Data analysis and graphics using R : an example-based approach / John Maindonald and John Braun.

Format:

Book

Author/Creator:

Maindonald, J. H. (John Hilary), 1937-

Contributor:

Braun, John, 1963-

Class of 1924 Book Fund.

Series:

Cambridge series on statistical and probabilistic mathematics

Cambridge series in statistical and probabilistic mathematics

Language:

English

Subjects (All):

Statistics--Data processing.

Statistics.

Statistics--Graphic methods--Data processing.

R (Computer program language).

Statistics--Graphic methods.

Physical Description:

xxiii, 362 pages : illustrations ; 26 cm.

Place of Publication:

Cambridge, UK ; New York : Cambridge University Press, 2003.

Summary:

Modern statistical software such as the powerful and freely available R system provides sophisticated tools for researchers who need to manipulate and display their data. Maindonald and Braun begin this example-based introduction to data analysis with a tutorial in R, and this allows them to demonstrate elementary concepts and methodologies for data analysis with real world examples drawn from their experience as teachers and consultants. The detailed discussion of regression methods that makes up the core of the book leads on to more advanced statistical concepts. As these are explained, the facilities that allow them to be implemented in the R system are illustrated. R code and data sets for all examples are available on the Internet, and can be reworked easily by the reader. This allows mathematical content to be kept to a minimum while statistical and scientific issues are still covered in depth. This book is therefore suitable for either the researcher requiring practical skills in data analysis, or the student looking for examples of applications to complement a more theoretically oriented course. Only basic statistical knowledge is assumed, approximately that for a first undergraduate course, and the methods demonstrated are suitable for use in fields as diverse as biology, social science, medicine and engineering.

Contents:

