# Interpretation of odds ratio when outcome is a percentage

I ran a GEE model, with a dependent variable of "percent of total students with an unexcused absence," using a binomial family. My dependent variable is basically a proportion, with range from 0 to 1 to obey the rules of the binomial family.

I understand that the difference between the non-event/event 0-1 is "zero percent of students with an unexcused absence" and "100% of students with an unexcused absence."

Questions:

• How can I interpret the Odds Ratio for this in a way that makes policy-level, real-world sense?

An interpretation of 1-unit change in independent variable X would be e.g. "a school with a 1-unit increase in X has 0.9 times the odds of having 100% of students unexcused from class at least once, compared to a school without the increase in X." Seems clunky!

You may ask why I used a binomial family rather than a Gaussian family, but according to "Comparison of Logistic Regression and Linear Regression in Modeling Percentage Data" by Zhao, Chen and Schaffner (2001), logistic regression can and should be used for any models with a dependent variable that's modeled as a percentage for various reasons.

If there's no other accurate way to interpret this coefficient through logistic regression and ORs, does anyone have any suggestions about how to model the data to be better interpretable?

In a school with a 1-unit higher X value a randomly picked student has 0.9 times the odds of having been unexcused from class at least once, compared to an other school. (Assuming that all other student and school characteristics modelled are the same.)

• Thanks! That's really helpful. I did not realize the interpretation could be taken down to the random student level, as my unit of analysis is the school. Apr 29, 2011 at 14:48
• I'm skeptical about this interpretation and also about the conclusion that logistic regression must be used when modelling percentages. Seems to amount to saying "we can't model at the student level, only at the school level." Which, by the way, seems to argue against @GaBorgulya's interpretation, neat as it is. I'd like to hear from other people more experienced than myself. Apr 30, 2011 at 0:44