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I am trying to make a model with a response variable of performance on a test (interval data), along with predictors for test performance. It's a threshold test, so anyone that passes it will not have to sit it again, but those that fail it may do so. The data stretches over a number of years.

This means the data has some repeated individuals in it over time, but the majority of those taking the test, do so only once. There are far fewer individuals that show up twice, and fewer still showing up more than twice.

I don't want to take individuals who retake the test out, but this means there is some non-independence in the data. From my relatively basic understanding of this, I think this means I need some sort of Generalized Linear Mixed Model (GLMM), or Generalized Estimating Equations (GEE) model to account for repeated measures, with the random effects being person ID. Is this correct?

If so, can I still undertake a GLMM or GEE if there are relatively few instances of someone taking a test more than once? Also, would it be best to include year of test sitting as a random effects variable or a fixed effect one?

I looked at other similar questions, but single observations per individual/company etc seemed to be in the minority in those examples.

Can I fit a mixed model with subjects that only have 1 observation?

Random intercepts model - one measurement per subject

Any advice would be much appreciated.

Edit: Thanks for getting back to me. To clarify: all of the results for everyone who have taken the test are in the dataset, including instances where they have failed. For example, person 1 could have scored 35 on their first attempt and failed, and then 40 on their second attempt and passed, and they would be in the dataset twice with only their scores differing.

Overall, I'm trying to infer from the data, the influence of the predictors we have on the test score. Overall, the data would perhaps be considered mostly to be pooled cross-sectional data, but with some instances of repeated measures (so from what I understand, it's a weird mix between pooled cross sectional data and panel data).

I couldn't see much online about what to do with such data, as I'm guessing it doesn't appear very much in statistical research.

I think, without the repeated individuals I could fit a standard multiple regression model with time dummies, as the data would be independent, but the addition of some repeated individuals has got me confused about how best to proceed.

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From your description, it seems that you have time-to-event data, i.e., the time until a subject passes the test. If you would fit a repeated measurements model, you would assume that even if a subject passed the test, he/she could take it again in the future and be either successful or not again.

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    $\begingroup$ it seems possibly more complicated than that. It sounds to me like the OP wants to predict a numerical score, with some conditioning; individuals who are in the data set more than once must have failed (at least) all but the last time (it's not clear to me if the scores are entered if the subjects failed on their most recent attempt, or if the data includes only people who have passed eventually) $\endgroup$
    – Ben Bolker
    Commented Jan 7, 2019 at 20:18
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    $\begingroup$ @BenBolker yes, I think it needs to be clarified what really the purpose is. $\endgroup$
    – Dimitris Rizopoulos
    Commented Jan 7, 2019 at 21:28

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