[R-sig-ME] independent random effects with equal variances

[Douglas Bates]

On Wed, May 4, 2011 at 1:02 PM, Christos Hatzis
<christos.hatzis at nuverabio.com> wrote:
> Independence, equal variance and the implicit normality assumption wouldn't
> imply that these random effects are IID from the same N(0, sigma)
> distribution?  Wouldn't then this be equivalent to

> y ~ x + (1|R)

> where R is the "combined" random effect?

Except that you can't define a factor R with the combined levels.
Consider, for example, the Penicillin data in the lme4 package.  A
model with independent random effects having one variance for the
plate and one variance for the sample random effects has the model
formula

diameter ~ 1 + (1|plate) + (1|sample)

for a total of 30 random effects (24 plates and 6 samples).  You can't
generate a factor with 30 levels that can be decomposed into 24 levels
for plate and 6 levels for samples.

> -----Original Message-----
> From: r-sig-mixed-models-bounces at r-project.org
> [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Douglas Bates
> Sent: Wednesday, May 04, 2011 1:56 PM
> To: Hae Kyung Im
> Cc: r-sig-mixed-models at r-project.org
> Subject: Re: [R-sig-ME] independent random effects with equal variances
>
> On Wed, May 4, 2011 at 10:47 AM, Hae Kyung Im <haky at uchicago.edu> wrote:
>> Dear list,
>
>> does anyone know of an easy way to enforce equal variance for two
> independent random effects?
>
>> So I would like to fit this model with equal variances for R1 and R2
>
>> y ~ x + (1|R1) + (1|R2)
>
> I don't think that would be easily done under the current setup.
>
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