Method of successive dichotomizations: An improved method for estimating measures of latent variables from rating scale data
Method of successive dichotomizations: An improved method for estimating measures of latent variables from rating scale data
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DOI：
10.1371/journal.pone.0206106
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发表时间：
2018-10-18
期刊：
影响因子：
3.7
通讯作者：
Massof, Robert W.
中科院分区：
文献类型：
--
作者：
Bradley, Chris;Massof, Robert W.
最常用的模型估计措施的潜变量的多分类评级量表的数据是Andrich评级量表模型和Samejima分级反应模型。安德里奇模型有一个不受欢迎的属性，即估计无序的评级类别阈值，建议模型的用户操纵数据以迫使阈值有序出现。Samejima模型估计有序的阈值，但具有在非不变尺度上估计人的度量的不期望的属性-尺度取决于人对哪些项目进行评级，并且使人之间的比较变得困难。我们得出的评级规模模型逻辑上隐含的普遍同意的定义评级规模一个真实的线划分有序阈值到有序的区间称为评级类别，并表明它估计有序阈值以及人和项目的措施不变的规模。导出的模型原来是Samejima模型的一个特例，但没有项目歧视参数和跨项目的共同阈值。在我们的模型中的所有参数估计使用一种快速有效的方法称为连续二分法，它适用于二分Rasch模型的次数，因为有阈值，并证明了派生的模型是一个多分Rasch模型，估计有序阈值。我们测试了连续二分法和Andrich模型对模拟评级量表数据，发现我们的模型的估计参数与真实值几乎完全相关，而Andrich模型的估计阈值随着评级类别数量的增加而与真实值呈负相关。我们的方法还估计参数的规模，保持不变的评级类别的数量，相反，Andrich模型。
The most commonly used models for estimating measures of latent variables from polytomous rating scale data are the Andrich rating scale model and the Samejima graded response model. The Andrich model has the undesirable property of estimating disordered rating category thresholds, and users of the model are advised to manipulate data to force thresholds to come out ordered. The Samejima model estimates ordered thresholds, but has the undesirable property of estimating person measures on a non-invariant scale-the scale depends on which items a person rates and makes comparisons across people difficult. We derive the rating scale model logically implied by the generally agreed upon definition of rating scale-a real line partitioned by ordered thresholds into ordered intervals called rating categories-and show that it estimates ordered thresholds as well as person and item measures on an invariant scale. The derived model turns out to be a special case of the Samejima model, but with no item discrimination parameter and with common thresholds across items. All parameters in our model are estimated using a fast and efficient method called the Method of Successive Dichotomizations, which applies the dichotomous Rasch model as many times as there are thresholds and demonstrates that the derived model is a polytomous Rasch model that estimates ordered thresholds. We tested both the Method of Successive Dichotomizations and the Andrich model against simulated rating scale data and found that the estimated parameters of our model were nearly perfectly correlated with the true values, while estimated thresholds of the Andrich model became negatively correlated with the true values as the number of rating categories increased. Our method also estimates parameters on a scale that remains invariant to the number of rating categories, in contrast to the Andrich model.