Random or Fixed effects appropriate?
Dear all, Thanks for the comments and apologies for not providing more information. I (mis)judged it would be better to discuss the issue abstractly. There should be enough levels to estimate the variance of C and at least one other random effect: Number of obs: 1242, groups: D, 269; C, 64; B, 8; A, 3 My interpretation of comments by all three respondents is as follows: 1) extracting the random effects/BLUPs/conditional modes is reasonable in general 2) a taxonomy might be considered fixed or random, depending on the question and the number of units/levels 3) In my case, it would be better to use the conditional modes for x|C than to fit x*C as an interaction term. Best wishes, Nick
On 08/04/2008, Andrew Robinson <A.Robinson at ms.unimelb.edu.au> wrote:
On Tue, Apr 08, 2008 at 07:10:16PM +0200, Reinhold Kliegl wrote:
> > My dataset has one continuous normally-distributed fixed effect and > > four random effects that are nested (in fact, it is a taxonomy). For > > simplicity, I've removed the variable names, so the dataset has the > > following structure: > > > > y ~ x | A/B/C/D
> It would be good to know how many units/levels you have for each of > your four random effects. Those with fewer than, say, five, are good > candidates for being specified as fixed effects. Think how many > observations you need to get a stable estimate of a variance! >
> > lmer( y ~ x + (1|A) + (1|B) + (1|C) + (1|D) + C + x:C) #error: > > Downdated X'X is not positive definite, 82
> You cannot include C both as a random and a fixed effect
I do not believe that this is generally true. See, for example,
> require(lme4) > (fm1 <- lmer(Reaction ~ Days + Subject + (Days|Subject), sleepstudy))
Therefore I am uncertain as to how you can draw this conclusion without more information about the design (which the poster really should have provided).
> > lmer( y ~ x + (1|A) + (1|B) + (1|C) + (1|D) + x:C) #gives sensible results
> If this gives sensible results, I suspect you have very few levels of > C, say, 2 or 3? > In this case, definitely specify C and x and their interaction as > fixed effects, e.g.: > lmer( y ~ x*C + (1|A) + (1|B) + (1|D) > > The following may not apply to your case, but it might: Sometimes > people think that a nested/taxonomic design implies a random effect > structure (e.g., schools, classes, students). This is not true. If you > have only a few units for each factor, you are better off to specify > it as a fixed-effects rather than a random-effects taxonomy. (Of > course, you lose generalizability, but if you want this you should > make sure you have sample that provides a basis for it.)
I can see the sense behind this position but sometimes a few units are all that is available, and including them in a model as fixed effects muddies the statistical waters, especially if they are the kinds of effects that a model user will be unlikely to naturally condition upon. I do agree that if there are problems with model fitting and/or interpretation when the design is rigorously followed, then a more flexible approach can and should be adopted, and appropriate allowances must be made.
> The interpretation of conditional modes (formerly knowns as BLUPs, > that is "predictions") is a tricky business, especially with few > units per levels.
Sorry, I think I've missed something. In what sense are the conditional modes formerly known as BLUPs? Andrew -- Andrew Robinson Department of Mathematics and Statistics Tel: +61-3-8344-6410 University of Melbourne, VIC 3010 Australia Fax: +61-3-8344-4599 http://www.ms.unimelb.edu.au/~andrewpr http://blogs.mbs.edu/fishing-in-the-bay/