Does anyone know of any good (theoretical or empirical) literature that presents evidence showing the merits of Bayesian measurement error models (where there’s uncertainty in the dependent / response variable) compared to the use of weighted OLS regression models?
To formalise things, consider the following model:
where Y is measured with error, say s .
In a multi-level Bayesian (say brms) setting, one can directly model the measurement error, which intuitively seems to be the right way to go.
The problem I have is—in the field of (economic) literature that I’m working in—most previous studies use weighted OLS regression models, where observations are weighted by, say, 1 / s^2 , to estimate this model.
My co-authors and I have scanned the economic literature but haven’t yet found any good references to support our empirical approach.
Any pointers are appreciated, and apologies in advance if we’ve missed any obvious references.