Parameters estimation for multidimensional item response theory: An effective method of determining dimensions and bayesian method parameters estimation

Broadly speaking, IRT models can be divided into two families: unidimensional and multidimensional. Unidimensional models require a single trait (ability) dimension θ. Multidimensional IRT models model response data hypothesized to arise from multiple traits. However, because of the greatly increased complexity, the majority of IRT research and applications utilize a unidimensional model. With the developmental, the MIRT is negative to be researcher. In this paper, we proposed the estimation method of determining the number of dimensions for multidimensional item response theory based on combination with Principal Component Analysis and χ² test. A Joint marginal likelihood estimation method based on Bayesian method is provided in paper. Finally, a suggestion about the issue of numerical calculation of multiple integrals is given.