2
$\begingroup$

I am working on a multilevel analysis aiming to investigate factors that impact student GPA. The data comes from 16 different schools. To include school effects, we are using a mixed effect model (with random intercepts). However, I would like to understand the effect of school tuition on student GPA and I am confused if this should be included as a fixed effect or random effect, since it is information about the higher level cluster (school).

My lme4 models I have constructed so far are either:

gpa ~ student_study_hours + student_income + 
       student_physical_activity + (1|school / school_tuition)

OR

gpa ~ student_study_hours + student_income + 
       student_physical_activity * school_tuition (1|school)
$\endgroup$
2
  • $\begingroup$ School tuition should be a fixed effect. $\endgroup$
    – Ben Bolker
    May 31, 2023 at 12:39
  • $\begingroup$ Thank you. I was worried that may be a redundacy or colinearity effect since every student from the same school will have the same tuition $\endgroup$
    – Rcs1917
    May 31, 2023 at 12:50

1 Answer 1

2
$\begingroup$

The second option (... + (1|school)) is probably correct. In general the variables that you use as a grouping variable should be categorical and exchangeable (i.e., you should be able to switch labels without changing the meaning). You could conceivably treat tuition as categorical ("low", "medium", "high"), but even then it probably wouldn't be sensibly thought of as exchangeable.

In general modern mixed-model frameworks don't 'care' at what level the fixed effects vary. It does determine whether you can model their variation across units — for example, you could conceivably model the variation of the effect of student family income across schools, but you can't model the variation of the effect of tuition across schools because it doesn't vary within schools.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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