Front Matter
Copyright
Dedication
Contents
Preface
1 Introduction
1.1 Problems With Assuming Normality
1.2 Transformations
1.3 The Influence Curve
1.4 The Central Limit Theorem
1.5 Is the ANOVA F Robust?
1.6 Regression
1.7 More Remarks
1.8 R Software
1.9 Some Data Management Issues
1.9.1 Eliminating Missing Values
1.10 Data Sets
2 A Foundation for Robust Methods
2.1 Basic Tools for Judging Robustness
2.1.1 Qualitative Robustness
2.1.2 Infinitesimal Robustness
2.1.3 Quantitative Robustness
2.2 Some Measures of Location and Their Influence Function
2.2.1 Quantiles
2.2.2 The Winsorized Mean
2.2.3 The Trimmed Mean
2.2.4 M-Measures of Location
2.2.5 R-Measures of Location
2.3 Measures of Scale
2.4 Scale-Equivariant M-Measures of Location
2.5 Winsorized Expected Values
3 Estimating Measures of Location and Scale
3.1 A Bootstrap Estimate of a Standard Error
3.1.1 R Function bootse
3.2 Density Estimators
3.2.1 Silverman's Rule of Thumb
3.2.2 Rosenblatt's Shifted Histogram
3.2.3 The Expected Frequency Curve
3.2.4 An Adaptive Kernel Estimator
3.2.5 R Functions skerd, kerSORT, kerden, kdplot, rdplot, akerd, and splot
3.3 The Sample Median and Trimmed Mean
3.3.1 R Functions mean, tmean, median, and lloc
3.3.2 Estimating the Standard Error of the Trimmed Mean
3.3.3 Estimating the Standard Error of the Sample Winsorized Mean
3.3.4 R Functions winmean, winvar, winsd, trimse, and winse
3.3.5 Estimating the Standard Error of the Sample Median
3.3.6 R Function msmedse
3.4 The Finite Sample Breakdown Point
3.5 Estimating Quantiles
3.5.1 Estimating the Standard Error of the Sample Quantile
3.5.2 R Function qse
3.5.3 The Maritz–Jarrett Estimate of the Standard Error of x̂q
3.5.4 R Function mjse
3.5.5 The Harrell–Davis Estimator
3.5.6 R Functions qest and hd
3.5.7 A Bootstrap Estimate of the Standard Error of θ̂q
3.5.8 R Function hdseb
3.6 An M-Estimator of Location
3.6.1 R Function mad
3.6.2 Computing an M-Estimator of Location
3.6.3 R Function mest
3.6.4 Estimating the Standard Error of the M-Estimator
3.6.5 R Function mestse
3.6.6 A Bootstrap Estimate of the Standard Error of μ̂m
3.6.7 R Function mestseb
3.7 One-Step M-Estimator
3.7.1 R Function onestep
3.8 W-Estimators
3.8.1 Tau Measure of Location
3.8.2 R Function tauloc
3.8.3 Zuo's Weighted Estimator
3.9 The Hodges–Lehmann Estimator
3.10 Skipped Estimators
3.10.1 R Functions mom, zwe, and bmean
3.11 Some Comparisons of the Location Estimators
3.12 More Measures of Scale
3.12.1 The Biweight Midvariance
3.12.2 R Function bivar
3.12.3 The Percentage Bend Midvariance and tau Measure of Variation
3.12.4 R Functions pbvar and tauvar
3.12.5 The Interquartile Range
3.12.6 R Functions idealf, idrange, idealfIQR, and quantile
3.13 Some Outlier Detection Methods
3.13.1 Rules Based on Means and Variances
3.13.2 A Method Based on the Interquartile Range
3.13.3 Carling's Modification
3.13.4 A MAD-Median Rule
3.13.5 R Functions outbox, out, and boxplot
3.13.6 R Functions adjboxout and adjbox
3.14 Exercises
4 Inferences in the One-Sample Case
4.1 Problems When Working With Means
4.1.1 P-Values and Testing for Equality: Hypothesis Testing Versus Decision Making
4.2 The g-and-h Distribution
4.2.1 R Functions ghdist, rmul, rngh, rmul.MAR, ghtrim, and gskew
4.3 Inferences About the Trimmed, Winsorized Means
4.3.1 Comments on Effect Size and Non-Normal Distributions
4.3.2 R Functions trimci, winci, D.akp.effect.ci, and depQSci
