So: I run my nested
year:country hierarchical model, but this time adding in:
sigma ~ 0 + year + country.
(Could not add in
year:country here since too many groups. Would take 2 weeks to run even on the high powered computer external server I am using).
The regression results after adding in the above almost do not change though; even though I would except them to since now the partial pooling will be done differently I would think? The random effects change very very very mildly (almost imperceptible). While fixed effect no change really except for one coefficient.
sigma_year2017 coefficients are all negative while the
sigma_countryZAF...sigma_countryUSA are a mixture of negative and positive. Does it make sense to have a negative coefficient in this instance?? \sigma should be positive but this brms() formulation of this problem I am still trying to understand.
A bit more info:
The hierarchical model is a non-nested model with groups j = 576 formed by interacting
country:year (we have 24 countries and 24 years). The regression is run on around 285,000 data points:
y ~ 1 + FE1 + FE2 + RE3 + (1 + RE1 + RE1 + RE3 | year:country)
I assume that the above formulation for sigma should lead to partial pooling taking place not just within RE1 and RE2 each coefficient, but also within each year and within each country, since now each is given their own \sigma, unless I am mistaken.