Residuals and diagnostics for multinomial regression models

IF 2.1 4区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Statistical Analysis and Data Mining Pub Date : 2023-09-29 DOI:10.1002/sam.11645

Eric A. E. Gerber, Bruce A. Craig

引用次数: 0

Abstract

Abstract In this paper, we extend the concept of a randomized quantile residual to multinomial regression models. Customary diagnostics for these models are limited because they involve difficult‐to‐interpret residuals and often focus on the fit of one category versus the rest. Our residuals account for associations between categories by using the squared Mahalanobis distances of the observed log‐odds relative to their fitted sampling distributions. Aside from sampling variation, these residuals are exactly normal when the data come from the fitted model. This motivates our use of the residuals to detect model misspecification and overdispersion, in addition to an overall goodness‐of‐fit Kolmogorov–Smirnov test. We illustrate the use of the residuals and diagnostics in both simulation and real data studies.

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多项回归模型的残差和诊断

摘要本文将随机分位数残差的概念推广到多项回归模型中。这些模型的常规诊断是有限的，因为它们涉及难以解释的残差，并且通常侧重于一个类别与其他类别的拟合。我们的残差通过使用观测到的对数概率相对于它们的拟合抽样分布的马氏距离的平方来解释类别之间的关联。除了抽样变化外，当数据来自拟合模型时，这些残差完全是正态的。这促使我们使用残差来检测模型的错误规范和过度分散，以及总体拟合优度Kolmogorov-Smirnov检验。我们说明了残差和诊断在模拟和实际数据研究中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistical Analysis and Data Mining COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCEC-COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.20

自引率

7.70%

发文量

期刊介绍： Statistical Analysis and Data Mining addresses the broad area of data analysis, including statistical approaches, machine learning, data mining, and applications. Topics include statistical and computational approaches for analyzing massive and complex datasets, novel statistical and/or machine learning methods and theory, and state-of-the-art applications with high impact. Of special interest are articles that describe innovative analytical techniques, and discuss their application to real problems, in such a way that they are accessible and beneficial to domain experts across science, engineering, and commerce. The focus of the journal is on papers which satisfy one or more of the following criteria: Solve data analysis problems associated with massive, complex datasets Develop innovative statistical approaches, machine learning algorithms, or methods integrating ideas across disciplines, e.g., statistics, computer science, electrical engineering, operation research. Formulate and solve high-impact real-world problems which challenge existing paradigms via new statistical and/or computational models Provide survey to prominent research topics.