[R-sig-ME] mixed effects models and multiple explanatory variables that are correlated

[Laurence O'Dwyer]

Hello to mixed-effects model experts,

                                                       I am currently
trying to run an analysis on structural MRI data and would like to use
glmer or MCMCglmm to model my data. I have basic statistical knowledge and
would appreciate any guidance in the use of these R-tools from experts in
mixed effects models.

                In a crude way, I am interested in a model that might look
something like the following:



moo = MCMCglmm(autism_spectrum_scores ~ Diagnosis + Striatum + Thalamus +
Amygdala + Hippocampus,

                                          random = ~ADHD_symptom_scores

                                                    + age

                                                    + scanner_type

                                                    + gender

                                                    + total_brain_volume,

                                          data=dat)



It is a study of ADHD and autism. I have data for ~170 children with ADHD,
~70 unaffected siblings, and ~80 controls - this is the fixed factor
"Diagnosis".

I have the volumes of particular structures in the brain. These are the
fixed factors Striatum, Thalamus, etc. I am interested to know their
relationship with a scale of autistic traits (NOT ADHD traits) within all
experimental groups. For example, smaller volumes in the Striatum may be
associated with increased autistic traits.

For the random effects, I want to control for differences in ADHD symptoms,
age, scanner type (two different scanners were used to collect the
volumetric data), gender and total brain volume.

A key point of the analysis would be to establish the relationship between
structural volumes and autistic scores, when levels of ADHD have been
controlled for.

One problem is that all the structural volumes are closely correlated.
Previously, when working with two structural volumes that were correlated,
I used the regression residuals of one structural volume relative to the
other to isolate the unique contribution of each explanatory variable,
independent from what was shared between them. But, I don't think I can use
this approach with four structures that are highly correlated.

                There are probably many other statistical flies in the
ointment relating to the above. If anyone has any pointers as to how to
deal with the situation when multiple explanatory variables are correlated,
in a mixed-effects models framework, they would be appreciated.

                Thanks; Larry