I'm having a hard time figuring out whether a MLM would buy me anything with an analysis I'm doing
Questionnaires were administered to university classes and lets say I'm interested in variables
X2 on that questionnaire. I'm interested in whether a students class grade can be predicted from those variables:
grade ~ b1X1 + b2X2. I predict that both
b2 will be significant and positive.
So far thats just straightforward multiple regression. The reason I started thinking about MLM is because class grades at this university are scaled and professors will scale differently. That means for one class, the mean grade might be 80, whereas for another class mean grade might be scaled down to 60. This might turn the model into something more like
grade ~ b1X1 + b2X2 + b3Class
I only just started learning about MLM so likely misunderstanding some of the concepts here. I initially thought that due to scaling, the regression surface for each class is going to have a different intercept so maybe I should run a random intercepts model. Further thinking changed my mind on that because I'm going in fully expecting mean grades for each class to be different precisely because of scaling, so seeing significant variance in grade due to class isnt going to tell me anything I dont already know/expect
Then I wondered whether a random slopes model would actually be more appropriate because while I expect the intercepts to be different for each class, I dont know if the slopes will differ, so maybe a different slope should be modelled for each class (even though I have no theoretical reason to suspect that slopes will differ between classes)
- Is grade scaling enough to warrant sacrificing power and running an MLM?
- Under what conditions might MLM be useful here?
- Is my logic correct in thinking that random intercepts should not be tested here?
OR, do I have this completely backwards, and should instead be testing whether classes differ on
X2 instead of grade?
I have about 800 samples in total
Split into 7 different classes
Each class has a different number of students. Most have around 130 students, one class has 80, and another one has about 50