1.1 A Short R Session 1

1.1.1 R must be installed! 1

1.1.2 Using the console (or command line) window 1

1.1.3 Reading data from a file 2

1.1.4 Entry of data at the command line 3

1.1.5 Online help 4

1.1.6 Quitting R 5

1.2 The Uses of R 5

1.3 The R Language 6

1.3.1 R objects 7

1.3.2 Retaining objects between sessions 7

1.4 Vectors in R 8

1.4.1 Concatenation

joining vector objects 8

1.4.2 Subsets of vectors 8

1.4.3 Patterned data 9

1.4.4 Missing values 9

1.4.5 Factors 10

1.5 Data Frames 11

1.5.1 Variable names 12

1.5.2 Applying a function to the columns of a data frame 13

1.5.3 Data frames and matrices 13

1.5.4 Identification of rows that include missing values 13

1.6 R Packages 14

1.6.1 Data sets that accompany R packages 14

1.7 Looping 14

1.8 R Graphics 15

1.8.1 The function plot () and allied functions 16

1.8.2 Identification and location on the figure region 19

1.8.3 Plotting mathematical symbols 20

1.8.4 Row by column layouts of plots 20

1.8.5 Graphs

additional notes 22

1.9 Additional Points on the Use of R in This Book 23

2 Styles of Data Analysis 29

2.1 Revealing Views of the Data 29

2.1.1 Views of a single sample 30

2.1.2 Patterns in grouped data 33

2.1.3 Patterns in bivariate data

the scatterplot 34

2.1.4 Multiple variables and times 36

2.1.5 Lattice (trellis style) graphics 37

2.1.6 What to look for in plots 41

2.2 Data Summary 42

2.2.1 Mean and median 43

2.2.2 Standard deviation and inter-quartile range 44

2.2.3 Correlation 46

2.3 Statistical Analysis Strategies 47

2.3.1 Helpful and unhelpful questions 48

2.3.2 Planning the formal analysis 48

2.3.3 Changes to the intended plan of analysis 49

3 Statistical Models 52

3.1 Regularities 53

3.1.1 Mathematical models 53

3.1.2 Models that include a random component 54

3.1.3 Smooth and rough 55

3.1.4 The construction and use of models 56

3.1.5 Model formulae 56

3.2 Distributions: Models for the Random Component 57

3.2.1 Discrete distributions 57

3.2.2 Continuous distributions 58

3.3 The Uses of Random Numbers 60

3.3.1 Simulation 60

3.3.2 Sampling from populations 61

3.4 Model Assumptions 62

3.4.1 Random sampling assumptions

independence 62

3.4.2 Checks for normality 63

3.4.3 Checking other model assumptions 66

3.4.4 Are non-parametric methods the answer? 66

3.4.5 Why models matter

adding across contingency tables 67

4 An Introduction to Formal Inference 71

4.1 Standard Errors 71

4.1.1 Population parameters and sample statistics 71

4.1.2 Assessing accuracy

the standard error 71

4.1.3 Standard errors for differences of means 72

4.1.4 The standard error of the median 73

4.1.5 Resampling to estimate standard errors: bootstrapping 73

4.2 Calculations Involving Standard Errors: the t-Distribution 74

4.3 Confidence Intervals and Hypothesis Tests 77

4.3.1 One- and two-sample intervals and tests for means 78

4.3.2 Confidence intervals and tests for proportions 82

4.3.3 Confidence intervals for the correlation 83

4.4 Contingency Tables 84

4.4.1 Rare and endangered plant species 86

4.4.2 Additional notes 87

4.5 One-Way Unstructured Comparisons 88

4.5.1 Displaying means for the one-way layout 90

4.5.2 Multiple comparisons 91

4.5.3 Data with a two-way structure 92

4.5.4 Presentation issues 92

4.6 Response Curves 93

4.7 Data with a Nested Variation Structure 94

4.7.1 Degrees of freedom considerations 95

4.7.2 General multi-way analysis of variance designs 96

4.8 Resampling Methods for Tests and Confidence Intervals 96

4.8.1 The one-sample permutation test 96

4.8.2 The two-sample permutation test 97

4.8.3 Bootstrap estimates of confidence intervals 98

4.9 Further Comments on Formal Inference 100

4.9.1 Confidence intervals versus hypothesis tests 100

4.9.2 If there is strong prior information, use it! 101

5 Regression with a Single Predictor 107

5.1 Fitting a Line to Data 107

5.1.1 Lawn roller example 108

5.1.2 Calculating fitted values and residuals 109

5.1.3 Residual plots 110

5.1.4 The analysis of variance table 113

5.2 Outliers, Influence and Robust Regression 114

5.3 Standard Errors and Confidence Intervals 116

5.3.1 Confidence intervals and tests for the slope 116

5.3.2 SEs and confidence intervals for predicted values 117

5.3.3 Implications for design 118

5.4 Regression versus Qualitative ANOVA Comparisons 119

5.5 Assessing Predictive Accuracy 121

5.5.1 Training/test sets, and cross-validation 121

5.5.3 Bootstrapping 123

5.6 A Note on Power Transformations 126

5.7 Size and Shape Data 127

5.7.1 Allometric growth 128

5.7.2 There are two regression lines! 129

5.8 The Model Matrix in Regression 130

6 Multiple Linear Regression 134

6.1 Basic Ideas: Book Weight and Brain Weight Examples 134

6.1.1 Omission of the intercept term 137

6.1.2 Diagnostic plots 138

6.1.3 Further investigation of influential points 139

6.1.4 Example: brain weight 140

6.2 Multiple Regression Assumptions and Diagnostics 142

6.2.1 Influential outliers and Cook's distance 143

6.2.2 Component plus residual plots 143

6.2.3 Further types of diagnostic plot 145

6.2.4 Robust and resistant methods 145

6.3 A Strategy for Fitting Multiple Regression Models 145

6.3.2 Model fitting 146

6.3.3 An example

the Scottish hill race data 147

6.4 Measures for the Comparison of Regression Models 152

6.4.1 R[superscript 2] and adjusted R[superscript 2] 152

6.4.2 AIC and related statistics 152

6.4.3 How accurately does the equation predict? 153

6.4.4 An external assessment of predictive accuracy 155

6.5 Interpreting Regression Coefficients

the Labor Training Data 155

6.6 Problems with Many Explanatory Variables 161

6.6.1 Variable selection issues 162

6.6.2 Principal components summaries 163

6.7 Multicollinearity 164

6.7.2 The variance inflation factor (VIF) 167

6.7.3 Remedying multicollinearity 168

6.8 Multiple Regression Models

Additional Points 168

