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Traditional Item Response Theory models assume the distribution of theabilities of the population in study to be Gaussian. However, this may notalways be a reasonable assumption, which motivates the development of moregeneral models. This paper presents a generalised approach for the distributionof the abilities in dichotomous 3-parameter Item Response models. A mixture ofnormal distributions is considered, allowing for features like skewness,multimodality and heavy tails. A solution is proposed to deal with modelidentifiability issues without compromising the flexibility and practicalinterpretation of the model. Inference is carried out under the BayesianParadigm through a novel MCMC algorithm. The algorithm is designed in a way tofavour good mixing and convergence properties and is also suitable forinference in traditional IRT models. The efficiency and applicability of ourmethodology is illustrated in simulated and real examples.

Bayesian Item Response model: a generalised approach for the abilities' distribution using mixtures