Preface to First Edition - lib

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146 DENSITY ESTIMATIONR> epa x epavals persp(x = x, y = x, z = epavals, xlab = "x", ylab = "y",+ zlab = expression(K(x, y)), theta = -35, axes = TRUE,+ box = TRUE)K(x, y)yxFigure 8.3 Epanechnikov kernel for a grid between (−1.1, −1.1) and (1.1, 1.1).which is implemented and depicted in Figure 8.3, here by using the perspfunction for plotting in three dimensions.According to Venables and Ripley (2002) the bandwidth should be chosento be proportional to n −1/5 ; unfortunately the constant of proportionalitydepends on the unknown density. The tricky problem of bandwidth estimationis considered in detail in Silverman (1986).© 2010 by Taylor and Francis Group, LLC
ANALYSIS USING R 1478.3 Analysis Using RThe R function density can be used to calculate kernel density estimatorswith a variety of kernels (window argument). We can illustrate the function’suse by applying it to the geyser data to calculate three density estimates ofthe data and plot each on a histogram of the data, using the code displayedwith Figure 8.4. The hist function places an ordinary histogram of the geyserdata in each of the three plotting regions (lines 4, 10, 17). Then, the densityfunction with three different kernels (lines 8, 14, 21, with a Gaussian kernelbeing the default in line 8) is plotted in addition. The rug statement simplyplaces the observations in vertical bars onto the x-axis. All three densityestimates show that the waiting times between eruptions have a distinctlybimodal form, which we will investigate further in Subsection 8.3.1.For the bivariate star data in Table 8.2 we can estimate the bivariate densityusing the bkde2D function from package KernSmooth (Wand and Ripley,2009). The resulting estimate can then be displayed as a contour plot (usingcontour) or as a perspective plot (using persp). The resulting contour plotis shown in Figure 8.5, and the perspective plot in 8.6. Both clearly show thepresence of two separated classes of stars.8.3.1 A Parametric Density Estimate for the Old Faithful DataIn the previous section we considered the non-parametric kernel density estimatorsfor the Old Faithful data. The estimators showed the clear bimodalityof the data and in this section this will be investigated further by fitting aparametric model based on a two-component normal mixture model. Suchmodels are members of the class of finite mixture distributions described ingreat detail in McLachlan and Peel (2000). The two-component normal mixturedistribution was first considered by Karl Pearson over 100 years ago(Pearson, 1894) and is given explicitly byf(x) = pφ(x,µ 1 , σ 2 1) + (1 − p)φ(x,µ 2 , σ 2 2)where φ(x,µ,σ 2 ) denotes a normal density with mean µ and variance σ 2 .This distribution has five parameters to estimate, the mixing proportion, p,and the mean and variance of each component normal distribution. Pearsonheroically attempted this by the method of moments, which required solvinga polynomial equation of the 9 th degree. Nowadays the preferred estimationapproach is maximum likelihood. The following R code contains a function tocalculate the relevant log-likelihood and then uses the optimiser optim to findvalues of the five parameters that minimise the negative log-likelihood.R> logL
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A Handbook ofStatisticalAnalysesUsi
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DedicationTo our wives, Mary-Elizab
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Preface to First EditionThis book i
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List of Figures1.1 Histograms of th
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6.8 Normal probability plot of resi
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12.2 R output of the linear mixed-e
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18.7 Within-cluster sum of squares
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4.6 Lanza data. Misoprostol randomi
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15.2 BCG data. Meta-analysis on BCG
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6 Simple and Multiple Linear Regres
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CHAPTER 1An Introduction to R1.1 Wh
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INSTALLING R 3One can change the ap
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DATA OBJECTS IN R 5http://CRAN.R-pr
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DATA OBJECTS IN R 7R> help("Forbes2
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DATA IMPORT AND EXPORT 9As a simple
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BASIC DATA MANIPULATION 11The funct
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BASIC DATA MANIPULATION 13name sale
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COMPUTING WITH DATA 15Max. : 20.960
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COMPUTING WITH DATA 17Error in quan
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COMPUTING WITH DATA 19R> layout(mat
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© 2010 by Taylor and Francis Group
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SUMMARY 23examples of these functio
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26 DATA ANALYSIS USING GRAPHICAL DI
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Table 2.2:CHFLS data. Chinese Healt
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Table 2.5:USstates data. Socio-demo
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CHAPTER 3Simple Inference: Guessing
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INTRODUCTION 47table. Here there ar
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STATISTICAL TESTS 49Table 3.4:pisto
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STATISTICAL TESTS 51assumed to have
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ANALYSIS USING R 53procedure is McN
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ANALYSIS USING R 551 R> layout(matr
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ANALYSIS USING R 57R> wilcox.test(I
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ANALYSIS USING R 59R> t.test(moorin
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ANALYSIS USING R 61R> cor.test(~ mo
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SUMMARY 63R> mcnemar.test(rearrests
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CHAPTER 4Conditional Inference: Gue
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INTRODUCTION 67Table 4.4:Lanza data
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CONDITIONAL TEST PROCEDURES 69and x
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ANALYSIS USING R 71R> hist(meandiff
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ANALYSIS USING R 73R> wilcox_test(y
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ANALYSIS USING R 75For the first st
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SUMMARY 77R> mh_test(anomalies)Asym
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CHAPTER 5Analysis of Variance: Weig
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INTRODUCTION 81The data in Table 5.