4.4 Basic Bootstrap Methods
4.4.1 The Percentile Bootstrap Method
4.4.2 R Functions onesampb and hdpb
4.4.3 Bootstrap-t Method
4.4.4 Bootstrap Methods When Using a Trimmed Mean
4.4.5 Singh's Modification
4.4.6 R Functions trimpb and trimcibt
4.5 Inferences About M-Estimators
4.5.1 R Functions mestci and momci
4.6 Confidence Intervals for Quantiles
4.6.1 Beware of Tied Values When Making Inferences About Quantiles
4.6.2 A Modification of the Distribution-Free Method for the Median
4.6.3 R Functions qmjci, hdci, sint, sintv2, qci, qcipb, and qint
4.7 Empirical Likelihood
4.8 Inferences About the Probability of Success
4.8.1 R Functions binom.conf.pv and cat.dat.ci
4.9 Concluding Remarks
4.10 Exercises
5 Comparing Two Groups
5.1 The Shift Function
5.1.1 The Kolmogorov–Smirnov Test
5.1.2 R Functions ks, kssig, kswsig, and kstiesig
5.1.3 Confidence Bands for the Shift Function
5.1.4 R Functions sband and wband
5.1.5 Confidence Band for Specified Quantiles
Method Q1
Method Q2
5.1.6 R Functions shifthd, qcomhd, qcomhdMC, and q2gci
5.1.7 R Functions g2plot and g5plot
5.2 Student's T Test
5.3 Comparing Medians and Other Trimmed Means
5.3.1 R Functions yuen and msmed
5.3.2 A Bootstrap-t Method for Comparing Trimmed Means
5.3.3 R Functions yuenbt and yhbt
5.3.4 Measuring Effect Size
A Standardized Difference
A Quantile Shift Perspective
Explanatory Power
A Classification Perspective
A Probabilistic Measure of Effect Size
5.3.5 R Functions ESfun, akp.effect.ci, KMS.ci, ees.ci, med.effect, qhat, and qshift
5.4 Inferences Based on a Percentile Bootstrap Method
5.4.1 Comparing M-Estimators
5.4.2 Comparing Trimmed Means and Medians
5.4.3 R Functions trimpb2, pb2gen, medpb2, and M2gbt
5.5 Comparing Measures of Scale
5.5.1 Comparing Variances
5.5.2 R Functions comvar2 and varcom.IND.MP
5.5.3 Comparing Biweight Midvariances and Deviations From the Median
5.5.4 R Functions b2ci, comvar.locdis, and g5.cen.plot
5.6 Permutation Tests
5.6.1 R Function permg
5.7 Methods Based on Ranks and the Typical Difference
5.7.1 The Cliff and Brunner–Munzel Methods
Cliff's Method
Brunner–Munzel Method
Inferences About θD
5.7.2 A Quantile Shift Measure of Effect Size Based on the Typical Difference
5.7.3 R Functions cidv2, bmp, wmwloc, wmwpb, loc2plot, shiftQSci, akp.effec.ci, ES.summary, ES.summary.CI, ES.sum.REL.MAG, and loc.dif.summary
5.8 Comparing Two Independent Binomial and Multinomial Distributions
5.8.1 R Functions binom2g and bi2CR
5.8.2 Comparing Discrete (Multinomial) Distributions
5.8.3 R Functions binband, splotg5, and cumrelf
5.9 Comparing Dependent Groups
5.9.1 A Shift Function for Dependent Groups
5.9.2 R Function lband
5.9.3 Comparing Specified Quantiles
Method D1
Method D2
Method D3
5.9.4 R Functions shiftdhd, Dqcomhd, qdec2ci, Dqdif, and difQpci
5.9.5 Comparing Trimmed Means
Effect Size
5.9.6 R Function yuend
5.9.7 A Bootstrap-t Method for Marginal Trimmed Means
5.9.8 R Function ydbt
5.9.9 Inferences About the Typical Difference
5.9.10 R Functions loc2dif, l2drmci, and dep.dif.fun
5.9.11 Percentile Bootstrap: Comparing Medians, M-Estimators, and Other Measures of Location and Scale
5.9.12 R Functions two.dep.pb and bootdpci
5.9.13 Handling Missing Values
Method M1
Method M2
Method M3
Comments on Choosing a Method
5.9.14 R Functions rm2miss and rmmismcp
5.9.15 Comparing Variances and Robust Measures of Scale
