I’m running a Heckman’s selection model with random effects. The first stage is a probit model using stan_glmer. How do I create the inverse Mill’s ratio for the second stage? I tried posterior_prediction but that does not create the predicted probability from stan_glmer.
The code is in R. It is straightforward.
# stage 1
fit.stan <- stan_glmer(college ~ race + sex + (1 | city) + (1| ind), data=datt, family=binomial(link="probit"))
# generate the inverse mill's ratio (not working)
pred_p <- posterior_predict(fit.stan,type="link")
datt$imr <- dnorm(pred_p)/pnorm(pred_p)
# stage 2
fit.stanlmer <- stan_lmer(salary ~ race + sex + (1 | city) + (1| ind) + imr, data=datt)