Marais Ida, Andrich David
Graduate School of Education, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009.
J Appl Meas. 2008;9(2):105-24.
By adding items with responses identical to a selected item, Smith (2005) investigated the effect of the response dependence on person and item parameter estimates in the dichotomous Rasch model. By varying the magnitude of response dependence among selected items, rather than their having perfect dependence, this paper provides additional insights into the effects of response dependence on the same estimates in the same model. Two sets of simulations are reported. In the first set, responses to all items except the first were dependent on either the first item or on the immediately preceding item; in the second set, subsets of items were formed first, and then within each of these subsets, responses to all items in a subset except the first were dependent on either the first item or on the immediately preceding item. The effects of dependence were noticeable in all of the statistics reported. In particular, the fit statistics and the parameter estimates showed increasing discrepancies from their theoretical values as a function of the magnitude of the dependence. In some cases, however, two related statistics gave the impression of improvement as a function of increased dependency; first the standard deviation of person estimates showed an increase, and second the index analogous to traditional reliability showed relative increase. In addition to the estimates and depending on the structure and magnitude of the dependence, the person distribution was affected systematically, ranging from becoming skewed to becoming bimodal. The effects on the distribution help explain some of the effects on the statistics reported. In the case of the second set of simulations in which the dependence is within subsets of items, it is possible to take account of the response dependence. This is done by summing the responses of the items within each subset to form a polytomous item and then analyzing the data in terms of a smaller number of polytomous items. This way of accounting for dependence, in which the maximum score for the test as a whole remains the same, gives a more accurate value of the reliability and a more realistic distribution of the person estimates than when the dependence within subsets of items is not taken into account.
通过添加与所选项目答案相同的项目，史密斯（2005年）研究了二分法Rasch模型中答案依赖性对人员和项目参数估计的影响。本文通过改变所选项目之间答案依赖性的程度，而不是让它们具有完全依赖性，进一步深入探讨了答案依赖性对同一模型中相同估计的影响。文中报告了两组模拟。在第一组模拟中，除第一个项目外，所有项目的答案都依赖于第一个项目或紧接在前的项目；在第二组模拟中，首先形成项目子集，然后在每个子集中，除第一个项目外，子集中所有项目的答案都依赖于第一个项目或紧接在前的项目。在所报告的所有统计数据中，依赖性的影响都很明显。特别是，拟合统计量和参数估计值显示，随着依赖性程度的增加，它们与理论值的差异越来越大。然而，在某些情况下，两个相关统计量却随着依赖性的增加而显示出改善的迹象；首先，人员估计值的标准差有所增加，其次，类似于传统信度的指标也相对增加。除了估计值外，根据依赖性的结构和程度，人员分布也受到系统性影响，范围从偏态分布到双峰分布。对分布的影响有助于解释对所报告统计数据的一些影响。在第二组模拟中，依赖性存在于项目子集中，此时可以考虑答案依赖性。具体做法是将每个子集中项目的答案相加，形成一个多分类项目，然后根据较少数量的多分类项目来分析数据。这种考虑依赖性的方法，在整个测试的最高分保持不变的情况下，比不考虑项目子集中的依赖性时，能给出更准确的信度值和更符合实际的人员估计分布。
