[R-sig-ME] Interactions between fixed and random effects
Jarrod Hadfield
j.hadfield at ed.ac.uk
Mon Apr 5 13:51:59 CEST 2010
Hi,
I agree with Ben, although I find the parameterisation:
lmer(DryMass~Water+(Water-1|Popuation))
easier to interpret. The 2 variances are then the between population
variances for each treatment, and the correlation is the correlation
in the effects of the two treatments over populations.
I also recommend fitting different residual variances for the two
treatments because if differences do exist (eg simple scaling effects)
you can get incorrect estimates of the interaction. I do not think you
can do this in lmer, but I think it is possible in lme.
Cheers,
Jarrod
On 5 Apr 2010, at 12:28, Ben Bolker wrote:
> Christopher Eckert wrote:
>> I apologize if the answer to this query is somewhere totally obvious,
>> but i couldn't find it.
>>
>> I am trying to analyze an experiment where a set of 22 populations of
>> a dune plant species (populations were randomly chosen from across
>> the species' geographic range) were grown in a glasshouse under two
>> different watering regimes (Water = Control vs. Drought). DryMass is
>> the response variable. There was about 20 individuals from each
>> population grown in each Water treatment.
>>
>> Population is a random effect, but I would like to test for an
>> interaction between Population and Water -to ask the question: do
>> different populations respond differently to drought?
>>
>>> From what I can gather this is analogous the random intercepts and
>>> slopes model discussed in Zuur et al and elsewhere, except that I
>>> am examining a categorical predictor (Water) rather than a
>>> continuous predictor.
>>
>> Am I right in thinking that the basic syntax using lme is:
>>
>> lme(DryMass~Water,random=~Water|Population)
>>
>> and the syntax using lmer is:
>>
>> lmer(DryMass~Water+(Water|Population))
>
> I think this is exactly right (and I disagree with the other
> respondent who thought you should just use a fixed effect: you may
> well
> be interested in the among-population variation within the species in
> drought response). One of the nice things about this formulation is
> that it allows you to look at/test the relationship between
> variation in
> Control growth and drought response -- i.e., is there a tradeoff
> between
> growth under good conditions and drought tolerance? -- by looking at
> the covariance in the random effects.
>
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