[R-sig-ME] Random or Fixed effects appropriate?
njbisaac at googlemail.com
Wed Apr 9 11:21:53 CEST 2008
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
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 Robinson
> Department of Mathematics and Statistics Tel: +61-3-8344-6410
> University of Melbourne, VIC 3010 Australia Fax: +61-3-8344-4599
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