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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.

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Have you thought about using a survival model (cox regression) here? I think such a model will take the temporal characteristic of your data better into account. Given that your treatment/exposure can vary over time, it also make sense to look at models for time varying exposures, e.g. here: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4351798/

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It seems like you may be getting a lot of overlaps in the 1-year follow-up periods for different scholarships obtained by the same student (e.g., first and second observations in your example). I don't know if it is true in your case, but I suppose it is also possible for a student to obtain a new scholarship during the 1-year follow-up period from a previous scholarship. So rather than simply having correlated observations for the same individual, you'll have different observations for the same outcome. My suggestion would be that rather than treating scholarships as separate observations, you could combine current observations, such that you have a clean 1-year follow-up period per observation (clean meaning no additional scholarships granted and no scholarships lost). Then the predictor variables can be constructed to indicate what scholarships were obtained leading up to the start of that 1-year period. The outcome variable would still measure if the student was still enrolled at the university one year later.

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  • $\begingroup$ Sorry, I just wanted to follow up for clarification. Do you mean that I should convert my data from a long format to wide format (i.e., one observation record per student/ID)? I'm also a little unsure about your suggestion here: "Then the predictor variables can be constructed to indicate what scholarships were obtained leading up to the start of that 1-year period." Does this mean that I would have to have one column per each scholarship type? $\endgroup$ – K Chi Apr 30 '19 at 14:05
  • $\begingroup$ I envision one observation per 1-year follow-up period, so sometimes I expect there to be multiple observations per student (if a student received multiple scholarships at least 1 year apart). So you can still model repeated measures in that case, but the key point is that you only have one observation per outcome (did student stay enrolled for 1 year). Creating separate variables for each scholarship type makes sense. There can also be variables for how many total scholarships there were and how far apart they were granted. $\endgroup$ – AlexK Apr 30 '19 at 18:58

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