{"title":"一般属性结构上合取模型中的完全q矩阵","authors":"Jürgen Heller","doi":"10.1111/bmsp.12266","DOIUrl":null,"url":null,"abstract":"<p>In cognitive diagnostic assessment a property of the <i>Q</i>-matrix, usually referred to as completeness, warrants that the cognitive attributes underlying the observed behaviour can be uniquely assessed. Characterizations of completeness were first derived under the assumption of independent attributes, and are currently under investigation for interdependent attributes. The dominant approach considers so-called attribute hierarchies, which are conceptualized through a partial order on the set of attributes. The present paper extends previously published results on this issue obtained for conjunctive attribute hierarchy models. Drawing upon results from knowledge structure theory, it provides novel sufficient and necessary conditions for completeness of the <i>Q</i>-matrix, not only for conjunctive models on attribute hierarchies, but also on more general attribute structures.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":"75 3","pages":"522-549"},"PeriodicalIF":1.5000,"publicationDate":"2022-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://bpspsychub.onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12266","citationCount":"0","resultStr":"{\"title\":\"Complete Q-matrices in conjunctive models on general attribute structures\",\"authors\":\"Jürgen Heller\",\"doi\":\"10.1111/bmsp.12266\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In cognitive diagnostic assessment a property of the <i>Q</i>-matrix, usually referred to as completeness, warrants that the cognitive attributes underlying the observed behaviour can be uniquely assessed. Characterizations of completeness were first derived under the assumption of independent attributes, and are currently under investigation for interdependent attributes. The dominant approach considers so-called attribute hierarchies, which are conceptualized through a partial order on the set of attributes. The present paper extends previously published results on this issue obtained for conjunctive attribute hierarchy models. Drawing upon results from knowledge structure theory, it provides novel sufficient and necessary conditions for completeness of the <i>Q</i>-matrix, not only for conjunctive models on attribute hierarchies, but also on more general attribute structures.</p>\",\"PeriodicalId\":55322,\"journal\":{\"name\":\"British Journal of Mathematical & Statistical Psychology\",\"volume\":\"75 3\",\"pages\":\"522-549\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2022-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://bpspsychub.onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12266\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"British Journal of Mathematical & Statistical Psychology\",\"FirstCategoryId\":\"102\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1111/bmsp.12266\",\"RegionNum\":3,\"RegionCategory\":\"心理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"British Journal of Mathematical & Statistical Psychology","FirstCategoryId":"102","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/bmsp.12266","RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Complete Q-matrices in conjunctive models on general attribute structures
In cognitive diagnostic assessment a property of the Q-matrix, usually referred to as completeness, warrants that the cognitive attributes underlying the observed behaviour can be uniquely assessed. Characterizations of completeness were first derived under the assumption of independent attributes, and are currently under investigation for interdependent attributes. The dominant approach considers so-called attribute hierarchies, which are conceptualized through a partial order on the set of attributes. The present paper extends previously published results on this issue obtained for conjunctive attribute hierarchy models. Drawing upon results from knowledge structure theory, it provides novel sufficient and necessary conditions for completeness of the Q-matrix, not only for conjunctive models on attribute hierarchies, but also on more general attribute structures.
期刊介绍:
The British Journal of Mathematical and Statistical Psychology publishes articles relating to areas of psychology which have a greater mathematical or statistical aspect of their argument than is usually acceptable to other journals including:
• mathematical psychology
• statistics
• psychometrics
• decision making
• psychophysics
• classification
• relevant areas of mathematics, computing and computer software
These include articles that address substantitive psychological issues or that develop and extend techniques useful to psychologists. New models for psychological processes, new approaches to existing data, critiques of existing models and improved algorithms for estimating the parameters of a model are examples of articles which may be favoured.