{"title":"The Fisher information function and scoring in binary ideal point item response models: a cautionary tale","authors":"Jay Verkuilen","doi":"10.1111/bmsp.12254","DOIUrl":null,"url":null,"abstract":"This article examines the Fisher information functions, I ( θ ) , and explores implications for scoring of binary ideal point item response models. These models typically appear to have I ( θ ) that are bimodal and identically equal to 0 at the ideal point. The article shows that this is an inherent property of ideal point IRT models, which either have this property or are indeterminate and thus violate the likelihood regularity conditions. For some models, the indeterminacy can be resolved, generating an effectively unimodal I ( θ ) , albeit with violated regularity conditions. In other cases, I ( θ ) diverges. All reasonable ideal point IRT models exhibit this behaviour. Users should exercise caution when relying on asymptotics, particularly for shorter assessments. Use of simulated plausible values or prediction from a fully Bayesian estimation is recommended for scoring.","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2021-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://bpspsychub.onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12254","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.12254","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
Abstract
This article examines the Fisher information functions, I ( θ ) , and explores implications for scoring of binary ideal point item response models. These models typically appear to have I ( θ ) that are bimodal and identically equal to 0 at the ideal point. The article shows that this is an inherent property of ideal point IRT models, which either have this property or are indeterminate and thus violate the likelihood regularity conditions. For some models, the indeterminacy can be resolved, generating an effectively unimodal I ( θ ) , albeit with violated regularity conditions. In other cases, I ( θ ) diverges. All reasonable ideal point IRT models exhibit this behaviour. Users should exercise caution when relying on asymptotics, particularly for shorter assessments. Use of simulated plausible values or prediction from a fully Bayesian estimation is recommended for scoring.
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.