Regression and Anova : An Integrated Approach Using SAS Software

by Muller, Keith E.; Fetterman, Bethel A.

• ISBN13: 9781580258906
• ISBN10: 1580258905
• Format: Paperback
• Copyright: 2002-04-01
• Publisher: Sas Inst

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