[R-sig-ME] random as fixed effect

Ben Bolker bbolker at gmail.com
Thu Oct 11 15:20:02 CEST 2012

 [cc'ing back to r-sig-mixed]

On 12-10-11 09:08 AM, Andrew Koeser wrote:
> Ben,
> I was going to expand on her question, but you beat me to the punch.
> In agriculture, we typically run the same CRD, RCBD, etc (with all fixed
> effects) for 2 to 3 years. In doing this (given instruction from past
> biometry teachers), I would call year/trial random as I do not really
> care about what year/trial is best and I hope to be able to talk about
> the wider range of conditions seen outside of our time frame. I noticed
> in an archived post that you stated 2-3 years/varieties/etc are not
> enough to base an estimate of the variance of the population of effects.
> Is that ultimately the deciding factor in determining whether or not
> year/trial is fixed or random? In other words, is that sufficient
> justification for calling year/trial fixed?
> This is my one major stumbling block in transitioning from SAS to R. I
> greatly appreciate you comments.

  I would argue this is not really a problem in transitioning from SAS
to R, but from classical method-of-moments ANOVA to modern mixed models;
you will have the same kinds of results with SAS PROC MIXED as you will
with nlme/lme4.  http://glmm.wikidot.com/faq#fixed_vs_random  goes into
more detail.  There is a distinction between _conceptual_ or
_philosophical_ random effects (we don't want to make inferences about
specific values, we want to make inferences about the population) and
_computational_ random effects (we want to estimate effects with
shrinkage, we have enough levels to estimate the variance reasonably
well). I would agree that in the best of all possible worlds you would
somehow be able to generalize from an experiment that was run in two
successive years to the performance of a crop variety across all
possible years (and estimate the variance among years accurately), but
that doesn't work particularly well on statistical grounds (the variance
is extremely poorly determined), and in the case of mixed models it
generally fails for computational reasons as well.

> Andrew
> On 10/11/2012 7:07 AM, Ben Bolker wrote:
>> joana martelo <jmmartelo at ...> writes:
>>> I’m modeling fish activity data with a gaussian distribution for scores
>>> obtained from Principal Component Analysis. My explanatory variables are
>>> group size, fish length, temperature and year. Because year has only two
>>> levels I know I can’t use it as a random effect. However, do you
>>> think that
>>> considering year a fixed effect will inflate the effect of the other
>>> explanatory variables?
>>    No.  On the basis of what you've told us, using year as a fixed
>> effect seems perfectly sensible.  You might want to check whether
>> there are important interactions between year and the other explanatory
>> variables ...
>>    (Your title seems a bit odd.)
>>    Ben Bolker
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