5.9.16 R Functions comdvar, rmVARcom, and RMcomvar.locdis
5.9.17 The Sign Test
5.9.18 R Function signt
5.9.19 Effect Size for Dependent Groups
5.9.20 R Function dep.ES.summary.CI
5.10 Exercises
6 Some Multivariate Methods
6.1 Generalized Variance
6.2 Depth
6.2.1 Mahalanobis Depth
6.2.2 Halfspace Depth
6.2.3 Computing Halfspace Depth
6.2.4 R Functions depth2, depth, fdepth, fdepthv2, and unidepth
6.2.5 Projection Depth
6.2.6 R Functions pdis, pdisMC, and pdepth
6.2.7 More Measures of Depth
6.2.8 R Functions zdist, zoudepth prodepth, Bagdist, bagdepth, and zonoid
6.3 Some Affine Equivariant Estimators
6.3.1 Minimum Volume Ellipsoid Estimator
6.3.2 The Minimum Covariance Determinant Estimator
6.3.3 S-Estimators and Constrained M-Estimators
6.3.4 R Functions tbs, DETS, and DETMCD
6.3.5 Donoho–Gasko Generalization of a Trimmed Mean
6.3.6 R Functions dmean and dcov
6.3.7 The Stahel–Donoho W-Estimator
6.3.8 R Function sdwe
6.3.9 Median Ball Algorithm
6.3.10 R Function rmba
6.3.11 OGK Estimator
6.3.12 R Function ogk
6.3.13 An M-Estimator
6.3.14 R Functions MARest and dmedian
6.4 Multivariate Outlier Detection Methods
6.4.1 The Relplot and Bagplot
6.4.2 R Functions relplot and Bagplot
6.4.3 The MVE Method
6.4.4 Methods MCD, DETMCD, and DDC
6.4.5 R Functions covmve and covmcd
6.4.6 R Functions out and outogk
6.4.7 The MGV Method
6.4.8 R Function outmgv
6.4.9 A Projection Method
6.4.10 R Functions outpro and out3d
6.4.11 Outlier Identification in High Dimensions
6.4.12 R Functions outproad and outmgvad
6.4.13 Methods Designed for Functional Data
6.4.14 R Functions FBplot, Flplot, medcurve, func.out, spag.plot, funloc, and funlocpb
6.4.15 Comments on Choosing an Outlier Detection Method
6.5 A Skipped Estimator of Location and Scatter
6.5.1 R Functions smean, mgvmean, L1medcen, spat, mgvcov, skip, and skipcov
6.6 Robust Generalized Variance
6.6.1 R Function gvarg
6.7 Multivariate Location: Inference in the One-Sample Case
6.7.1 Inferences Based on the OP Measure of Location
6.7.2 Extension of Hotelling's T2 to Trimmed Means
6.7.3 R Functions smeancrv2 and hotel1.tr
6.7.4 Inferences Based on the MGV Estimator
6.7.5 R Function smgvcr
6.8 The Two-Sample Case
6.8.1 Independent Case
Effect Size
6.8.2 Comparing Dependent Groups
6.8.3 R Functions smean2, mul.loc2g, MUL.ES.sum, Dmul.loc2g, matsplit, and mat2grp
Data Management
6.8.4 Comparing Robust Generalized Variances
6.8.5 R Function gvar2g
6.8.6 Rank-Based Methods
6.8.7 R Functions mulrank, cmanova, and cidMULT
6.9 Multivariate Density Estimators
6.10 A Two-Sample, Projection-Type Extension of the Wilcoxon–Mann–Whitney Test
6.10.1 R Functions mulwmw and mulwmwv2
6.11 A Relative Depth Analog of the Wilcoxon–Mann–Whitney Test
6.11.1 R Function mwmw
6.12 Comparisons Based on Depth
6.12.1 R Functions lsqs3 and depthg2
6.13 Comparing Dependent Groups Based on All Pairwise Differences
6.13.1 R Function dfried
6.14 Robust Principal Component Analysis
6.14.1 R Functions prcomp and regpca
6.14.2 Maronna's Method
6.14.3 The SPCA Method
6.14.4 Methods HRVB and MacroPCA
6.14.5 Method OP
6.14.6 Method PPCA
6.14.7 R Functions outpca, robpca, robpcaS, SPCA, Ppca, and Ppca.summary
6.14.8 Comments on Choosing the Number of Components
6.15 Cluster Analysis
6.15.1 R Functions Kmeans, kmeans.grp, TKmeans, and TKmeans.grp
6.16 Classification Methods
6.16.1 Some Issues Related to Error Rates
Estimating and Comparing Error Rates
