[R-sig-ME] zero variance and standard deviation in random effects

[Phillip Alday]

I think one useful case for treating small, closed populations as a
random-effect is that you get the shrinkage/regularization. Of course,
the estimated variances will be nonsense. But the regularization may
still be useful for other things, cf. "new style" random effects:

http://www.biostat.umn.edu/~hodges/PubH8492/Hodges-ClaytonREONsubToStatSci.pdf

http://www.biostat.umn.edu/~hodges/PubH8492/Lectures_13.pdf

Of course, this is the statistical equivalent of "if you have to ask,
you can't afford it" / "shouldn't be using it".

(This is a general comment and _not_ advocating for any approach in this
particular case -- I haven't looked at the OP's problem enough to have
any idea about which approach is suitable there.)

Phillip

On 2/11/21 6:58 pm, Rolf Turner wrote:
> 
> On Tue, 2 Nov 2021 11:20:25 -0400
> Ben Bolker <bbolker using gmail.com> wrote:
> 
> <SNIP>
> 
>> -- it's just hard to estimate variance reliably from a sample of
>> three. (See
>> https://rpubs.com/bbolker/4187
>> for some simulated examples.) One standard approach to this problem
>> is to treat province as a *fixed* effect.
> 
> <SNIP>
> 
> To me it makes little or no sense to treat "province" as a random
> effect in any case.  Conceivably Alberta, Saskatchewan and Manitoba
> could have been chosen at random from the 10 provinces, but it sure
> doesn't look like it.  Moreover drawing inferences about the
> "population of provinces" (which is the whole idea of random effects)
> would be highly dubious, given the completely different nature of (e.g.
> PEI) from the three prairie provinces in the "sample".
> 
> The data set involves the three prairie provinces; inferences drawn can
> really only apply to those provinces.  Ergo "province" is a fixed
> effect.
> 
> cheers,
> 
> Rolf Turner
>