Bayesian Inference Of IRT Model With Skew Normal Latent Trait

Item response theory (IRT) comprises a set of statistical models which are useful inmany fields, especially when there is interest in studying latent variables. These latentvariables are directly considered in the IRT models and they are usually called latent traits. Aususl assumption for parameter estimation of the IRT model, is to assume that the latent traitsare random variables which follow a standard normal distribution. However, many workssuggest that this assumption does not apply in many cases. Furthermore, when thisassumption does not hold, the paremeter estimates tend to be biased and misleading inferencecan be obtained. Therefore, it is important to model the distribution of the latent traitsproperly.In this paper, we present an alternative latent traits modeling based on the so-calledskew-normal distribution，and discuss the parameter estimation of SN-IRT model. The mainresearch works are as follows:1、We briefly outlines some preliminaries of the skew normal distribution and IRTmodels. Consider a recent study on the IRT models, one is the asymmetric models for IRT.We present an IRT two parameter probit model with skew normal distribution for the latenttraits.We show a hierarchical representation for the SN-IRT model by incorporating two latentvariables. Based on data augmentation scheme, we derive the Gibbs sampling algorithm usedin simulating posterior distributions to carry out Bayesian inferences. In addition, we performa simulation study to compare the SN-IRT model with the normal latent traits. Thiscomparative study is done using the Bayesian inference.2、we put application SN latent traits to Multilevel IRT model. Based on the model, wealso derive the corresponding Gibbs sampling algorithm for Bayesian estimation. And a realdata is given to validate the feasibility and validity of the SN latent traits.