6.16.2 R Functions CLASS.fun, CLASS.bag, class.error.com, and menES
6.17 Exercises
7 One-Way and Higher Designs for Independent Groups
7.1 Trimmed Means and a One-Way Design
7.1.1 A Welch-Type Procedure and a Robust Measure of Effect Size
Robust, Heteroscedastic Measures of Effect Size
7.1.2 R Functions t1way, t1wayv2, t1way.EXES.ci, KS.ANOVA.ES, fac2list, t1wayF, and ESprodis
Data Management
7.1.3 A Generalization of Box's Method
7.1.4 R Function box1way
7.1.5 Comparing Medians and Other Quantiles
7.1.6 R Functions med1way and Qanova
7.1.7 Bootstrap-t Methods
A Method Based on Bailey's Transformation
7.1.8 R Functions t1waybt, btrim, and t1waybtsqrk
7.2 Two-Way Designs and Trimmed Means
7.2.1 R Functions t2way and bb.es.main
7.2.2 Comparing Medians
7.2.3 R Functions med2way and Q2anova
7.3 Three-Way Designs, Trimmed Means, and Medians
7.3.1 R Functions t3way, fac2list, and Q3anova
7.4 Multiple Comparisons Based on Medians and Other Trimmed Means
7.4.1 Basic Methods Based on Trimmed Means
A Step-Down Multiple-Comparison Procedure
7.4.2 R Functions lincon, conCON, IND.PAIR.ES, and stepmcp
Effect Size
7.4.3 Multiple Comparisons for Two-Way and Three-Way Designs
7.4.4 R Functions bbmcp, RCmcp, mcp2med, twoway.pool, bbbmcp, mcp3med, con2way, and con3way
7.4.5 A Bootstrap-t Procedure
7.4.6 R Functions linconbt, bbtrim, and bbbtrim
7.4.7 Controlling the Familywise Error Rate: Improvements on the Bonferroni Method
Rom's Method
Hochberg's Method
Hommel's Method
Benjamini–Hochberg Method
The k-FWER Procedures
7.4.8 R Functions p.adjust and mcpKadjp
7.4.9 Percentile Bootstrap Methods for Comparing Medians, Other Trimmed Means, and Quantiles
7.4.10 R Functions linconpb, bbmcppb, bbbmcppb, medpb, Qmcp, med2mcp, med3mcp, and q2by2
7.4.11 Deciding Which Group Has the Largest Measure of Location
Methods RS and MCWB
Method RS2-GPB
Method RS2-IP
7.4.12 R Functions anc.best.PV, anc.bestpb, PMD.PCD, RS.LOC.IZ, best.DO, and bestPB.DO
7.4.13 Determining the Order of the Population Trimmed Means
7.4.14 R Function ord.loc.PV
7.4.15 Judging Sample Sizes
7.4.16 R Function hochberg
7.4.17 Measures of Effect Size: Two-Way and Higher Designs
Interactions: ME1
Interactions: ME2
Interactions: IE1
Another Non-Parametric Approach
7.4.18 R Functions twowayESM, RCES, interES.2by2, interJK.ESmul, and IND.INT.DIF.ES
7.4.19 Comparing Curves (Functional Data)
7.4.20 R Functions funyuenpb and Flplot2g
7.4.21 Comparing Variances and Robust Measures of Scale
7.4.22 R Functions comvar.mcp and robVARcom.mcp
7.5 A Random Effects Model for Trimmed Means
7.5.1 A Winsorized Intraclass Correlation
7.5.2 R Function rananova
7.6 Bootstrap Global Tests
7.6.1 R Functions b1way, pbadepth, and boot.TM
7.6.2 M-Estimators and Multiple Comparisons
Variation of a Bootstrap-t Method
A Percentile Bootstrap Method: Method SR
7.6.3 R Functions linconm and pbmcp
7.6.4 M-Estimators and the Random Effects Model
7.6.5 Other Methods for One-Way Designs
7.7 M-Measures of Location and a Two-Way Design
7.7.1 R Functions pbad2way and mcp2a
7.8 Ranked-Based Methods for a One-Way Design
7.8.1 The Rust–Fligner Method
7.8.2 R Function rfanova
7.8.3 A Rank-Based Method That Allows Tied Values
7.8.4 R Function bdm
7.8.5 Inferences About a Probabilistic Measure of Effect Size
Method CHMCP
Method WMWAOV
Method DBH
7.8.6 R Functions cidmulv2, wmwaov, and cidM
7.9 A Rank-Based Method for a Two-Way Design
