simulating test and estimating item parameter under the weighted-score Logistic model

A new polytomously scored item response theory model, the weighted-score Logistic model, WSLM, is presented. The weighted-score Logistic model is also based on the Logistic function, in which the weighted-score parameter is added into the two dichotomous parameter Logistic model. There is only one difficulty parameter (i.e., the mean difficulty parameter) in the WSLM to represent the overall item difficulty. The weighted-score Logistic model is estimated by marginal maximum likelihood estimation and the EM algorithm. The item parameter estimation program has been written, and the discrimination parameters and the mean difficulty parameters based on the WSLM have been successfully estimated.