 1/p like this', and in rlm there is a difference between (a) and (b) and you would want to use wt.method="case" for (e)).
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