Linear models with R

1040/2nd Jan 2015
Rs.6060/-

Contents
Preface xi
1 Introduction 1
1.1 Before You Start 1
1.2 Initial Data Analysis 2
1.3 When to Use Linear Modeling 7
1.4 History 8
2 Estimation 13
2.1 Linear Model 13
2.2 Matrix Representation 14
2.3 Estimating β 15
2.4 Least Squares Estimation 16
2.5 Examples of Calculating ˆ
β 17
2.6 Example 17
2.7 QR Decomposition 20
2.8 Gauss–Markov Theorem 22
2.9 Goodness of Fit 23
2.10 Identifiability 26
2.11 Orthogonality 28
3 Inference 33
3.1 Hypothesis Tests to Compare Models 33
3.2 Testing Examples 35
3.3 Permutation Tests 40
3.4 Sampling 42
3.5 Confidence Intervals for β 43
3.6 Bootstrap Confidence Intervals 46
4 Prediction 51
4.1 Confidence Intervals for Predictions 51
4.2 Predicting Body Fat 52
4.3 Autoregression 54
4.4 What Can Go Wrong with Predictions? 56
5 Explanation 59
5.1 Simple Meaning 59
5.2 Causality 61
5.3 Designed Experiments 62
5.4 Observational Data 63
5.5 Matching 65
5.6 Covariate Adjustment 68
5.7 Qualitative Support for Causation 69
6 Diagnostics 73
6.1 Checking Error Assumptions 73
6.1.1 Constant Variance 73
6.1.2 Normality 78
6.1.3 Correlated Errors 81
6.2 Finding Unusual Observations 83
6.2.1 Leverage 83
6.2.2 Outliers 85
6.2.3 Influential Observations 89
6.3 Checking the Structure of the Model 92
6.4 Discussion 96
7 Problems with the Predictors 99
7.1 Errors in the Predictors 99
7.2 Changes of Scale 103
7.3 Collinearity 106
8 Problems with the Error 113
8.1 Generalized Least Squares 113
8.2 Weighted Least Squares 116
8.3 Testing for Lack of Fit 119
8.4 Robust Regression 123
8.4.1 M-Estimation 123
8.4.2 Least Trimmed Squares 126
9 Transformation 133
9.1 Transforming the Response 133
9.2 Transforming the Predictors 137
9.3 Broken Stick Regression 137
9.4 Polynomials 139
9.5 Splines 141
9.6 Additive Models 144
9.7 More Complex Models 145
10 Model Selection 149
10.1 Hierarchical Models 150
10.2 Testing-Based Procedures 151
10.3 Criterion-Based Procedures 153
10.4 Summary 159
11 Shrinkage Methods 161
11.1 Principal Components 161
11.2 Partial Least Squares 172
11.3 Ridge Regression 174
11.4 Lasso 177
12 Insurance Redlining — A Complete Example 183
12.1 Ecological Correlation 183
12.2 Initial Data Analysis 185
12.3 Full Model and Diagnostics 188
12.4 Sensitivity Analysis 190
12.5 Discussion 194
13 Missing Data 197
13.1 Types of Missing Data 197
13.2 Deletion 198
13.3 Single Imputation 200
13.4 Multiple Imputation 202
14 Categorical Predictors 205
14.1 A Two-Level Factor 205
14.2 Factors and Quantitative Predictors 209
14.3 Interpretation with Interaction Terms 212
14.4 Factors With More Than Two Levels 213
14.5 Alternative Codings of Qualitative Predictors 219
15 One Factor Models 223
15.1 The Model 223
15.2 An Example 224
15.3 Diagnostics 227
15.4 Pairwise Comparisons 228
15.5 False Discovery Rate 230
16 Models with Several Factors 235
16.1 Two Factors with No Replication 235
16.2 Two Factors with Replication 239
16.3 Two Factors with an Interaction 243
16.4 Larger Factorial Experiments 246
17 Experiments with Blocks 251
17.1 Randomized Block Design 252
17.2 Latin Squares 256
17.3 Balanced Incomplete Block Design 259
A About R 265
Bibliography 267
Index 271