On Wed, 24 May 2006, Peter Dalgaard wrote: > [EMAIL PROTECTED] 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, [EMAIL PROTECTED] 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 ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
