I have fitted multionomial regression models to two different datasets, but from the same country, corresponding to the same event.
Dataset A is an aggregated dataset (at country level), relating a 6 level response scale to a explanatory variable V. The sample size is 41, each individual point in the sample representing the counts of instances of each response level for a given value of V.
Dataset B is a disaggregated dataset, at city level (1 city), relating the same 6 level response scale to the same V as dataset A. Each indidvidual point in the sample is a pair of (V, response level). The sample size is 265.
I expected that, given the information loss through aggregation for dataset A, the fit of the model would be worse than when performing the fitting of the model to B. However, I observe the opposite: the use of A yields obviously better observed vs. expected probabilities than the use of B.
Why can this be?
Is the use of a small sample of aggregated data still inferior to using a large sample of disaggregated data but in a way that is not detectable just through examination of the observed and expected probabilities?