No, I don't see how it makes any particular sense.  You don't offer
a rationale, and I don't see one, for computing covariances around
the pooled mean. Especially if you are expecting that mean to
have changed over time.

Technically, the difference between inter- and intra-class is
that you use the separate means when you computer an interclass r,
and you use a pooled estimate of means for an intraclass r.   There
are several versions of ICCs because there are several distinct versions
of what you may elect to pool, for more complex designs.

I remember computing an ICC 40 years ago by duplicating a set
of X,Y data, and reversing the order for the second set (to Y, X),
so that a simple Pearson would estimate the intraclass r by
forcing the means to be the pooled value. 

Rich Ulrich

> Date: Fri, 16 Sep 2011 12:20:19 -0400
> Subject: Re: Building a hybrid regression model incorporating intraclass correlation
> Great point of clarification Bruce, and thank you.
> Yes, the intention is to build a prediction model in order to guide
> decisions about reliable change. It is in fact the exact same variable
> that we are measuring twice in the same person that we want to assess.
> It seems that in this situation, the ICC is more appropriate measure of
> association (rather than a Pearson r) but it is not typically used in a
> regression model. Does this make sense, and if so, how do we build a
> model that would include it?
[snip, previous]