SUFFICIENT STATISTICS AND LATENT TRAIT MODELS
SUFFICIENT STATISTICS AND LATENT TRAIT MODELS
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DOI：
10.1007/bf02293746
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发表时间：
1977-01-01
期刊：
影响因子：
3
通讯作者：
ANDERSEN, EB
中科院分区：
文献类型：
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作者：
ANDERSEN, EB
对于具有两个答案类别的调查问卷，已经证明了如果单个参数存在最小充分统计量，并且对于项目参数的所有值都是相同的统计量，则原始分数（或正确答案的数量）是最小充分统计量。因此，该模型必须是具有Logistic项目特征曲线和等项目区分能力的Rasch型，本文将这些结果推广到多项选择问卷。它示出的最小充分统计量的个别参数是所谓的得分向量的函数。它还表明，所谓的等距评分是唯一的评分问卷，允许一个真实的值足够的统计量，是独立的项目参数，如果一定的排序属性足够的统计量举行。
For questionnaires with two answer categories, it has been proven in complete generality that if a minimal sufficient statistic exists for the individual parameter and if it is the same statistic for all values of the item parameters, then the raw score (or the number of correct answers) is the minimal sufficient statistic. It follows that the model must by of the Rasch type with logistic item characteristic curves and equal item-discriminating powers.This paper extends these results to multiple choice questionnaires. It is shown that the minimal sufficient statistic for the individual parameter is a function of the so-called score vector. It is also shown that the so-called equidistant scoring is the only scoring of a questionnaire that allows for a real valued sufficient statistic that is independent of the item parameters, if a certain ordering property for the sufficient statistic holds.