The R Book

Cover
......Page 1
Half-title
......Page 2
Title
......Page 4
Copyright
......Page 5
Contents......Page 6
Preface......Page 8
Acknowledgements......Page 9
Running R......Page 10
Getting Help in R......Page 11
Worked Examples of Functions......Page 12
Contents of Libraries......Page 13
Data Editor......Page 14
Significance Stars......Page 15
Linking to Other Computer Languages......Page 16
Tidying Up......Page 17
Screen prompt......Page 18
Built-in Functions......Page 19
Modulo and Integer Quotients......Page 20
Rounding......Page 21
Infinity and Things that Are Not a Number (NaN)......Page 22
Missing values NA......Page 23
Creating a Vector......Page 24
Named Elements within Vectors......Page 25
Vector Functions......Page 26
Using with rather than attach......Page 27
Subscripts and Indices......Page 29
Working with Vectors and Logical Subscripts......Page 30
Finding Closest Values......Page 32
Trimming Vectors Using Negative Subscripts......Page 33
Logical Arithmetic......Page 34
Evaluation of combinations of TRUE and FALSE......Page 35
Repeats......Page 36
Generate Factor Levels......Page 37
Generating Regular Sequences of Numbers......Page 38
Sorting, Ranking and Ordering......Page 39
The sample Function......Page 41
Matrices......Page 42
Arrays......Page 49
Character Strings......Page 52
Writing functions in R......Page 56
Variance......Page 60
Degrees of freedom......Page 61
Variance Ratio Test......Page 62
Using Variance......Page 63
Error Bars......Page 65
Loops and Repeats......Page 67
The switch Function......Page 72
Optional Arguments......Page 73
Variable Numbers of Arguments......Page 74
Returning Values from a Function......Page 75
Flexible Handling of Arguments to Functions......Page 76
Evaluating Functions with apply, sapply and lapply......Page 77
Looking for runs of numbers within vectors......Page 83
Saving Data Produced within R to Disc......Page 85
Testing for Equality......Page 86
Sets: union, intersect and setdiff......Page 87
Pattern Matching......Page 88
Testing and Coercing in R......Page 96
Dates and Times in R......Page 98
The scan Function......Page 106
Common Errors when Using read.table......Page 107
Separators and Decimal Points......Page 108
Checking Files from the Command Line......Page 110
Reading Data from Files with Non-standard Formats Using scan......Page 111
The readLines Function......Page 113
4 Dataframes......Page 116
Subscripts and Indices......Page 120
Sorting Dataframes......Page 122
Using Logical Conditions to Select Rows from the Dataframe......Page 125
Omitting Rows Containing Missing Values, NA......Page 128
Complex Ordering with Mixed Directions......Page 130
Creating a Dataframe from Another Kind of Object......Page 132
Eliminating Duplicate Rows from a Dataframe......Page 134
Dates in Dataframes......Page 135
Using the match Function in Dataframes......Page 136
Merging Two Dataframes......Page 138
Adding Margins to a Dataframe......Page 139
Summarizing the Contents of Dataframes......Page 141
Plots with Two Variables......Page 144
Plots for Single Samples......Page 170
Plots with multiple variables......Page 178
Special Plots......Page 182
Summary......Page 190
Summary Tables......Page 192
Tables of Counts......Page 196
Expanding a Table into a Dataframe......Page 197
Converting from a Dataframe to a Table......Page 198
Calculating tables of proportions......Page 199
The scale function......Page 200
The model.matrix function......Page 201
Mathematical Functions......Page 204
Continuous Probability Distributions......Page 217
Discrete probability distributions......Page 251
Matrix Algebra......Page 267
Calculus......Page 283
Differential equations......Page 284
Single Samples......Page 288
Two samples......Page 298
9 Statistical Modelling......Page 332
Maximum Likelihood......Page 333
Types of Statistical Model......Page 334
Steps Involved in Model Simplification......Page 336
Model Formulae in R......Page 338
Box–Cox Transformations......Page 345
Model checking......Page 348
Summary of Statistical Models in R......Page 358
Optional arguments in model-fitting functions......Page 359
Dataframes containing the same variable names......Page 361
Akaike’s Information Criterion......Page 362
Leverage......Page 363
Misspecified Model......Page 365
Model checking in R......Page 366
Contrasts......Page 377
10 Regression......Page 396
Linear Regression......Page 397
Polynomial Approximations to Elementary Functions......Page 412
Polynomial Regression......Page 413
Fitting a Mechanistic Model to Data......Page 416
Linear Regression after Transformation......Page 418
Prediction following Regression......Page 421
Testing for Lack of Fit in a Regression with Replicated Data at Each Level of x......Page 424
Bootstrap with Regression......Page 427
Jackknife with regression......Page 430
Jackknife after Bootstrap......Page 432
Serial correlation in the residuals......Page 433
Piecewise Regression......Page 434
Robust Fitting of Linear Models......Page 439
Model Simplification......Page 442
The Multiple Regression Model......Page 443
One-Way ANOVA......Page 458
Factorial Experiments......Page 475
Pseudoreplication: Nested Designs and Split Plots......Page 478
ANOVA with aov or lm......Page 488
Effect Sizes......Page 489
Multiple Comparisons......Page 491
Projections of Models......Page 495
Multivariate Analysis of Variance......Page 496
12 Analysis of Covariance......Page 498
Analysis of Covariance in R......Page 499
A More Complex ANCOVA: Two Factors and One Continuous Covariate......Page 509
