Hi all,

I am looking to adapt the subgroup analysis from p.292 of the Gelman and Hill ARM text and just want to be sure I have specified the model correctly. In the example:

y = log earnings

z = mean-centered height

J = 4 ethnic groups

K = 3 age categories

model is:

yi ~ N(a[j,k] + B[j,k]z, sigma2)

I am between two specifications of this, neither of which I’m entirely confident is right:

`stan_lm(y ~ -1 + z + (1 + z | J:K))`

Which I interpret as no fixed intercept, and a varying slope + intercept for every age category in every ethnic group. The reason I think this might not be right is because I think it implies that K is nested in J. The only other formulation I’ve come up with is:

`stan_lm(y ~ -1 + z + (1 + z | J) + (1 + z|K))`

Which seems more in line with what I know about specifying crossed effects in lmer, but then I’m not sure how I get at the interaction of coefficients for age groups by ethnicity.

Thanks