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I am working on a dataset where I have the percentage of students who passed at a test for each 189 schools in my sample. The data is aggregated, so I have the total number of student who sat the test within each schools, the number of student who passed it, and with this, I computed the schools' students success rates. I am working with R.

I would like to run a regression with schools' success rates as my dependent variable, and a set of independent variables as follow:

  • a binary variable for school type (whether public or private)
  • an ordinal variable for school socio-economic composition (1 Upper Class, 2 Intermediate, 3 Working Class)
  • a variable which indicates the proportion of deprived neighborhoods within the schools' district.

If I understand well, I am looking at two levels: school level, and school district level (with my variable on proportion of deprived neighborhoods in a school's district).

I am a bit confused as to what model would fit this data the best. From what I have seen, I can run a quasi-binomial logistic regression to treat properly my dependent variable. Though, I am confused about whether I should used a logistic model at all, and whether it should be a multi-level model.

Thank you very much for your help!

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It seems that the outcome is bounded between 0 and 1, so you could use a beta glmm with random intercepts for school districts. GLMMadaptive can fit such a model in R.

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