{"title":"Inferential Tools for Assessing Dependence Across Response Categories in Multinomial Models with Discrete Random Effects","authors":"","doi":"10.1007/s00357-024-09466-2","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>We propose a discrete random effects multinomial regression model to deal with estimation and inference issues in the case of categorical and hierarchical data. Random effects are assumed to follow a discrete distribution with an a priori unknown number of support points. For a <em>K</em>-categories response, the modelling identifies a latent structure at the highest level of grouping, where groups are clustered into subpopulations. This model does not assume the independence across random effects relative to different response categories, and this provides an improvement from the multinomial semi-parametric multilevel model previously proposed in the literature. Since the category-specific random effects arise from the same subjects, the independence assumption is seldom verified in real data. To evaluate the improvements provided by the proposed model, we reproduce simulation and case studies of the literature, highlighting the strength of the method in properly modelling the real data structure and the advantages that taking into account the data dependence structure offers.</p>","PeriodicalId":50241,"journal":{"name":"Journal of Classification","volume":"62 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Classification","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s00357-024-09466-2","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
We propose a discrete random effects multinomial regression model to deal with estimation and inference issues in the case of categorical and hierarchical data. Random effects are assumed to follow a discrete distribution with an a priori unknown number of support points. For a K-categories response, the modelling identifies a latent structure at the highest level of grouping, where groups are clustered into subpopulations. This model does not assume the independence across random effects relative to different response categories, and this provides an improvement from the multinomial semi-parametric multilevel model previously proposed in the literature. Since the category-specific random effects arise from the same subjects, the independence assumption is seldom verified in real data. To evaluate the improvements provided by the proposed model, we reproduce simulation and case studies of the literature, highlighting the strength of the method in properly modelling the real data structure and the advantages that taking into account the data dependence structure offers.
摘要 我们提出了一种离散随机效应多叉回归模型，用于处理分类和分层数据的估计和推断问题。假设随机效应遵循离散分布，支持点的数量先验未知。对于 K 个类别的响应，建模确定了最高分组层次的潜在结构，其中各组被聚类为子群体。该模型不假定相对于不同响应类别的随机效应之间的独立性，这就改进了之前文献中提出的多项式半参数多层次模型。由于特定类别的随机效应来自相同的受试者，因此在实际数据中很少验证独立性假设。为了评估所提出的模型所带来的改进，我们重现了文献中的模拟和案例研究，强调了该方法在正确模拟真实数据结构方面的优势，以及考虑数据依赖结构所带来的优势。
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To publish original and valuable papers in the field of classification, numerical taxonomy, multidimensional scaling and other ordination techniques, clustering, tree structures and other network models (with somewhat less emphasis on principal components analysis, factor analysis, and discriminant analysis), as well as associated models and algorithms for fitting them. Articles will support advances in methodology while demonstrating compelling substantive applications. Comprehensive review articles are also acceptable. Contributions will represent disciplines such as statistics, psychology, biology, information retrieval, anthropology, archeology, astronomy, business, chemistry, computer science, economics, engineering, geography, geology, linguistics, marketing, mathematics, medicine, political science, psychiatry, sociology, and soil science.
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