基于HO-DINA模型的多级评分认知诊断模型的开发

A Polytomous Extension of Higher-Order DINA Model

本文对具有较好发展前景的HO-DINA模型进行拓展,将仅适用于0-1评分数据资料的HO-DINA模型拓广至可用于多级评分,采用MCMC算法实现了对新模型参数的估计,并对新模型性能进行了研究。

Almost all cognitive diagnosis models are only adaptive for dichotomous data,which cannot meet the demands in real work and limit the application and development of cognitive diagnosis. In this paper,the dichotomous HO-DINA model was extended to a polytomous model,and the MCMC algorithm was employed to estimate its parameters. To explore the feasibility of the MCMC algorithm and the estimated precision,and to probe the properties of the polytomous HO-DINA model,the Monte Carlo method is used. There are two experiments. （1） In the first experiment,there were six cognitive attributes,60 test items and 500 examinees. The purpose of this experiment is to explore the feasibility of the MCMC algorithm and the estimated precision. （2） The second experiment is to study the properties of the polytomous HO-DINA model. In this experiment,the number of the cognitive attributes varied from 4 to 8. Simulation results： （1） Under the polytomous HO-DINA model,the estimation of the MCMC algorithm is fairly adequate,and its precision of item and ability parameters is great,which indicates the MCMC algorithm method is feasible. （2） The estimated precision of parameters and the attribute match ratio （MMR PMR） are decreasing with the increasing number of attributes. But the reverse is true for the estimated precision of parameters. （3） If PMR is asked to be higher than 80%,then the number of attributes is suggested not to be greater than seven.