[R-sig-ME] Adding Level for non-repeated measurements

[David Duffy]

> But in my case, it seems adding a level is not theoretically possible. So,
> there certainly is a gap in my knowledge resulting from a carryover from
> mixed meta-regression models where we actually can have an
> individual-specific random effects with the exact same data structure.

A meta-regression is not that different from your setup, where schools replace studies,  which is where the meta-analysis 
variances are coming from (they are summary statistics which you estimate yourself if you have the study datasets).

Instead of correlated residuals, consider an interaction model, where the phenotype of student 1 is a cause of that in student 2 (recursively, rather than ordinary AR). This leads to increased (or decreased) within-school variance depending on the sign of the interaction, which you can 
detect by comparison to groups where you assume the interaction is zero. Such models are also relevant when there is rating contagion (student 1 is compared by the rater to peers). This could be in addition to the school effect, which is like a single factor with equal loadings for each pupil (there are path diagrams for all these different possible models, which may not make clear what data you need to make them estimable/identified). 

HTH, David Duffy.