6.8.1 Confusion between explanatory and dependent variables 168

6.8.2 Missing explanatory variables 169

6.8.3 The use of transformations 169

6.8.4 Non-linear methods

an alternative to transformation? 170

7 Exploiting the Linear Model Framework 175

7.1 Levels of a Factor

Using Indicator Variables 175

7.1.1 Example

sugar weight 175

7.1.2 Different choices for the model matrix when there are factors 178

7.2 Polynomial Regression 179

7.2.1 Issues in the choice of model 181

7.3 Fitting Multiple Lines 183

7.4 Methods for Passing Smooth Curves through Data 187

7.4.1 Scatterplot smoothing

regression splines 188

7.4.2 Other smoothing methods 191

7.4.3 Generalized additive models 191

7.5 Smoothing Terms in Multiple Linear Models 192

8 Logistic Regression and Other Generalized Linear Models 197

8.1 Generalized Linear Models 197

8.1.1 Transformation of the expected value on the left 197

8.1.2 Noise terms need not be normal 198

8.1.3 Log odds in contingency tables 198

8.1.4 Logistic regression with a continuous explanatory variable 199

8.2 Logistic Multiple Regression 202

8.2.1 A plot of contributions of explanatory variables 208

8.2.2 Cross-validation estimates of predictive accuracy 209

8.3 Logistic Models for Categorical Data

an Example 210

8.4 Poisson and Quasi-Poisson Regression 211

8.4.1 Data on aberrant crypt foci 211

8.4.2 Moth habitat example 213

8.4.3 Residuals, and estimating the dispersion 215

8.5 Ordinal Regression Models 216

8.5.1 Exploratory analysis 217

8.5.2 Proportional odds logistic regression 217

8.6 Other Related Models 220

8.6.1 Loglinear models 220

8.6.2 Survival analysis 220

8.7 Transformations for Count

Data 221

9 Multi-level Models, Time Series and Repeated Measures 224

9.2 Example

Survey Data, with Clustering 225

9.2.1 Alternative models 225

9.2.2 Instructive, though faulty, analyses 228

9.2.3 Predictive accuracy 229

9.3 A Multi-level Experimental Design 230

9.3.1 The ANOVA table 232

9.3.2 Expected values of mean squares 232

9.3.3 The sums of squares breakdown 234

9.3.4 The variance components 236

9.3.5 The mixed model analysis 237

9.3.6 Predictive accuracy 239

9.3.7 Different sources of variance

complication or focus of interest? 239

9.4 Within and between Subject Effects

an Example 239

9.5 Time Series

Some Basic Ideas 242

9.5.1 Preliminary graphical explorations 242

9.5.2 The autocorrelation function 243

9.5.3 Autoregressive (AR) models 244

9.5.4 Autoregressive moving average (ARMA) models

theory 245

9.6 Regression Modeling with Moving Average Errors

an Example 246

9.7 Repeated Measures in Time

Notes on the Methodology 252

9.7.1 The theory of repeated measures modeling 253

9.7.2 Correlation structure 253

9.7.3 Different approaches to repeated measures analysis 254

9.8 Further Notes on Multi-level Modeling 255

9.8.1 An historical perspective on multi-level models 255

9.8.2 Meta-analysis 256

10 Tree-based Classification and Regression 259

10.1 The Uses of Tree-based Methods 259

10.1.1 Problems for which tree-based regression may be used 259

10.1.2 Tree-based regression versus parametric approaches 260

10.1.3 Summary of pluses and minuses 261

10.2 Detecting Email Spam

an Example 261

10.2.1 Choosing the number of splits 264

10.3 Terminology and Methodology 264

10.3.1 Choosing the split

regression trees 265

10.3.2 Within and between sums of squares 266

10.3.3 Choosing the split

classification trees 267

10.3.4 The mechanics of tree-based regression

a trivial example 268

10.4 Assessments of Predictive Accuracy 270

10.4.1 Cross-validation 270

10.4.2 The training/test set methodology 271

10.4.3 Predicting the future 271

10.5 A Strategy for Choosing the Optimal Tree 271

10.5.1 Cost-complexity pruning 271

10.5.2 Prediction error versus tree size 272

10.6 Detecting Email Spam

the Optimal Tree 273

10.6.1 The one-standard-deviation rule 273

10.7 Interpretation and Presentation of the rpart Output 275

10.7.1 Data for female heart attack patients 275

10.7.2 Printed Information on Each Split 276

11 Multivariate Data Exploration and Discrimination 281

11.1 Multivariate Exploratory Data Analysis 282

11.1.1 Scatterplot matrices 282

11.1.2 Principal components analysis 282

11.2 Discriminant Analysis 285

11.2.1 Example

plant architecture 286

11.2.2 Classical Fisherian discriminant analysis 287

11.2.3 Logistic discriminant analysis 289

11.2.4 An example with more than two groups 290

11.3 Principal Component Scores in Regression 291

11.4 Propensity Scores in Regression Comparisons

Labor Training Data 295

12 The R System

Additional Topics 300

12.1 Graphs in R 300

12.2.1 Common useful functions 303

12.2.2 User-written R functions 307

12.2.3 Functions for working with dates 310

12.3 Data input and output 310

12.5 Missing Values 317

12.6 Lists and Data Frames 320

12.6.1 Data frames as lists 320

12.6.2 Reshaping data frames; reshape () 320

12.6.3 Joining data frames and vectors

cbind () 322

12.6.4 Conversion of tables and arrays into data frames 322

12.6.5 Merging data frames

merge () 322

12.6.6 The function sapply () and related functions 323

12.6.7 Splitting vectors and data frames into lists

split () 324

12.7 Matrices and Arrays 324

12.7.1 Outer products 326

12.7.2 Arrays 327

12.8 Classes and Methods 328

12.8.1 Printing and summarizing model objects 328

12.8.2 Extracting information from model objects 329

12.9 Data-bases and Environments 330

12.9.1 Workspace management 331

12.9.2 Function environments, and lazy evaluation 331

12.10 Manipulation of Language Constructs 333

Epilogue

Models 338

Appendix S-PLUS Differences 341.

Notes:

Includes bibliographical references (pages [346]-351) and indexes.

Local Notes:

Acquired for the Penn Libraries with assistance from the Class of 1924 Book Fund.

ISBN:

0521813360

OCLC:

50520552

Online:

Publisher description