计数数据重复试验的优化设计

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference Pub Date : 2025-08-14 DOI:10.1016/j.jspi.2025.106334

Parisa Parsamaram , Heinz Holling , Rainer Schwabe

{"title":"计数数据重复试验的优化设计","authors":"Parisa Parsamaram , Heinz Holling , Rainer Schwabe","doi":"10.1016/j.jspi.2025.106334","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we develop optimal designs for growth curve models with count data based on the Rasch Poisson-Gamma counts model (RPGCM). This model is often used in educational and psychological testing when test results yield count data. In the RPGCM, the test scores are determined by respondents ability and item difficulty. Locally <span><math><mi>D</mi></math></span>-optimal designs are derived for maximum quasi-likelihood estimation to efficiently estimate the mean abilities of the respondents over time. Using the log link, both unstructured, linear and nonlinear growth curves of log mean abilities are taken into account. Finally, the sensitivity of the derived optimal designs due to an imprecise choice of parameter values is analyzed using <span><math><mi>D</mi></math></span>-efficiency.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"241 ","pages":"Article 106334"},"PeriodicalIF":0.8000,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimal design in repeated testing for count data\",\"authors\":\"Parisa Parsamaram , Heinz Holling , Rainer Schwabe\",\"doi\":\"10.1016/j.jspi.2025.106334\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we develop optimal designs for growth curve models with count data based on the Rasch Poisson-Gamma counts model (RPGCM). This model is often used in educational and psychological testing when test results yield count data. In the RPGCM, the test scores are determined by respondents ability and item difficulty. Locally <span><math><mi>D</mi></math></span>-optimal designs are derived for maximum quasi-likelihood estimation to efficiently estimate the mean abilities of the respondents over time. Using the log link, both unstructured, linear and nonlinear growth curves of log mean abilities are taken into account. Finally, the sensitivity of the derived optimal designs due to an imprecise choice of parameter values is analyzed using <span><math><mi>D</mi></math></span>-efficiency.</div></div>\",\"PeriodicalId\":50039,\"journal\":{\"name\":\"Journal of Statistical Planning and Inference\",\"volume\":\"241 \",\"pages\":\"Article 106334\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Statistical Planning and Inference\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0378375825000722\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Planning and Inference","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378375825000722","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们基于Rasch Poisson-Gamma计数模型（RPGCM）开发了具有计数数据的生长曲线模型的优化设计。当测试结果产生计数数据时，该模型经常用于教育和心理测试。在RPGCM中，测试成绩由被调查者的能力和项目难度决定。局部d -最优设计的最大拟似然估计，有效地估计平均能力的受访者随着时间的推移。利用对数链，同时考虑了非结构化、线性和非线性的对数平均能力增长曲线。最后，利用d -效率分析了由于参数值选择不精确而导致的优化设计的灵敏度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Optimal design in repeated testing for count data

In this paper, we develop optimal designs for growth curve models with count data based on the Rasch Poisson-Gamma counts model (RPGCM). This model is often used in educational and psychological testing when test results yield count data. In the RPGCM, the test scores are determined by respondents ability and item difficulty. Locally

D

-optimal designs are derived for maximum quasi-likelihood estimation to efficiently estimate the mean abilities of the respondents over time. Using the log link, both unstructured, linear and nonlinear growth curves of log mean abilities are taken into account. Finally, the sensitivity of the derived optimal designs due to an imprecise choice of parameter values is analyzed using

D

-efficiency.

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

Journal of Statistical Planning and Inference 数学-统计学与概率论

CiteScore

2.10

自引率

11.10%

发文量

审稿时长

3-6 weeks

期刊介绍： The Journal of Statistical Planning and Inference offers itself as a multifaceted and all-inclusive bridge between classical aspects of statistics and probability, and the emerging interdisciplinary aspects that have a potential of revolutionizing the subject. While we maintain our traditional strength in statistical inference, design, classical probability, and large sample methods, we also have a far more inclusive and broadened scope to keep up with the new problems that confront us as statisticians, mathematicians, and scientists. We publish high quality articles in all branches of statistics, probability, discrete mathematics, machine learning, and bioinformatics. We also especially welcome well written and up to date review articles on fundamental themes of statistics, probability, machine learning, and general biostatistics. Thoughtful letters to the editors, interesting problems in need of a solution, and short notes carrying an element of elegance or beauty are equally welcome.