  Most Item Response Theory (IRT) models for dichotomous responses are based on
probit or logit link functions which assume a symmetric relationship between
the probability of a correct response and the latent traits of individuals
submitted to a test. This assumption restricts the use of those models to the
case in which all items have a symmetric behaviour. On the other hand,
asymmetric models proposed in the literature impose that all the items in a
test have an asymmetric behaviour. This assumption is inappropriate for great
part of the tests which are, in general, composed by both symmetric and
asymmetric items. Furthermore, a straightforward extension of the existing
models in the literature would require a prior selection of the items'
symmetry/asymmetry status. This paper proposes a Bayesian IRT model that
accounts for symmetric and asymmetric items in a flexible though parsimonious
way. That is achieved by assigning a finite mixture prior to the skewness
parameter, with one of the mixture components being a point-mass at zero. This
allows for analyses under both model selection and model averaging approaches.
Asymmetric item curves are designed through the centred skew normal
distribution, which has a particularly appealing parametrisation in terms of
parameter interpretation and computational efficiency. An efficient MCMC
algorithm is proposed to perform Bayesian inference and its performance is
investigated in some simulated examples. Finally, the proposed methodology is
applied to a data set from a large scale educational exam in Brazil.