7.9.1 R Function bdm2way
7.9.2 The Patel–Hoel, De Neve–Thas, and Related Approaches to Interactions
7.9.3 R Functions rimul, inter.TDES, LCES, linplot, and plot.inter
7.10 MANOVA Based on Trimmed Means
7.10.1 R Functions MULtr.anova, MULAOVp, fac2Mlist, and YYmanova
7.10.2 Linear Contrasts
7.10.3 R Functions linconMpb, linconSpb, YYmcp, and fac2BBMlist
Data Management
7.11 Nested Designs
7.11.1 R Functions anova.nestA, mcp.nestAP, and anova.nestAP
7.12 Methods for Binary Data
7.12.1 R Functions lincon.bin and binpair
7.12.2 Identifying the Group With the Highest Probability of Success
7.12.3 R Functions bin.best, bin.best.DO, and bin.PMD.PCD
7.13 Exercises
8 Comparing Multiple Dependent Groups
8.1 Comparing Trimmed Means
8.1.1 Omnibus Test Based on the Trimmed Means of the Marginal Distributions Plus a Measure of Effect Size
Effect Size
8.1.2 R Functions rmanova and rmES.pro
8.1.3 Pairwise Comparisons and Linear Contrasts Based on Trimmed Means
8.1.4 Linear Contrasts Based on the Marginal Random Variables
8.1.5 R Functions rmmcp, rmmismcp, trimcimul, wwlin.es, deplin.ES.summary.CI, and boxdif
8.1.6 Judging the Sample Size
8.1.7 R Functions stein1.tr and stein2.tr
8.1.8 Identifying the Group With the Largest Population Measure of Location
8.1.9 Identifying the Variable With the Smallest Robust Measure of Variation
8.1.10 R Functions comdvar.mcp, ID.sm.varPB, rmbestVAR.DO, rmanc.best.PV, RM.PMD.PCD, rmanc.best.PB, RMPB.PMD.PCD, and rmanc.best.DO
Measure of Location: Analogs of Method RS1
Measure of Location: Analogs of Method RS2
8.2 Bootstrap Methods Based on Marginal Distributions
8.2.1 Comparing Trimmed Means
8.2.2 R Function rmanovab
8.2.3 Multiple Comparisons Based on Trimmed Means
8.2.4 R Functions pairdepb and bptd
8.2.5 Percentile Bootstrap Methods
Method RMPB3
Method RMPB4
Missing Values
8.2.6 R Functions bd1way and ddep
8.2.7 Multiple Comparisons Using M-Estimators or Skipped Estimators
8.2.8 R Functions lindm and mcpOV
8.2.9 Comparing Robust Measures of Scatter
8.2.10 R Function rmrvar
8.3 Bootstrap Methods Based on Difference Scores and a Measure of Effect Size
8.3.1 R Functions rmdzero and rmES.dif.pro
8.3.2 Multiple Comparisons
8.3.3 R Functions rmmcppb, wmcppb, dmedpb, lindepbt, and qdmcpdif
8.3.4 Measuring Effect Size: R Function DEP.PAIR.ES
8.3.5 Comparing Multinomial Cell Probabilities
8.3.6 R Functions cell.com, cell.com.pv, and best.cell.DO
8.4 Comments on Which Method to Use
8.5 Some Rank-Based Methods
8.5.1 R Functions apanova and bprm
8.6 Between-by-Within and Within-by-Within Designs
8.6.1 Analyzing a Between-by-Within Design Based on Trimmed Means
8.6.2 R Functions bwtrim, bw.es.main, and tsplit
8.6.3 Data Management: R Function bw2list
8.6.4 Bootstrap-t Method for a Between-by-Within Design
8.6.5 R Functions bwtrimbt and tsplitbt
8.6.6 Percentile Bootstrap Methods for a Between-by-Within Design
8.6.7 R Functions sppba, sppbb, and sppbi
8.6.8 Multiple Comparisons
Method BWMCP
Method BWAMCP: Comparing Levels of Factor A for Each Level of Factor B
Method BWBMCP: Dealing With Factor B
Method BWIMCP: Interactions
Methods SPMCPA, SPMCPB, and SPMCPI
8.6.9 R Functions bwmcp, bwmcppb, bwmcppb.adj, bwamcp, bw.es.A, bw.es.B, bwbmcp, bw.es.I, bwimcp, bwimcpES, spmcpa, spmcpb, spmcpbA, and spmcpi
8.6.10 Within-by-Within Designs
8.6.11 R Functions wwtrim, wwtrimbt, wwmcp, wwmcppb, wwmcpbt, ww.es, wwmed, and dlinplot
