interpreting variability explained by exposure in multilevel model with binary outcome

[kb4]

Hi Sas community! I am analyzing whether a census-tract level variable (exposure), which is ordinal and has 5 levels, is associated with a binary outcome (outcome), after adjusting for race (racecat), age (agegrp) and clustering by census tract (tract10). My reference category for exposure is 5 and I found significant associations between each lower level of the variable and the reference category of 5. This is the code I used:

proc glimmix data=dat;                                                                                  

class tract10 exposure racecat agegrp;

model outcome (event='1') = exposure racecat agegrp/ dist=binary link=logit ddfm=bw solution oddsratio cl;

random intercept / subject=tract10 ;                                                                                                                                                              run; 

I have been asked to look into what % variability can be explained by the exposure variable or by the model, but because I can’t use R^2 for this kind of model, I am at a loss. Can anyone provide some guidance on how to answer this question??

[StatsMan]

Under a linear regression, the parameter estimates are chosen in such a way to minimize the residual variance.  That minimization gives you the concept of an R**2 statistic, and you can talk about the percentage of variance that a model explains.

With a logistic regression, you are calculating the parameter estimates using maximum likelihood.  You are not minimizing a residual variance, hence you don't have a traditional R**2 statistic to fall back on.  Several psuedo-R**2 measures have been proposed in the statistical literature, but I don't know that any universal acceptance has been reached on one measure over another.