Regression and Anova : An Integrated Approach Using SAS Software,9781580258906

Regression and Anova : An Integrated Approach Using SAS Software

by ;
ISBN13: 9781580258906
ISBN10: 1580258905
Format: Paperback
Pub. Date: 2002-04-01
Publisher(s): Sas Inst
List Price: $80.20

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Author Biography

Keith E. Muller, Ph.D., is Associate Professor of Biostatistics at the University of North Carolina at Chapel Hill Bethel A. Fetterman, M.S., is Director of Clinical Data Processing and Analysis at PharmaLinkFHI in Research Triangle Park, North Carolina

Table of Contents

Preface ix
Examples and Limits of the GLM
1(6)
Motivation
1(1)
A Review of Basic Statistical Ideas
2(2)
GLM Definition
4(1)
GLM Examples
4(1)
Student Goals
5(1)
Homework Exercises
5(2)
Statement of the Model, Estimation, and Testing
7(22)
Motivation
7(1)
Statement of the Model
8(2)
Least Squares Assumptions
10(1)
Discussion of Homogeneity
11(2)
Gaussian Errors Assumption
13(1)
Estimation of the GLM
14(6)
Hypothesis Testing for the GLM
20(7)
Homework Exercises
27(2)
Some Distributions for the GLM
29(14)
Motivation
29(1)
A Full-Rank Basis for Less-than-Full-Rank Models
30(1)
Definitions and Theorems
31(1)
GLM Distributions
32(4)
Definitions and Properties of Residuals
36(5)
Homework Exercises
41(2)
Multiple Regression: General Considerations
43(24)
Motivation
43(1)
Definitions of Basic Sums of Squares
44(3)
The Nature of the Intercept
47(1)
Models that Span but May Not Include an Intercept
48(1)
Corrected SS
49(4)
Intercept-Only Model
53(2)
Null Model
55(1)
Overall ANOVA Table for Multiple Regression
56(3)
Usual (``Corrected'') Overall Test for Regression
59(2)
``Uncorrected'' Overall Test for Regression
61(1)
Strength of Association
62(2)
Homework Exercises
64(3)
Testing Hypotheses in Multiple Regression
67(30)
Motivation
67(1)
Choosing an Error Term
68(1)
Review of GLH Concepts
69(1)
Model Pools
69(4)
Test Class 1: Overall
73(5)
Test Class 2: Addition of One Variable
78(4)
Test Class 3: Tests of the Intercept
82(4)
Test Class 4: Addition of a Group of Variables
86(5)
Test Class 5: GLH Tests
91(2)
The Multiple Testing Issue
93(1)
Interaction
94(1)
Homework Exercises
95(2)
Correlations
97(24)
Motivation
97(1)
Interpreting p2
97(5)
Correlation Formulas
102(1)
Partial Correlation
103(3)
Semipartial Correlation
106(2)
Relating Semipartial Correlations to Standardized Regression Coefficients
108(1)
Multiple Partial Correlation
109(1)
Multiple Semipartial Correlation
110(1)
Hypothesis Tests for Correlations
111(3)
Relating Multiple Partials and Semipartials to Regression Coefficient Tests
114(1)
Using Correlations to Interpret Added-in-Order Tests
115(1)
Computing Partial Correlations
116(2)
Some Useful Properties of Correlations
118(1)
The Importance and Utility of Correlations
119(1)
Homework Exercises
120(1)
GLM Assumption Diagnostics
121(42)
Motivation
121(1)
The First Step: Get to Know Your Data
122(11)
Residual Analysis
133(13)
Outliers
146(14)
Homework Exercises
160(3)
GLM Computation Diagnostics
163(22)
Motivation
163(1)
Single Variable Problems and Solutions
163(1)
Collinearity Definitions and Concepts
164(1)
Matrices of Interest
165(3)
Models Corresponding to Cross-Products Matrices
168(4)
Eigenanalysis
172(5)
R2j, Tolerance and VIF
177(3)
Detecting Numerical Inaccuracy
180(2)
Treating Regression Problems
182(1)
Homework Exercises
183(2)
Polynomial Regression
185(20)
Motivation
185(1)
Polynomial Models of Most Interest
186(1)
Examples
186(2)
Lack-of-Fit Tests
188(1)
Limitations of Natural Polynomials
189(2)
Orthogonal Polynomials
