[R-sig-ME] models with no fixed effects
a.fugard at ed.ac.uk
Fri Sep 12 00:57:07 CEST 2008
On 11 Sep 2008, at 22:06, Peter Dixon wrote:
> On Sep 11, 2008, at 2:15 PM, Andy Fugard wrote:
>> Peter Dixon wrote:
>>> On Sep 11, 2008, at 1:15 PM, Douglas Bates wrote:
>>>> I should definitely add a check on p to the validate method. (In
>>>> ways I'm surprised that it got as far as mer_finalize before
>>>> an error). I suppose that p = 0 could be allowed and I could add
>>>> conditional code in the appropriate places but does it really make
>>>> sense to have p = 0? The random effects are defined to have mean
>>>> zero. If you have p = 0 that means that E[Y] = 0. I would have
>>>> difficulty imagining when I would want to make that restriction.
>>>> Let me make this offer - if someone could suggest circumstances in
>>>> which such a model would make sense, I will add the appropriate
>>>> conditional code to allow for p = 0. For the time being I will just
>>>> add a requirement of p > 0 to the validate method.
>>> I think it would make sense to consider a model in which E[Y] = 0
>>> when the data are (either explicitly or implicitly) difference
>>> scores. (In fact, I tried to fit such a model with lmer a few
>>> months ago and ran into exactly this problem.)
>> Wouldn't you still need the intercept? The fixed effect tells you
>> whether on average the difference differs from zero. The random
>> effect estimates tell you by how much each individual's difference
>> differs from the mean difference.
>> Andy Fugard, Postgraduate Research Student
>> Psychology (Room S6), The University of Edinburgh,
>> 7 George Square, Edinburgh EH8 9JZ, UK
>> +44 (0)78 123 87190 http://figuraleffect.googlepages.com/
>> The University of Edinburgh is a charitable body, registered in
>> Scotland, with registration number SC005336.
> In the context in which this arose, I was interested in assessing the
> evidence for an overall positive difference score (i.e., that E(Y)>0),
> and my strategy was to compare the fit of two models, essentially,
> (1|Subject) and D~1+(1|Subject), using AIC values. To get a sensible
> assessment of the evidence for the fixed effect, it seemed to me that
> one would want to have the same random effects in the two models being
> compared. The second model is clearly more obvious, but the
> interpretation of D~0+(1|Subject) could be that subjects differ
> randomly in their response to the treatment, but that there is no
> consistent effect in the population.
I /think/ I get this, by analogy with how I use AIC/BIC/LRTs to test
predictors. But still a bit confused. The two models are:
y_ij = a + b_j + e_ij (1)
y_ij = c_j + e_ij (2)
Suppose a != 0 in model 1. Then in model 2:
c_j = b_j + a.
(Maybe it's not as simple as this!) But I'm not sure what effect that
would have on the e_ij's - and my intuition says that's what's going
to affect the fit. Also I would have thought model 2 would give a
better fit since having one fewer predictor is going to have less of a
penalising effect in the AIC and BIC.
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.
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