{"title":"A Generalized Factor Rotation Framework with Customized Regularization.","authors":"Yongfeng Wu, Xiangyi Liao, Qizhai Li","doi":"10.1017/psy.2025.1","DOIUrl":null,"url":null,"abstract":"<p><p>Factor rotation is a crucial step in interpreting the results of exploratory factor analysis. Several rotation methods have been developed for simple structure solutions, but their extensions to bi-factor analysis are often not well established. In this article, we propose a mathematical framework that incorporates customized factor structure as a regularization to produce the optimal orthogonal or oblique rotation. We demonstrate the utility of the framework using examples of simple structure rotation and bi-factor rotation. Through detailed simulations, we show that the new method is accurate and robust in recovering the factor structures and latent correlations when bi-factor analysis is applied. The new method is applied to a test data and a Quality of Life survey data. Results show that our method can reveal bi-factor structures that are consistent with the theories.</p>","PeriodicalId":54534,"journal":{"name":"Psychometrika","volume":" ","pages":"1-25"},"PeriodicalIF":2.9000,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Psychometrika","FirstCategoryId":"102","ListUrlMain":"https://doi.org/10.1017/psy.2025.1","RegionNum":2,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
Factor rotation is a crucial step in interpreting the results of exploratory factor analysis. Several rotation methods have been developed for simple structure solutions, but their extensions to bi-factor analysis are often not well established. In this article, we propose a mathematical framework that incorporates customized factor structure as a regularization to produce the optimal orthogonal or oblique rotation. We demonstrate the utility of the framework using examples of simple structure rotation and bi-factor rotation. Through detailed simulations, we show that the new method is accurate and robust in recovering the factor structures and latent correlations when bi-factor analysis is applied. The new method is applied to a test data and a Quality of Life survey data. Results show that our method can reveal bi-factor structures that are consistent with the theories.
期刊介绍：
The journal Psychometrika is devoted to the advancement of theory and methodology for behavioral data in psychology, education and the social and behavioral sciences generally. Its coverage is offered in two sections: Theory and Methods (T& M), and Application Reviews and Case Studies (ARCS). T&M articles present original research and reviews on the development of quantitative models, statistical methods, and mathematical techniques for evaluating data from psychology, the social and behavioral sciences and related fields. Application Reviews can be integrative, drawing together disparate methodologies for applications, or comparative and evaluative, discussing advantages and disadvantages of one or more methodologies in applications. Case Studies highlight methodology that deepens understanding of substantive phenomena through more informative data analysis, or more elegant data description.
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