Contrasts and the Parameters of ANCOVA Models......Page 513
Order matters in summary.aov......Page 516
13 Generalized Linear Models......Page 520
Error Structure......Page 521
Link Function......Page 522
Proportion Data and Binomial Errors......Page 523
Count Data and Poisson Errors......Page 524
Quasi-likelihood......Page 525
Offsets......Page 527
Residuals......Page 529
Misspecified Link Function......Page 530
Overdispersion......Page 531
Bootstrapping a GLM......Page 532
A Regression with Poisson Errors......Page 536
Analysis of Deviance with Count Data......Page 538
Analysis of Covariance with Count Data......Page 543
Frequency Distributions......Page 545
Overdispersion in Log-linear Models......Page 549
Negative binomial errors......Page 552
Use of lmer with Complex Nesting......Page 555
A Two-Class Table of Counts......Page 558
A Four-Class Table of Counts......Page 559
Two-by-Two Contingency Tables......Page 560
Using Log-linear Models for Simple Contingency Tables......Page 561
The Danger of Contingency Tables......Page 562
Quasi-Poisson and Negative Binomial Models Compared......Page 565
A Contingency Table of Intermediate Complexity......Page 567
Schoener’s Lizards: A Complex Contingency Table......Page 569
Plot Methods for Contingency Tables......Page 573
16 Proportion Data......Page 578
Count Data on Proportions......Page 579
Odds......Page 580
Overdispersion and Hypothesis Testing......Page 582
Applications......Page 583
Converting Complex Contingency Tables to Proportions......Page 593
Analysing Schoener’s Lizards as Proportion Data......Page 595
Generalized mixed models lmer with proportion data......Page 599
17 Binary Response Variables......Page 602
Incidence functions......Page 604
Graphical Tests of the Fit of the Logistic to Data......Page 605
ANCOVA with a Binary Response Variable......Page 607
Binary Response with Pseudoreplication......Page 613
18 Generalized Additive Models......Page 620
Non-parametric Smoothers......Page 621
Generalized Additive Models......Page 623
An example with strongly humped data......Page 629
Generalized Additive Models with Binary Data......Page 632
Three-Dimensional Graphic Output from gam......Page 634
19 Mixed-Effects Models......Page 636
Replication and Pseudoreplication......Page 638
The lme and lmer Functions......Page 639
Best Linear Unbiased Predictors......Page 640
A Designed Experiment with Different Spatial Scales: Split Plots......Page 641
Hierarchical Sampling and Variance Components Analysis......Page 647
Model Simplification in Hierarchical Sampling......Page 649
Mixed-Effects Models with Temporal Pseudoreplication......Page 650
Time Series Analysis in Mixed-Effects Models......Page 654
Random Effects in Designed Experiments......Page 657
Regression in Mixed-Effects Models......Page 659
Generalized Linear Mixed Models......Page 664
Fixed Effects in Hierarchical Sampling......Page 665
Error Plots from a Hierarchical Analysis......Page 666
20 Non-linear Regression......Page 670
Comparing Michaelis–Menten and Asymptotic Exponential......Page 673
Generalized Additive Models......Page 674
Grouped Data for Non-linear Estimation......Page 676
Non-linear Time Series Models (Temporal Pseudoreplication)......Page 680
Self-starting Functions......Page 683
Self-starting four-parameter logistic......Page 687
Bootstrapping a Family of Non-linear Regressions......Page 690
21 Tree Models......Page 694
Background......Page 695
Regression Trees......Page 697
Classification trees with categorical explanatory variables......Page 702
Classification trees for replicated data......Page 704
Testing for the existence of humps......Page 707
Nicholson’s Blowflies......Page 710
Moving Average......Page 717
Seasonal Data......Page 718
Built-in Time Series Functions......Page 723
Testing for a Trend in the Time Series......Page 724
Spectral Analysis......Page 726
Multiple Time Series......Page 727
Simulated Time Series......Page 731
Time Series Models......Page 735
Time series modelling on the Canadian lynx data......Page 736
Principal Components Analysis......Page 740
Factor Analysis......Page 744
Cluster Analysis......Page 747
Neural Networks......Page 756
Point Processes......Page 758
Nearest Neighbours......Page 759
Tests for Spatial Randomness......Page 763
Libraries for spatial statistics......Page 771
Geostatistical data......Page 783
Regression Models with Spatially Correlated Errors: Generalized Least Squares......Page 787
A Monte Carlo Experiment......Page 796
Background......Page 799
The Exponential Distribution......Page 801
Kaplan–Meier Survival Distributions......Page 802
Age-Specific Hazard Models......Page 803
Survival analysis in R......Page 804
Parametric analysis......Page 806
Cox’s Proportional Hazards......Page 808
Models with Censoring......Page 810
Temporal Dynamics: Chaotic Dynamics in Population Size......Page 820
Temporal and Spatial Dynamics: a Simulated Random Walk in Two Dimensions......Page 823
Spatial Simulation Models......Page 825
Pattern Generation Resulting from Dynamic Interactions......Page 831
Graphs for Publication......Page 836
Shading......Page 837
Logarithmic Axes......Page 839
Different font families for text......Page 840
Mathematical Symbols on Plots......Page 841
Phase Planes......Page 842
Fat Arrows......Page 844
Trellis Plots......Page 845
Three-Dimensional Plots......Page 851
An Alphabetical Tour of the Graphics Parameters......Page 856
References and Further Reading......Page 882
Index......Page 886