多分属性层级结构下引入逻辑约束的理想掌握模式
The Ideal Mastery Pattern for Polytomous Attributes with Hierarchical Structure Incorporating Mastery Level Restriction

多分属性比传统的2分属性提供更多更详细的诊断反馈信息,具有广阔的应用前景.在多分属性情境下,当属性之间存在层级结构时,会出现原2分属性情境下不存在的逻辑问题:如果被试仅低程度地掌握了父属性,那么他是否还有可能高程度地掌握子属性?从逻辑上讲,这种“父属性掌握程度低而子属性掌握程度高”的发展情况并不具有普适性.对此,该文首先在多分属性情境下,基于现有的计算理想掌握模式的方法提出了满足“属性掌握水平约束假设”的理想掌握模式计算方法.然后,通过模拟研究说明该逻辑约束的使用方法及忽略该逻辑约束可能对诊断结果带来的危害.
The polytomous attributes,particularly those defined as part of the test development process,can provide additional diagnostic information.When polytomous attributes follow a hierarchical structure,a latent logical problem will emerge,which is if a student has only acquired the low level of a father attribute(i.e.,pre-requisite attribute),will he acquire the high level of the son attribute? This situation is uncommon in reality.In terms of logical,the process of learning generally proceeds sequentially,so a good mastery of one attribute must base on a good enough pattern prepared for the pre-requisite attribute.Ideal mastery pattern(IMP)included the all possible mastery pattern for students within an assessment.Unfortunately,the existing calculation for IMP from the polytoumous reachability matrix and the polytomous reduced Q matrix ignored the logical problem above-mentioned.Then there will be some students be classified into illogical attribute pattern,such as the(122)and(112)in linear hierarchical structure.Aimed at this problem,a logical restraint of IMP for polytomous attributes is proposed,i.e.restrict the mastery level of father attribute is higher or equal to the son attribute.A simulation study was given to demonstrate applications and implications of the mastery level restriction.Results show that ignoring the mastery level restraint would result in worse model-data fit and worse attribute(pattern)correct classification rate,when the response data was generated from true attributes that followed the mastery level restraint