Statistical Regression Modeling With R: Longitudinal And Multi-level Modeling

Why Read This Book......Page 6
Structure of the Book......Page 7
Acknowledgments......Page 9
Contents......Page 10
About the Authors......Page 15
1.1.1 Data and Summary Statistics......Page 16
1.1.2 Preliminary Graphical Analysis......Page 17
1.2.1 Multiple Linear Regression Model......Page 18
1.2.3 The Method of Least Squares Estimation (LSE)......Page 19
1.2.4 The Properties of LSE......Page 20
1.3.1 Model Fitting......Page 21
1.3.2 Model Diagnostics......Page 22
1.4.1 Statistical Interaction/Moderation......Page 23
1.4.2 Main-Effect Model......Page 26
1.5.1 R Stepwise Model Selection Algorithm: Step......Page 27
1.5.2 Data Analysis with step Algorithm......Page 29
1.5.3 Discussions on Stepwise Regression......Page 35
1.6.1 Normality......Page 36
1.6.2 Homogeneity......Page 39
1.6.3 Independence......Page 40
1.7 Exercises......Page 41
2.1.1 Sampling......Page 42
2.1.1.3 Cluster Sampling......Page 43
2.2 Intra-Class Correlation......Page 44
2.2.2 Why ICC Is the Correlation for Individuals Within Clusters......Page 45
2.2.3 How to Estimate the ICC......Page 46
2.2.3.3 Estimate ρI......Page 47
2.2.4.2 Model Misspecification......Page 48
2.3 Why Random-Intercept and Random-Slope MLM......Page 49
2.4.1 NULL Model......Page 53
2.4.3 Random-Slope Model......Page 54
2.5 Three-Level MLMs......Page 56
2.6.2 Special Error Structure for Longitudinal Data......Page 57
2.7.2.1 Maximum Likelihood Estimation......Page 58
2.8 Exercises......Page 59
3.1 The Two-Level MLM......Page 60
3.2.1 Data on Public Examination Scores in 73 Schools......Page 61
3.2.2 Graphical Analysis......Page 63
3.2.3 Response Feature Analysis......Page 65
3.2.4 Fitting the Null Model (i.e., the Mean Model)......Page 69
3.2.5 Fitting MLM with Random-Intercept Model......Page 71
3.2.6 If Classical Linear Regression Is Used......Page 74
3.2.7 Fitting MLM with Random-Slope Model......Page 75
3.2.8 Fitting Interactions–Moderation Analysis......Page 76
3.3.1 Likelihood Ratio Chi-Square Test......Page 78
3.3.2 Refit the Models with Maximum LikelihoodEstimation......Page 79
3.3.3 ANOVA for Model Selection......Page 82
3.4 Confidence Intervals for Parameter Estimates......Page 84
3.5 Exercises......Page 85
4.1.1 Data Description......Page 86
4.1.2 Graphical Analysis......Page 88
4.2 Understanding Three-Level MLMs......Page 90
4.3 R Implementation with lme......Page 91
4.3.1 Fitting the Null Model......Page 92
4.3.2 Random-Intercept MLM: Adding IndependentVariables......Page 95
4.3.3 Random-Slope MLM......Page 97
4.3.4 Moderation Analysis with Three-Level MLM......Page 99
4.3.5 Model Selection......Page 102
4.4 Exercises......Page 103
5.1 Data on Breast Cancer Post-surgery Assessment......Page 105
5.2 Graphic Analysis......Page 109
5.3 Response Feature Analysis......Page 110
5.4.1 Random-Slope Model......Page 116
5.4.2 Fitting Random-Slope Model Using lme......Page 117
5.4.3 Fitting Random-Intercept Model Using lme......Page 118
5.4.4 Fitting Random-Slope MLM with Moderators......Page 119
5.4.5 Changing Covariance Structures of LongitudinalModels......Page 123
5.4.5.1 R Implementation for Random-Intercept Longitudinal Model......Page 124
5.4.5.2 R Implementation for Random-Slope Longitudinal Model......Page 126
5.5 Exercises......Page 127
6.1 Population Growth Models......Page 128
6.1.1 Model Development......Page 129
6.1.2 Illustration of the Logistic Growth Model......Page 131
6.2.1 R Packages for Nonlinear Regression......Page 132
6.2.2 Theory of Nonlinear Regression in nls......Page 135
6.3.1 Data on US Population......Page 136
6.3.2 Fitting the US Population Data Using nls......Page 138
6.4 Exercises......Page 142
7.1 Dataset of Loblolly Pine Trees' Growth......Page 143
7.2 Nonlinear Regression for Loblolly Growth......Page 144
7.3.1 Nonlinear MLM......Page 147
7.3.3 Model Fitting......Page 148
7.4 Exercise......Page 154
8.1.1 Data in Medical Diagnostics: The Stress Test......Page 155
8.1.2 Why Do We Not Model Binary Outcome Data Using Linear Regression?......Page 157
8.1.3 The Logistic Regression Model......Page 158
8.1.4 Maximum Likelihood Estimation......Page 159
8.1.5 Illustration of the Likelihood Function......Page 161
8.1.6 R Implementation in glm......Page 164
8.2.1 Research Papers by Graduate Students in Biochemistry PhD Programs......Page 167
8.2.2 Again Why Not Classical Linear Regression......Page 168
8.2.3 Poisson Regression......Page 170
8.2.4 Models for Overdispersed Counts Data......Page 171
8.2.4.1 Quasi-Poisson Regression......Page 172
8.2.4.2 Negative-Binomial Regression......Page 173
8.3 Exercises......Page 175
9.1 Data on the 1988 USA Presidential Election......Page 176
9.2 Logistic Regression......Page 182
9.3.1 Random-Intercept GLMM......Page 185
9.3.2 Random-Slope GLMM......Page 188
9.3.3 Model Selection......Page 190
9.4 Exercises......Page 191
10.1 Data on Red Grouse Ticks......Page 192
10.2 Graphical Analysis......Page 194
10.3.1 Random-Intercept Model......Page 196
10.3.2 Random-Slope Model......Page 201
10.4 Generalized Linear Mixed-Effects Model with Negative-Binomial Distribution......Page 203
10.5 Summary of Model Fitting......Page 205
A.1 WHO Statistics on Life Expectancy......Page 208
A.2 Public Examination Scores in 73 Schools......Page 211
A.3 Health Behavior in School-Aged Children (HBSC)......Page 212
A.4 Performance for Pupils in 50 Inner London Schools......Page 216
A.5 Longitudinal Breast Cancer Post-Surgery Assessment......Page 217
A.6 National Longitudinal Survey of Freshmen (NLSF)......Page 220
A.7 US Population Data......Page 223
A.8 State of North Carolina COVID-19 Data......Page 225
A.9 Political Polls on the 1988 US Presidential Election......Page 227
B R  Packages......Page 230
B.1 Function lme in R Package nlme for Linear Mixed-Effects Modeling......Page 231
B.2 Function nlme in R Package nlme for Nonlinear Mixed-Effects Modeling......Page 232
B.3 Function glmer in R Package lme4 for Generalized Linear Mixed-Effects Modeling......Page 233
Bibliography......Page 234
Index......Page 236