[R-sig-ME] random as fixed effect

John Maindonald john.maindonald at anu.edu.au
Fri Oct 12 00:46:58 CEST 2012

1. "we want to make inferences about the population": 
Even making year a random effect is not really enough.  We are dealing with 
a time series, and modelling it as a random effect is a weak concession to that 
issue.  If one does nonetheless fit year as a fixed effect, one should at least 
examine the results for the separate years separately, and check on the extent 
to which they point in the same direction.  Published use of the analysis should 
acknowledge the consequent uncertainty.  

Note however that for certain types of balanced models, the estimates of treatment 
effects will be the same irrespective of whether one fits years as random or fixed.
The model is not allowing for a year by treatment interaction, just as the standard
form of analysis of block designs does not and cannot allow for a block x treatment

2. "statistical grounds (the variance is extremely poorly determined)": 
but of course ignoring this component of variance, if it does affect treatment or other 
estimates, does not cause it to go away.

3. "computational reasons": 
The algorithms used in lme4 are general to the extent that they are able to handle
a huge variety of designs.  My experience is using Genstat, which uses quite a
different algorithm. was that it rarely failed for the balanced or approximately
balanced designs that are usual in field and suchlike experimentation.  ASREML
would no doubt perform similarly.

John Maindonald             email: john.maindonald at anu.edu.au
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 12/10/2012, at 12:20 AM, Ben Bolker <bbolker at gmail.com> wrote:

> [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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