1
$\begingroup$

I am having trouble accounting for interdependence in data that I would like to model with binomial regression. I am looking at school attendance during two months (43 school days), counting whether a student attended the school on a given day or not (0/1). I would like to model these data with individual-level predictors (e.g. socio-economic status, religiosity, or sex), and I am not interested in predicting attendance on a specific day. This looks like an ideal situation for aggregated binomial regression with 43 trials and binary success/failure outcomes.

For example, in R, I could fit:

glm(cbind(attend, not_attend) ~ sex, family = 'binomial')

where 'attend' is the number of days a student attended the school while 'not_attend' is the number of days the student were not at school. Note that I need to use ratio (instead of counts) because some students were recorded only for 40 days.

However, I am not sure how to take into account the fact that the 43 trials are not independent. E.g. if a student has fever and fails to attend the school one day, it's more likely that the student will not attend also the following day. I considered using beta-binomial regression, but the probability of attending is not random, it is interdependent (although see Ben Bolker's answer here).

The only reasonable solution I could come up with was to nest the data within individual using a multi-level model. For instance:

 glmer(cbind(attend, not_attend) ~ sex + (1|id), family = 'binomial')

where 'id' is a student's identification number. If I understand the model correctly, 'sex' models the varying intercept for each individual rather than the probability of attendance on a particular day. This is getting close to what I would like to do, but I am worried that this approach still does not account for the temporal interdependence within the data.

This looks like a simple question, yet I am failing to find a satisfactory answer.

$\endgroup$
0
1
$\begingroup$

This looks reasonable. One point: "'sex' models the varying intercept for each individual" should be "for each gender". The random constant for each child " (1|id) " models the differences between children not accounted for by 'sex' or other covariables. Then you could do, after fitting, residual analysis and some testing for overdispersion.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.