I have several dependent variables that are measures of racial disproportionality; I've calculated them as:
% of events caused by racial minority group / % of events caused by racial majority group
I have a dependent variable for each racial minority group in my sample. I am running longitudinal Generalized Estimating Equations (GEE) on these models, however I am somewhat stumped as to which family is appropriate for these dependent variables. The probability range for my ratios are truncated at 0, as it's not possible to have negative values in my DVs. This makes me question the validity of using a Gaussian family for my models.
The idea behind these variables is that a ratio greater than 1 indicates some level of greater burden of events that a given racial minority is bearing compared to the racial majority, and a ratio less than 1 indicates the opposite.
- What would be the most appropriate family to use for my GEE regressions?
I misspoke about the racial disproportionality measure I was using. The correct formula is:
% events by minority / % of total enrollment that is minority OVER % events by non-minority / % of total enrollment that is non-minority
Because they are ratios, the number of observations with value less than 1 is comparable to the number of observations greater than 1, with the lower bound being 0 and the upper bound being non-bounded. Looking at the histograms of my response variables, they definitely seem to fit a negative binomial distribution better than the normal. The QIC (GEE adjustment to AIC) confirms this suspicion. My questions now are:
- Can I trust this evidence to move forward with the negative binomial family?
- If so, how do I possibly interpret the exponentiated coefficients from the resulting models? They don't see to be Incidence Rate Ratios, as one would interpret them to be from count variables...