8.6.12 A Rank-Based Approach
8.6.13 R Function bwrank
8.6.14 Rank-Based Multiple Comparisons
8.6.15 R Function bwrmcp
8.6.16 Multiple Comparisons When Using a Patel–Hoel Approach to Interactions
8.6.17 R Function BWPHmcp
8.7 Three-Way Designs
8.7.1 Global Tests Based on Trimmed Means
8.7.2 R Functions bbwtrim, bwwtrim, wwwtrim, bbwtrimbt, bwwtrimbt, wwwtrimbt, and wwwmed
8.7.3 Data Management: R Functions bw2list and bbw2list
8.7.4 Multiple Comparisons
8.7.5 R Functions wwwmcp, bbwmcp, bwwmcp, bbwmcppb, bwwmcppb, wwwmcppb, and wwwmcppbtr
Bootstrap-t Methods
Percentile Bootstrap Methods
8.8 Exercises
9 Correlation and Tests of Independence
9.1 Problems With Pearson's Correlation
9.1.1 Features of Data That Affect r and T
9.1.2 Heteroscedasticity and the Classic Test That ρ=0
9.2 Two Types of Robust Correlations
9.3 Some Type M Measures of Correlation
9.3.1 The Percentage Bend Correlation
9.3.2 A Test of Independence Based on ρpb
9.3.3 R Function pbcor
9.3.4 A Test of Zero Correlation Among p Random Variables
9.3.5 R Function pball
9.3.6 The Winsorized Correlation
9.3.7 R Function wincor
9.3.8 The Biweight Midcovariance and Correlation
9.3.9 R Functions bicov and bicovm
9.3.10 Kendall's tau
9.3.11 Spearman's rho
9.3.12 R Functions tau, spear, cor, taureg, COR.ROB, and COR.PAIR
9.3.13 Heteroscedastic Tests of Zero Correlation
9.3.14 R Functions corb, corregci, pcorb, pcorhc4, and rhohc4bt
9.4 Some Type O Correlations
9.4.1 MVE and MCD Correlations
9.4.2 Skipped Measures of Correlation
9.4.3 The OP Correlation
9.4.4 Inferences Based on Multiple Skipped Correlations
Method IND
Method ECP
Method H1
9.4.5 R Functions scor, scorall, scorci, mscorpb, mscorci, mscorciH, scorreg, scorregci, and scorregciH
9.5 A Test of Independence Sensitive to Curvature
9.5.1 R Functions indt, indtall, and medind
9.6 Comparing Correlations: Independent Case
9.6.1 Comparing Pearson Correlations
9.6.2 Comparing Robust Correlations
9.6.3 R Functions twopcor, tworhobt, and twocor
9.7 Exercises
10 Robust Regression
10.1 Problems With Ordinary Least Squares
10.1.1 Computing Confidence Intervals Under Heteroscedasticity
Method HC4WB-D
Method HC4WB-C
10.1.2 An Omnibus Test
10.1.3 R Functions lsfitci, olshc4, hc4test, and hc4wtest
10.1.4 Comments on Comparing Means via Dummy Coding
10.1.5 Salvaging the Homoscedasticity Assumption
10.2 The Theil–Sen Estimator
10.2.1 R Functions tsreg, tshdreg, correg, regplot, and regp2plot
10.3 Least Median of Squares
10.3.1 R Function lmsreg
10.4 Least Trimmed Squares Estimator
10.4.1 R Function ltsreg
10.5 Least Trimmed Absolute Value Estimator
10.5.1 R Function ltareg
10.6 M-Estimators
10.7 The Hat Matrix
10.8 Generalized M-Estimators
10.8.1 R Function bmreg
10.9 The Coakley–Hettmansperger and Yohai Estimators
10.9.1 MM-Estimator
10.9.2 R Functions chreg and MMreg
10.10 Skipped Estimators
10.10.1 R Functions mgvreg and opreg
10.11 Deepest Regression Line
10.11.1 R Functions rdepth.orig, Rdepth, mdepreg.orig, and mdepreg
10.12 A Criticism of Methods With a High Breakdown Point
10.13 Some Additional Estimators
10.13.1 S-Estimators and τ-Estimators
10.13.2 R Functions snmreg and stsreg
10.13.3 E-Type Skipped Estimators
10.13.4 R Functions mbmreg, tstsreg, tssnmreg, and gyreg
10.13.5 Methods Based on Robust Covariances
10.13.6 R Functions bireg, winreg, and COVreg
10.13.7 L-Estimators
10.13.8 L1 and Quantile Regression
