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I have some data about people applying for a service - they are either successful or not successful in their application. I'm using logistic regression to investigate whether there is a relationship between being successful and some demographic variables (e.g. gender, ethnicity).

There is a maximum to the number of people that can have access this service. So each application isn't independent - whether or not a particular person is successful can depend on who else applied.

Is my use of logistic regression appropriate, given applications aren't independent?

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  • $\begingroup$ In addition to the lack of independence, if the number of trials is not fixed, how could binomial be appropriate? $\endgroup$
    – John Coleman
    Commented Mar 26, 2018 at 11:11

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In general, it's not appropriate.

The remaining question is, wether the practical impact in your application is relevant to your usecase. To assess this, you could for example perturbate the applications in the training set (let people apply in different groups than they did in originally) and check how that imacts your test error. Depending on the impact you can decide if that is acceptable.

If it's not acceptable you should probably restructure the problem.

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  • $\begingroup$ So the issue with non-independence is the effect it will have on standard errors in my model? $\endgroup$
    – edstatsuser
    Commented Apr 4, 2018 at 20:54
  • $\begingroup$ Ultimately that is the issue, yes. $\endgroup$
    – Denwid
    Commented Apr 6, 2018 at 5:07
  • $\begingroup$ Are you able to point me in the direction of an example where your suggested check for the impact of non-independence is used (doesn't have to be be logistic regression specifically)? $\endgroup$
    – edstatsuser
    Commented Apr 7, 2018 at 5:36
  • $\begingroup$ I don't have a reference at hand. I proposed this based on common sense: If perturbing the groups has a large impact on the test error, then at least you know 1. the grouping does mess up your logistic regression, and 2. assuming independence (which is what you do by using logistic regression) is probably a bad idea. Or maybe you find out the groups have only a small impact on the test error and you can decide to roll with it -- but at least you quantified the "price you pay" by doing that. $\endgroup$
    – Denwid
    Commented Apr 8, 2018 at 7:04
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As mentioned by the existing answer, it is in princple not appropriate to use logistic regression in this kind of situation. It could be that you would still get decent results, but I would go for a different approach.

I assume you will find an extensive literature on this topic, if you look into statistical models for university/college admission.

One idea would be the following: Assume that there is some kind of implicit "qualification score" that is formed by those selecting people. Let's assume that it's a continuous number (e.g. for a university entrance some kind of academic aptitude score plus bonus points for extracuricular activities) and the score everyone gets is unchanged depending on who else is applying (i.e. this would assume that there's no attempt to get the number of people with certain backgrounds balanced in any other way than giving some groups bonus points on the overall score). In that case you could look at this as observing that the successful applicants had higher qualification scores than those that were not successful. However, you do not know how the successful and unsuccessful ones were ordered - although you might learn a little bit about this if e.g. some successful applicants do accept the offer and the next most suitable ones get an offer.

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  • $\begingroup$ I'm not sure how your suggestion is useful is practice, could you please expand on that? $\endgroup$
    – edstatsuser
    Commented Apr 4, 2018 at 20:58

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