Hi Nikolay and Yulia,
I wanted to try out using the example to specify a Rasch model, which seems correct (the parameter estimates are also reasonably close to those derived from jMetrik using the same data):
webuse masc1, clear
qui: g int id = _n
qui: reshape long q, i(id) j(item)
fvset base none id item
set seed 14
#d ;
// 1PL Example from Blog Post
bayesmh q = ({discrim}*({subj:}-{diff:})), likelihood(logit)
redefine(diff:i.item) redefine(subj:i.id) prior({subj:i.id}, normal(0, 1))
prior({discrim}, lognormal(0, 1)) prior({diff:i.item}, normal(0, 1))
init({discrim} 1) exclude({subj:i.id}) burnin(5000);
// Rasch example based on blog post
bayesmh q = (1*({subj:}-{diff:})), likelihood(logit) redefine(diff:i.item)
redefine(subj:i.id) prior({subj:i.id}, normal(0, 1))
prior({diff:i.item}, normal(0, 1)) exclude({subj:i.id}) burnin(5000) ;
However, it isn't quite as clear how one could derive infit/outfit statistics, residuals for the person and item estimates, or the best way to fix the person estimate (e.g., using the sum score across items). It seems like the estimates in this example are all the Bayesian derivatives of the Marginal MLE estimator, but is there a way to fit the same models using the Joint MLE (for cases when the person parameters need to be estimated at the same time as the item parameters)? Last, is there any chance for a follow up to this post that would potentially show how to fit many facet rasch models and/or multidimensional IRT models using bayesmh (either case would be pretty amazing to see)?
Thanks again and nice work on the blog post,
Billy