10.13.9 R Functions qreg, rqfit, and qplotreg
10.13.10 Methods Based on Estimates of the Optimal Weights
10.13.11 Projection Estimators
10.13.12 Methods Based on Ranks
10.13.13 R Functions Rfit and Rfit.est
10.13.14 Empirical Likelihood Type and Distance-Constrained Maximum Likelihood Estimators
10.13.15 Ridge Estimators: Dealing With Multicollinearity
10.13.16 R Functions ols.ridge, rob.ridge, and rob.ridge.liu
10.13.17 Robust Elastic Net and Lasso Estimators: Reducing the Number of Independent Variables
10.13.18 R Functions lasso.est, lasso.rep, RA.lasso, LAD.lasso, H.lasso, HQreg, and LTS.EN
10.14 Comments About Various Estimators
10.14.1 Contamination Bias
10.15 Outlier Detection Based on a Robust Fit
10.15.1 Detecting Regression Outliers
10.15.2 R Functions reglev and rmblo
10.16 Logistic Regression and the General Linear Model
10.16.1 R Functions glm, logreg, logreg.pred, wlogreg, logreg.plot, logreg.P.ci, and logistic.lasso
10.16.2 The General Linear Model
10.16.3 R Function glmrob
10.17 Multivariate Regression
10.17.1 The RADA Estimator
10.17.2 The Least Distance Estimator
10.17.3 R Functions MULMreg, mlrreg, and Mreglde
10.17.4 Multivariate Least Trimmed Squares Estimator
10.17.5 R Function MULtsreg
10.17.6 Other Robust Estimators
10.18 Exercises
11 More Regression Methods
11.1 Inferences About Robust Regression Parameters
11.1.1 Omnibus Tests for Regression Parameters
Methods Based on a Ridge Estimator
Method RT1
Method RT2
11.1.2 R Functions regtest, ridge.test and ridge.Gtest
11.1.3 Inferences About Individual Parameters
11.1.4 R Functions regci, regciMC and wlogregci
11.1.5 Methods Based on the Quantile Regression Estimator
11.1.6 R Functions rqtest, qregci, and qrchk
11.1.7 Inferences Based on the OP-Estimator
11.1.8 R Functions opregpb and opregpbMC
11.1.9 Hypothesis Testing When Using a Multivariate Regression Estimator RADA
11.1.10 R Function mlrGtest
11.1.11 Robust ANOVA via Dummy Coding
11.1.12 Confidence Bands for the Typical Value of y, Given x
11.1.13 R Functions regYhat, regYci, and regYband
11.1.14 R Function regse
11.2 Comparing the Regression Parameters of J >=2 Groups
11.2.1 Methods for Comparing Independent Groups
Methods Based on the Least Squares Regression Estimator
Multiple Comparisons
Methods Based on Robust Estimators
11.2.2 R Functions reg2ci, reg1way, reg1wayISO, ancGpar, ols1way, ols1wayISO, olsJmcp, olsJ2, reg1mcp, and olsWmcp
11.2.3 Methods for Comparing Two Dependent Groups
Methods Based on a Robust Estimator
Methods Based on the Least Squares Estimator
11.2.4 R Functions DregG, difreg, and DregGOLS
11.3 Detecting Heteroscedasticity
11.3.1 A Quantile Regression Approach
11.3.2 The Koenker–Bassett Method
11.3.3 R Functions qhomt and khomreg
11.4 Curvature and Half-Slope Ratios
11.4.1 R Function hratio
11.5 Curvature and Non-Parametric Regression
11.5.1 Smoothers
11.5.2 Kernel Estimators and Cleveland's LOWESS
Kernel Smoothing
Cleveland's LOWESS
11.5.3 R Functions lplot, lplot.pred, and kerreg
11.5.4 The Running-Interval Smoother
11.5.5 R Functions rplot, runYhat, rplotCI, and rplotCIv2
11.5.6 Smoothers for Estimating Quantiles
11.5.7 R Function qhdsm
11.5.8 Special Methods for Binary Outcomes
11.5.9 R Functions logSM, logSM2g, logSMpred, rplot.bin, runbin.CI, rplot.binCI, and multsm
11.5.10 Smoothing With More Than One Predictor
11.5.11 R Functions rplot, runYhat, rplotsm, runpd, and RFreg
