Estimation Method Of Item Parameters For Longitudinal Item Response Data

In the study of longitudinal item response data, because of the dimension of the latent variables are not one-dimensional, in which multiple integrals problem increases the difficulty of computing, we need to search a method to deal with the multidimensional integral to get a precise estimation of the item parameters. In this article, we use the two-parameter Logistic Model and the Normal Ogive Model. In the case of the known distribution of the population ability parameters, we estimated the difficulty parameters and the discrimination parameter using the maximum likelihood method. We introduce the Hermite-Gauss method and M-H method to deal with the multidimensional integral issue. Finally, we use simulation to verify these different circumstances of probabilistic model, the covariance matrix and method of dealing with multi-dimensional integral.