  It is reasonable to consider, in many cases, that individuals' latent traits
have a hierarchical structure such that more general traits are a suitable
composition of more specific ones. Existing item response models that account
for such hierarchical structure feature have considerable limitations in terms
of modelling and/or inference. Motivated by those limitations and the
importance of the theme, this paper aims at proposing an improved methodology
in terms of both modelling and inference to deal with hierarchically structured
latent traits in an item response theory context. From a modelling perspective,
the proposed methodology allows for genuinely multidimensional items and all of
the latent traits in the assumed hierarchical structure are on the same scale.
Items are allowed to be dichotomous or of graded response. An efficient MCMC
algorithm is carefully devised to sample from the joint posterior distribution
of all the unknown quantities of the proposed model. In particular, all the
latent trait parameters are jointly sampled from their full conditional
distribution in a Gibbs sampling algorithm. The proposed methodology is applied
to simulated data and a real dataset concerning the Enem exam in Brazil.