11.5.12 LOESS
11.5.13 Other Approaches
11.5.14 R Functions adrun, adrunl, gamplot, and gamplotINT
11.5.15 Detecting and Describing Associations via Quantile Grids
11.5.16 R Functions smgridAB, smgridLC, smgrid, smtest, and smbinAB
11.6 Checking the Specification of a Regression Model
11.6.1 Testing the Hypothesis of a Linear Association
11.6.2 R Function lintest
11.6.3 Testing the Hypothesis of a Generalized Additive Model
11.6.4 R Function adtest
11.6.5 Inferences About the Components of a Generalized Additive Model
11.6.6 R Function adcom
11.6.7 Detecting Heteroscedasticity Based on Residuals
11.6.8 R Function rhom
11.7 Regression Interactions and Moderator Analysis
11.7.1 R Functions kercon, riplot, runsm2g, ols.plot.inter, olshc4.inter, reg.plot.inter, and regci.inter
11.7.2 Mediation Analysis
11.7.3 R Functions ZYmediate, regmed2, and regmediate
11.8 Comparing Parametric, Additive, and Non-Parametric Fits
11.8.1 R Functions reg.vs.rplot, reg.vs.lplot, and logrchk
11.9 Measuring the Strength of an Association Given a Fit to the Data
11.9.1 R Functions RobRsq, qcorp1, and qcor
11.9.2 Comparing Two Independent Groups via the LOWESS Version of Explanatory Power
11.9.3 R Functions smcorcom and smstrcom
11.10 Comparing Predictors
11.10.1 Comparing Correlations
11.10.2 R Functions TWOpov, TWOpNOV, corCOMmcp, twoDcorR, and twoDNOV
11.10.3 Methods for Characterizing the Relative Importance of Independent Variables
Prediction Error
The 0.632 Estimator
The Leave-One-Out Cross-Validation Method
Which Independent Variable Has the Strongest Association With the Independent Variable?
11.10.4 R Functions regpre, regpreCV, corREG.best.DO, and PcorREG.best.DO
11.10.5 Inferences About Which Predictors Are Best
Method IBS
Method BTS
Method SM
11.10.6 R Functions regIVcom, regIVcommcp, logIVcom, ts2str, and sm2strv7
11.11 Marginal Longitudinal Data Analysis: Comments on Comparing Groups
11.11.1 R Functions long2g, longreg, longreg.plot, and xyplot
11.12 Exercises
12 ANCOVA
12.1 Methods Based on Specific Design Points and a Linear Model
12.1.1 Method S1
12.1.2 Method S2
12.1.3 Linear Contrasts for a One-Way or Higher Design
12.1.4 Dealing With Two or More Covariates
12.1.5 R Functions ancJN, ancJNmp, ancJNmpcp, anclin, reg2plot, reg2g.p2plot, and ancJN.LC
12.2 Methods When There Is Curvature and a Single Covariate
12.2.1 Method Y
12.2.2 Method BB: Bootstrap Bagging
12.2.3 Method UB
12.2.4 Method TAP
12.2.5 Method G
12.2.6 A Method Based on Grids
12.2.7 R Functions ancova, anc.ES.sum, anc.grid, anc.grid.bin, anc.grid.cat, ancovaWMW, ancpb, rplot2g, runmean2g, lplot2g, ancdifplot, ancboot, ancbbpb, qhdsm2g, ancovaUB, ancovaUB.pv, ancdet, ancmg1, and ancGLOB
12.3 Dealing With Two or More Covariates When There Is Curvature
12.3.1 Method MC1
12.3.2 Method MC2
12.3.3 Methods MC3 and MC4
12.3.4 R Functions ancovamp, ancovampG, ancmppb, ancmg, ancov2COV, ancdes, ancdet2C, ancdetM4, and ancM.COV.ES
12.4 Some Global Tests
12.4.1 Method TG
12.4.2 R Functions ancsm and Qancsm
12.5 Methods for Dependent Groups
12.5.1 Methods Based on a Linear Model
12.5.2 R Functions Dancts and Dancols
12.5.3 Dealing With Curvature: Methods DY, DUB, and DTAP and a Method Based on Grids
12.5.4 R Functions Dancova, Dancova.ES.sum, Dancovapb, DancovaUB, Dancdet, Dancovamp, Danc.grid, and ancDEP.MULC.ES
Functions for Two or More Covariates
12.6 Exercises
References
Index