Whether or not you need a mixed model, e.g. random versus fixed slopes, depends on how you intend to use results.
Suppose you have lines of depression vs lawn roller weight calculated for a number of lawns. If the data will always be used to make predictions for one of those same lawns, a fixed slopes model is fine. If you want to use the data to make a prediction for another lawn from the same "population" (the population from which this lawn is a random sample, right?), you need to model the slope as a random effect. Now for a more subtle point: In the prediction for another lawn situation, it is possible that the slope random effect can be zero, and analysts do very commonly make this sort of assumption, maybe without realizing that this is what they are doing. You can test whether the slope random effect is zero but, especially if you have data from a few lawns only, failure to reject the null (zero random effect) is not a secure basis for inferences that assume that the slope is indeed zero. The "test for zero random effect, then infer" is open to Box's pithy objection that "... to make preliminary tests on variances is rather like putting to sea in a rowing boat to find out whether conditions are sufficiently calm for an ocean liner to leave port". John Maindonald email: [EMAIL PROTECTED] phone : +61 2 (6125)3473 fax : +61 2(6125)5549 Centre for Mathematics & Its Applications, Room 1194, John Dedman Mathematical Sciences Building (Building 27) Australian National University, Canberra ACT 0200. On 8 Nov 2007, at 1:55 AM, Irene Mantzouni wrote: > Is there a formal way to prove the need of a mixed model, apart from > e.g. comparing the intervals estimated by lmList fit? > For example, should I compare (with AIC ML?) a model with seperately > (unpooled) estimated fixed slopes (i.e.using an index for each > group) with a model that treats this parameter as a random effect > (both models treat the remaining parameters as random)? > > Thank you! > > _______________________________________________ > [EMAIL PROTECTED] mailing list > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
