Plane Answers to Complex Questions: The Theory of Linear Models
暫譯: 平面解答複雜問題：線性模型理論

Christensen, Ronald

Plane Answers to Complex Questions: The Theory of Linear Models

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商品描述

This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author's emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate-level course. All of the standard topics are covered in depth: estimation including biased and Bayesian estimation, significance testing, ANOVA, multiple comparisons, regression analysis, and experimental design models.  In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: best linear and best linear unbiased prediction, split plot models, balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, diagnostics, collinearity, and variable selection. This new edition includes new sections on alternatives to least squares estimation and the variance-bias tradeoff, expanded discussion of variable selection, new material on characterizing the interaction space in an unbalanced two-way ANOVA, Freedman's critique of the sandwich estimator, and much more.

商品描述(中文翻譯)

這本教科書提供了線性模型在數據分析中的使用與理論的廣泛介紹。作者強調對線性模型的統一處理，包括基於投影、正交性及其他向量空間概念的變異數分析模型和迴歸模型。每一章都附有大量的練習題和範例，使其非常適合研究生級別的課程。所有標準主題都深入探討：估計，包括偏差估計和貝葉斯估計、顯著性檢驗、ANOVA、多重比較、迴歸分析和實驗設計模型。此外，本書還涵蓋了一些通常在此級別不會處理但本身重要的主題：最佳線性和最佳線性無偏預測、分割圖模型、平衡不完全區塊設計、擬合不足檢驗、獨立性檢驗、具有奇異協方差矩陣的模型、診斷、共線性和變數選擇。這一新版包括了最小平方估計的替代方案和方差-偏差權衡的新章節，擴展了對變數選擇的討論，新增了關於不平衡雙向ANOVA中互動空間特徵的新材料，Freedman對三明治估計量的批評，以及更多內容。

作者簡介

Ronald Christensen is a Professor of Statistics at the University of New Mexico, Fellow of the American Statistical Association (ASA) and the Institute of Mathematical Statistics, former Chair of the ASA Section on Bayesian Statistical Science and former Editor of The American Statistician. His book publications include Advanced Linear Modeling (Springer, new edition forthcoming), Log-Linear Models and Logistic Regression (Springer 1997), Analysis of Variance, Design, and Regression (1996, 2016), and Bayesian Ideas and Data Analysis (2010, with Johnson, Branscum and Hanson).

作者簡介(中文翻譯)

羅納德·克里斯滕森（Ronald Christensen）是新墨西哥大學的統計學教授，美國統計協會（American Statistical Association, ASA）和數學統計學會（Institute of Mathematical Statistics）的會士，曾擔任ASA貝葉斯統計科學分會的主席及《美國統計學家》（The American Statistician）的編輯。他的著作包括《進階線性模型》（Advanced Linear Modeling，Springer，新的版本即將出版）、《對數線性模型與邏輯回歸》（Log-Linear Models and Logistic Regression，Springer 1997）、《變異數分析、設計與回歸》（Analysis of Variance, Design, and Regression，1996, 2016）以及《貝葉斯思想與數據分析》（Bayesian Ideas and Data Analysis，2010，與約翰遜（Johnson）、布蘭斯卡姆（Branscum）和漢森（Hanson）合著）。

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