I am working on a study of how different scholarship programs at a university may influence student retention (i.e., if students are still enrolled at the university one year later). Each student can receive a different combination of scholarships--they can also lose or gain scholarships over time. All students in the study started in the same cohort/semester.
My data has the following variables:
- Student ID: identifier for each student
- Term: semester that the student had the scholarship (categorical)
- Award Type: whether scholarships are awarded based on merit, financial need, or special interest (categorical)
- Award Prop: the proportion of student expenses that the scholarship covers - for example, an Award Prop of 0.50 means that the scholarship will cover half of a student's college expenses (continuous)
- Outcome: whether or not the student persisted a year later (binary)
An example of the data is provided below:
ID Term Award Type Award Prop Outcome (Persisted?) 0025 Fall 2012 Merit 0.25 Y 0025 Fall 2012 Need 0.50 Y 0025 Spring 2013 Need 0.50 Y 1310 Fall 2012 Interest 0.30 N 1310 Spring 2013 Interest 0.30 N 1229 Spring 2013 Need 0.90 Y 1229 Spring 2013 Interest 0.10 Y 2843 Fall 2012 Merit 0.50 N
Due to the fact that I'm modeling a binary outcome for individuals sampled several times, I am thinking of approaching this with a mixed effects logistic regression with repeated measures using
lme4 in R.
I think the way to structure this might be to nest ID within Term as a random effect:
glmer(Outcome ~ AwardType + AwardProp + 1|(Term/ID), family=binomial)
First, based on the parameters above, does this seem to be a sound way to approach this analysis?
Second, should I be concerned about potential issues with missing/unbalanced data (since each person has different scholarships, a person with a scholarship one semester may not have it in other semesters, etc.)? One article I read said that mixed effects modeling should take care of this.