191(4)
Strategies for Accurate Computations with Polynomials
195(5)
Strategy for Choosing a Model
200(1)
Polynomial Interactions and Response Surfaces
201(1)
Homework Exercises
202(3)
Transformations
205(18)
Motivation
205(1)
General Principles
206(1)
Power Transformation of the Response
206(12)
Other Comments
218(1)
Transformations of Predictors
219(1)
Pitfalls
219(1)
Homework Exercises
220(3)
Selecting the Best Model
223(76)
Motivation
223(1)
Overview of Solution Strategies
224(1)
Step 1: Specify the Maximum Model
224(1)
Step 2: Specify a Criterion
225(4)
Step 3: Specify a Strategy
229(4)
Step 4: Conduct the Analysis
233(1)
Step 5: Evaluate the Reliability
233(5)
Overall Implementation
238(59)
Homework Exercises
297(2)
Coding Schemes for Regression
299(14)
Motivation
299(1)
Reference Cell Coding
300(3)
Cell Mean Coding
303(1)
Classical ANOVA Coding
304(2)
Effect Coding
306(2)
Polynomial Coding
308(1)
The Essence Matrix
309(1)
Comments on Coding Schemes
310(1)
Relationships among Coding Schemes
311(1)
Homework Exercises
311(2)
One-Way ANOVA
313(26)
Motivation
313(1)
Specification of the Model
313(3)
(Usual) Overall Test
316(9)
Defining and Estimating Cell Means
325(2)
Which Means Are Different?
327(1)
Contrasts
328(2)
Conducting Multiple Comparisons
330(7)
Homework Exercises
337(2)
Complete, Two-Way Factorial ANOVA
339(46)
Motivation
339(1)
Model Concepts
340(2)
Coding Schemes
342(3)
Generating Cell Means
345(3)
Computing Estimates and Tests
348(2)
Contrast Matrices for Marginal Means
350(20)
Choosing and Interpreting Tests
370(3)
Step-Down Tests
373(7)
Missing Data
380(2)
Homework Exercises
382(3)
Special Cases of Two-Way ANOVA and Random Effects Basics
385(16)
Motivation
385(1)
Blocking Variables and Block Designs
385(1)
Fixed Block Design
386(2)
Introduction to Random Effects Models
388(1)
The Classical Approach to a Random Block Design
388(1)
Role of Nonindependence of Observations
389(1)
Computations for Mixed Models
390(1)
Review Comments
390(9)
Homework Exercises
399(2)
The Full Model in Every Cell (ANCOVA as a Special Case)
401(46)
Motivation
401(1)
Cell Mean Style Coding of Full Model
402(1)
Properties of the Model
403(6)
Testing Strategies
409(1)
Implementing Strategy 1, Adjusted ANOVA
410(1)
Implementing Strategy 2, GLM Testing
411(2)
Models of Interest
413(2)
Implementing Strategy 3: Backwards Groupwise
415(2)
Difference Scores: A Special Case of ANCOVA
417(2)
Other Contrasts of Interest in ANCOVA
419(1)
Other Test of Interest in the Full Model
420(1)
Regression (Reference Cell) Style Coding
421(11)
Effect Style Coding
432(10)
Modeling a Baseline Covariate
442(1)
Comparing Coding Schemes
443(1)
Generalizations
444(1)
Homework Exercises
444(3)
Understanding and Computing Power for the GLM
447(12)
Motivation
447(1)
GLM Theory
448(3)
Factors in Choosing a Design
451(1)
Using Parameter Estimates in Power Analysis
452(1)
Example Power Analysis
452(1)
Reporting Power
453(3)
Tables and Software
456(1)
How Much To Do?
457(1)
Benefits
457(1)
Homework Exercises
457(2)
A Matrix Algebra for Linear Models 459(18)
Basics
459(4)
Matrix Properties and Decompositions
463(6)
Principal Components (Basics)
469(5)
Homework Exercises in Matrix Arithmetic
474(1)
Homework Exercises for a Matrix Language
474(3)
B Statistical Tables 477(12)
C Study Guide for Linear Model Theory 489(6)
D Homework and Example Data 495(16)
E Introduction to SAS/IML 511(2)
F A Brief Manual for LINMOD 513(6)
G SAS/IML Power Program User's Guide 519(16)
H Regression Model Selection Data 535(10)
References 545(6)
Index 551

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