随机效应广义部分信贷模型的凸性约束参数化。

IF 1.5 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
David J Hessen
{"title":"随机效应广义部分信贷模型的凸性约束参数化。","authors":"David J Hessen","doi":"10.1111/bmsp.12365","DOIUrl":null,"url":null,"abstract":"<p><p>An alternative closed-form expression for the marginal joint probability distribution of item scores under the random effects generalized partial credit model is presented. The closed-form expression involves a cumulant generating function and is therefore subjected to convexity constraints. As a consequence, complicated moment inequalities are taken into account in maximum likelihood estimation of the parameters of the model, so that the estimation solution is always proper. Another important favorable consequence is that the likelihood function has a single local extreme point, the global maximum. Furthermore, attention is paid to expected a posteriori person parameter estimation, generalizations of the model, and testing the goodness-of-fit of the model. Procedures proposed are demonstrated in an illustrative example.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A convexity-constrained parameterization of the random effects generalized partial credit model.\",\"authors\":\"David J Hessen\",\"doi\":\"10.1111/bmsp.12365\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>An alternative closed-form expression for the marginal joint probability distribution of item scores under the random effects generalized partial credit model is presented. The closed-form expression involves a cumulant generating function and is therefore subjected to convexity constraints. As a consequence, complicated moment inequalities are taken into account in maximum likelihood estimation of the parameters of the model, so that the estimation solution is always proper. Another important favorable consequence is that the likelihood function has a single local extreme point, the global maximum. Furthermore, attention is paid to expected a posteriori person parameter estimation, generalizations of the model, and testing the goodness-of-fit of the model. Procedures proposed are demonstrated in an illustrative example.</p>\",\"PeriodicalId\":55322,\"journal\":{\"name\":\"British Journal of Mathematical & Statistical Psychology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-10-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"British Journal of Mathematical & Statistical Psychology\",\"FirstCategoryId\":\"102\",\"ListUrlMain\":\"https://doi.org/10.1111/bmsp.12365\",\"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://doi.org/10.1111/bmsp.12365","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}
引用次数: 0

摘要

本文提出了随机效应广义部分学分模型下项目分数边际联合概率分布的另一种闭式表达式。该闭式表达式涉及累积生成函数,因此受到凸性约束。因此,在对模型参数进行最大似然估计时,会考虑到复杂的矩不等式,从而使估计解始终是正确的。另一个重要的有利结果是,似然函数只有一个局部极值点,即全局最大值。此外,我们还关注了预期后验人参数估计、模型的泛化以及模型拟合度测试。通过一个示例演示了所提出的程序。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A convexity-constrained parameterization of the random effects generalized partial credit model.

An alternative closed-form expression for the marginal joint probability distribution of item scores under the random effects generalized partial credit model is presented. The closed-form expression involves a cumulant generating function and is therefore subjected to convexity constraints. As a consequence, complicated moment inequalities are taken into account in maximum likelihood estimation of the parameters of the model, so that the estimation solution is always proper. Another important favorable consequence is that the likelihood function has a single local extreme point, the global maximum. Furthermore, attention is paid to expected a posteriori person parameter estimation, generalizations of the model, and testing the goodness-of-fit of the model. Procedures proposed are demonstrated in an illustrative example.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
5.00
自引率
3.80%
发文量
34
审稿时长
>12 weeks
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信