29.7 Adding group-level predictors
If there are group-level predictors, such as average income in a state, or vote share in a previous election, these may be used as predictors in the regression. They will not pose an obstacle to poststratification because they are at the group level. For example, suppose the average income level in the state is available as the data variable
real<lower = 0> income;
then a regression coefficient
psi can be added for the effect of
average state income,
with a fixed prior,
psi ~ normal(0, 2);
This prior assumes the
income predictor has been standardized.
Finally, a term is added to the regression for the fixed predictor,
y ~ bernoulli_logit(alpha + beta[age] + ... + delta[state] + income[state] * psi);
And finally, the formula in the generated quantities block is also updated,
expect_pos += P[b, c, d] * inv_logit(alpha + beta[b] + gamma[c] + delta[d] + income[d] * psi);
d is the loop variable looping over states. This ensures that
the poststratification formula matches the likelihood formula.