[R-sig-ME] Mean of random effects same as fixed effect?

[Douglas Bates]

On Sun, Jan 8, 2012 at 1:55 AM, Jens Åström <jens.astrom at slu.se> wrote:
> Hi all,
>
> A couple of weeks ago I posted a question but got no answers. Here goes
> a second attempt, now shorter and more general.
>
>
> Are the following two model specifications interchangeable, or is there
> a statistical reason for why it is not OK to express model 1 in the form
> of model 2?
>
> Model 1)
> y=fixed.intercept+fixed.slope*x+random.intercept+random.slope*x
>
> Model 2)
> y=random.intercept*x+random.slope*x
> fixed.intercept=mean(random.intercept)
> fixed.slope=mean(random.slope)

You would need at least equal group sizes and identical values of the
covariate with respect to which you have a random slope to be able to
count on this.  Even then I'm not entirely sure it would work.

Generally the unconditional distribution of the random effects is
defined to have a mean of zero.  I don't know how you are defining
yours (and prefer not to wade through BUGS/JAGS model specifications
to find out).

> The reasons for my asking is that I have trouble getting convergence
> with model specification 1, when the random intercepts and random slopes
> are correlated, but specifying it as model 2 seemed to work. This is me
> trying to implement some standard mixed models in BUGS/JAGS. Original
> post with complete working example is here:
> http://markmail.org/message/vhqeq4j3kldttlt5
>
>
>
> I'm happy for any comments, with or without BUGS/JAGS code.
>
> /Jens Astrom
>
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