repeated-measures correlation coefficient?

The answer is "sort of". If you've already looked at measures like
intra-class correlation, then you might start to see some of the
problems. A parallel issue on the difficulties with R^2 and the trouble
defining it for the (G)LMM case is discussed on the FAQ:

https://rawgit.com/bbolker/mixedmodels-misc/master/glmmFAQ.html#how-do-i-compute-a-coefficient-of-determination-r2-or-an-analogue-for-glmms

including a link back to one of Doug Bates' enlightening "half-rants".
(No sarcasm there -- DB doesn't speak up too often on the list, but I
always learn a lot when he does!)

There are two intuitive problems. One is a direct carryover from
multiple regression -- measuring correlation between x1 and y is always
tricky if you want it conditional on x2 or the interaction x1 and x2.
The other is that it's not entirely clear what a good regression measure
is with a multilevel model because of things like Simpson's Paradox --
it's quite possible for the correlation within each level (e.g. within
each participant) to be in one direction, but the correlation across
participants to go in the other direction. Which one is the "correct"
correlation? The obvious measures of "correlation across trials,
ignoring grouping levels", "average of correlations computed within
groups" and "correlation across within-group averages" would/could all
individually fail to capture the complex relationship between x and y
and may be misleading in certain circumstances, but might suffice for
what you're doing. It really depends on what question you're trying to
answer. When you have multiple grouping factors (e.g. participants and
items), things only get more complicated.

Maybe somebody else has heard of a new measure that addresses these
issues?

Phillip

I've seen linear mixed-effects models described as "repeated-measures
regression analyses" and I'm wondering whether there exists something like
a "repeated-measures" version of the Pearson correlation coefficient. For
my dataset the linguistic content of interviews has been coded on several
dozen dimensions (like proportion of words that are pronouns, proportion of
words that involve positive emotion, overall number of words, etc.), and
I've been asked to show the correlations between lots and lots of these
dimensions. The problem is that the data come from perhaps 35 different
interviewees, who are represented in the data different numbers of times
(from 1 to 90 interviews). My searches on this topic all point to the
intrac-class correlation, but when I read the details it seems obvious to
me that this is not what I want.

--Lee

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