Suppose we have a hierarchical model regression model (pupils nested in schools) with random intercept for schools. We run a model with data covering a particular period, and observe the variance of the random intercept.
Now we run the same model (same model formulation: ie, same outcome and predictors etc) on a dataset consisting of the same schools, but for different pupils at a different time.
Now, suppose also that the incidence of the model outcome is significantly different in the two models, but the fixed effects and the the variance of the random intercept is the same (or very similar): what can we conclude from this ? Is it valid to say that whatever has happened to change the outcome has affected all the schools uniformly ?
The outcome of my model is the incidence of bullying. I wondered if maybe the incidence changed because of something that does not affect individual schools differently, such as the local education authority having an awareness/monitoring/policing/funding policy that affected all schools the same - in that case, wouldn't the random intercept be unchanged ?