I have a question about the use of fixed versus random effects models. Let us consider the following example for motivation:
Suppose we are interested in the relationship between the performance of students on tests and their study time. We randomly select 99 students at a University and record the study time and score for each student in 9 tests.
Now, there are unobserved characteristics that we should control, for example general ability of the student and previous courses taken. These characteristics correlate with the study time so, in order to avoid omitted variable bias, one should use a fixed effects model. However, on the other hand the students where chosen randomly from a large population which suggests we should use a random effects model ...
How can one determine in this case what type of model is appropriate ? Statistically one could use the data and use the Hausman test I suppose, but I wonder whether there is a decision rule that is perhaps motivated a priori by the design of fixed / random effects models and the context of the study?