[R-sig-ME] Random or Fixed effects appropriate?

[Nick Isaac]

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/
>