[R-sig-ME] number of random-effects levels

[Andrea Cantieni]

Dear Ben,

Thank you very much! That helps me.

Best, Andrea


Am 05.12.2012 um 04:56 schrieb Ben Bolker <bbolker at gmail.com>:

> Andrea Cantieni <andrea.cantieni at ...> writes:
> 
> 
>> I am fitting a classroom data set with lmer() with completely nested
>> data, i.e. pupils are nested within classes, and classes are nested
>> within schools. I have read about the random effects levels:
>> "...there must be a reasonable number of random-effects levels
>> (e.g. blocks) — more than 5 or 6 at a minimum."
>> (http://glmm.wikidot.com/faq).
> 
>> 
>> The model looks like
>> 
>> fit0 <- lmer(theta ~ (1|CLASSID) + (1|SCHOOLID), data.ml)
>> 
>> and the contingency table looks like
>> 
>> xtabs(~ SCHOOLID, unique(subset(data.ml, select=c(SCHOOLID,CLASSID))))
>> 
>> SCHOOLID
>> 1  2  3  5  6  7  8  9 10 12 13 14 15 16 
>> 5  3  3  4  8  3  1  3  4  2  5  3  3  2 
> 
>> My question is, whether the reasonable number of random-effects
>> levels of 5 or 6 means the total number of levels (i.e. 49 for
>> CLASSID, and 14 for SCHOOLID) or the numbers of levels for CLASSID
>> within SCHOOLID (i.e. 1 to 8 for CLASSID).
> 
>  It's the former; it's the number of random-effects values from which you're
> trying to estimate the relevant variances.  Since you're assuming that
> the variance of classes within schools is the same for all schools,
> you have all 49 classes with which to estimate the variance.
> If you were trying to fit a model where the variance itself varied
> from school to school, you'd probably be in trouble, because then
> you'd be trying to fit the variance from very small numbers of
> samples (although you could imagine making the variance itself
> a random effect that varied among schools ... but (a) this would
> be a bit hard to specify in lmer [I would probably try BUGS for that
> model] and (b) you might still have trouble because of lack of
> data for this model -- my guess would be that you'd end up with
> an estimate of zero among-school variation in variance ...)
> 
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