I have used -gllamm- with adaptive quadrature to model a repeated
measurement in time of a continuous outcome , using a model that has both a
level 2 random intercept and slope. I would like to be able to make a
statement about the relative proportion of the total variance associated
with the 2nd level random effects relative to the proportion that is
explained by a fixed effect treatment variable.
My reading (Snijders & Bosker, 1999; Hox, 2002) suggests this is
problematic for a number of reasons. However, I think, in my case, that it
would be very useful to be able to make such a statement, even if only
approximate, about the relative magnitude of the total variance
attributable to the level 2 random effects as it contrasts with the
relative magnitude of the variance explained by a treatment variable. ( In
my case, I would like to point out that despite the treatment being
significant, the magnitude of the effect is small versus the inherent
variance ascribable to the level 2 units.)
Can you suggest a reasonable basis for making this statement when gllamm is
used for a model such as this? I would be more comfortable deriving an
approximate R2 if the model was a random intercept only, I am unsure of how
to do this given a random coefficient also. I will confess to following
conceptually, but not specifically, the Snijders & Bosker discussion, and
don't think I am proficient enough to implement it.
I would be most appreciative of any insight you can share on this.
