I am trying to implement a very simple graded response model using the brms R package. My first question is when implementing the model using the brms R package, the model specification allows for the inclusion of an item parameter, a person parameter, and an item discriminant parameter, which we assign priors to. However, in other standard software, such as SAS, that implement IRT models, there is no item parameter in the model specification. I am wondering why the brms package includes an item difficulty parameter, and if this is a standard specification of the graded response model? It seems like an obvious answer, but to remove the item difficulty parameter from the model, you should simply omit the item parameter in the formula statement, correct? So the formula and priors can be specified as:
formula_grm <- bf(
resp ~ 1 + (1 |i| item) + (1 | id),
disc ~ 1 + (1 |i| item)
set_prior(“cauchy(0, 5)”, class = “sd”, group = “id”) +
set_prior(“normal(0, 1)”, class = “sd”, group = “item”, dpar = “disc”)
A second related question I have is whether the GRM model specification in brms is equivalent to the model specification in SAS. Let t be the threshold, p be the person parameter, i be the item parameter, and a be the item discrimination parameter. In SAS, the term inside the exponential is a*(p-t), see pg. 2 of the attached SAS manual GRM SAS Documentation.pdf (803.5 KB). In brms, the term inside the exponential is the t-a*(p+i), see pg. 4 of Buerkner (2019), which I have attached Burkner, 2019.pdf (852.4 KB). Of course, from my first question, I want to omit i.