Bertoli-Barsotti Lucio
Department of Mathematics, Statistics, Computer Science and Applications, University of Bergamo, I-24127 Bergamo, Italy.
J Appl Meas. 2005;6(1):71-9.
The Rating Scale Model (RSM) and the Partial Credit Model (PCM) are fairly well-known examples of Rasch models for polytomously scored items. In addition to a number of threshold parameters, both the models contain two scalar parameters characterizing item and person location on a common interval-level scale. The rank order of items and persons defined by the Likert summative scores (i.e. the raw total scores) is compared with that obtained from the Rasch-based measures (i.e. the maximum likelihood estimates of person and item parameters). It is proved that: 1) the property of comonotonicity between Likert summative scores and Rasch-based measures holds for both the person and item parameters of the RSM; 2) the property of comonotonicity between Likert summative scores and Rasch-based measures holds for the PCM only with reference to the person parameters; 3) violations of comonotonicity are possible, for particular datasets, for the item parameters of the PCM.
评分量表模型（RSM）和部分计分模型（PCM）是用于多分类计分项目的Rasch模型中相当著名的例子。除了一些阈值参数外，这两个模型都包含两个标量参数，用于在共同的区间水平量表上表征项目和人员的位置。将由李克特累加分数（即原始总分）定义的项目和人员的排名顺序与从基于Rasch的测量中获得的排名顺序（即人员和项目参数的最大似然估计）进行比较。结果证明：1）对于RSM的人员和项目参数，李克特累加分数与基于Rasch的测量之间的共单调性属性均成立；2）李克特累加分数与基于Rasch的测量之间的共单调性属性仅在涉及人员参数时对于PCM成立；3）对于特定数据集，PCM的项目参数可能会出现共单调性违反的情况。
