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.本文提出了一种新型多级计分项目反应理论模型——加权计分逻辑斯蒂模型（weighted-score Logistic model, WSLM）。该模型同样基于逻辑斯蒂函数，在二参数逻辑斯蒂模型的基础上引入了加权计分参数。加权计分逻辑斯蒂模型仅包含一个难度参数（即平均难度参数）以表征项目的整体难度。该模型采用边际极大似然估计与EM算法进行参数估计，目前已完成项目参数估计程序的编写，并成功基于WSLM估计得到了区分度参数与平均难度参数。