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ANALYSIS USING R 83set out in the f
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ANALYSIS USING R 85being far more t
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ANALYSIS USING R 87R> plot.design(f
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ANALYSIS USING R 89always be the ca
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ANALYSIS USING R 91The cbind statem
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ANALYSIS USING R 93Df Roy approx F
Page 115 and 116: SUMMARY 95Table 5.4:schooldays data
Page 117 and 118: CHAPTER 6Simple and Multiple Linear
Page 119 and 120: SIMPLE LINEAR REGRESSION 99hours be
Page 121 and 122: MULTIPLE LINEAR REGRESSION 101The e
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Page 133 and 134: SUMMARY 113R> plot(clouds_fitted, c
Page 135 and 136: SUMMARY 115R> plot(clouds_lm)Cook's
Page 137 and 138: CHAPTER 7Logistic Regression and Ge
Page 139 and 140: INTRODUCTION 119Table 7.2:womensrol
Page 141 and 142: LOGISTIC REGRESSION AND GENERALISED
Page 143 and 144: ANALYSIS USING R 123R> data("plasma
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Page 153 and 154: ANALYSIS USING R 133R> summary(poly
Page 155 and 156: ANALYSIS USING R 1357.3.4 Driving a
Page 157 and 158: SUMMARY 137Table 7.5:bladdercancer
Page 159 and 160: CHAPTER 8Density Estimation: Erupti
Page 161 and 162: DENSITY ESTIMATION 141The Hertzspru
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Page 165: DENSITY ESTIMATION 1451 R> plot(xgr
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Page 171 and 172: ANALYSIS USING R 1510.360891 54.612
Page 173 and 174: ANALYSIS USING R 153The results are
Page 175 and 176: SUMMARY 155R> layout(matrix(1:2, nc
Page 177 and 178: SUMMARY 157Table 8.4: birthdeathrat
Page 179 and 180: SUMMARY 159Table 8.5:schizophrenia
Page 181 and 182: 162 RECURSIVE PARTITIONINGTable 9.1
Page 183 and 184: 164 RECURSIVE PARTITIONINGBoth sets
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Page 189 and 190: 170 RECURSIVE PARTITIONINGOne way o
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Page 197 and 198: INTRODUCTION 179Table 10.2:USairpol
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Page 215 and 216: 198 SURVIVAL ANALYSISTable 11.1:gli
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200 SURVIVAL ANALYSISspect to time
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202 SURVIVAL ANALYSISHazard0.00 0.0
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204 SURVIVAL ANALYSISIn the Cox mod
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206 SURVIVAL ANALYSISExact Logrank
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208 SURVIVAL ANALYSISR> summary(GBS
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210 SURVIVAL ANALYSISR> layout(matr
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212 SURVIVAL ANALYSISmodels includi
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214 ANALYSING LONGITUDINAL DATA Iti
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216 ANALYSING LONGITUDINAL DATA ITa
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218 ANALYSING LONGITUDINAL DATA Iot
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220 ANALYSING LONGITUDINAL DATA IR>
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226 ANALYSING LONGITUDINAL DATA IKe
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228 ANALYSING LONGITUDINAL DATA Ido
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CHAPTER 13Analysing Longitudinal Da
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METHODS FOR NON-NORMAL DISTRIBUTION
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ANALYSIS USING R: GEE 239R> summary
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ANALYSIS USING R: GEE 245R> layout(
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ANALYSIS USING R: RANDOM EFFECTS 24
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ANALYSIS USING R: RANDOM EFFECTS 24
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SUMMARY 251Table 13.3:schizophrenia
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254 SIMULTANEOUS INFERENCE AND MULT
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CHAPTER 15Meta-Analysis: Nicotine G
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SYSTEMATIC REVIEWS AND META-ANALYSI
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STATISTICS OF META-ANALYSIS 271Sele
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ANALYSIS USING R 273the parameters
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ANALYSIS USING R 275R> plot(smoking
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PUBLICATION BIAS 277R> summary(BCG_
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SUMMARY 279R> summary(BCG_mod)Call:
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SUMMARY 2811 / standard error2 4 6
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Table 15.4:aspirin data. Meta-analy
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CHAPTER 16Principal Component Analy
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PRINCIPAL COMPONENT ANALYSIS 287nie
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ANALYSIS USING R 289R> score plot(
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ANALYSIS USING R 291R> score plot(
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ANALYSIS USING R 293Yuping (CHN) Ha
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SUMMARY 295R> biplot(heptathlon_pca
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SUMMARY 297rainJuly: rainfall in Ju
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Table 17.1:watervoles data. Water v
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302 MULTIDIMENSIONAL SCALINGn in nu
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304 MULTIDIMENSIONAL SCALINGwill be
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306 MULTIDIMENSIONAL SCALINGR> x y
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308 MULTIDIMENSIONAL SCALINGR> libr
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310 MULTIDIMENSIONAL SCALINGR> plot
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Table 17.3:eurodist data (package d
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CHAPTER 18Cluster Analysis: Classif
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INTRODUCTION 317mass, mass), the pe
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CLUSTER ANALYSIS 319x 20 2 4 6 8 10
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CLUSTER ANALYSIS 32141031678925Figu
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CLUSTER ANALYSIS 3231. Find some in
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ANALYSIS USING R 32518.3 Analysis U
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ANALYSIS USING R 327R> pottery_sing
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ANALYSIS USING R 329R> rge planet.
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ANALYSIS USING R 331R> plot(planet_
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ANALYSIS USING R 333R> scatterplot3
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BibliographyAdler, D. and Murdoch,
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BIBLIOGRAPHY 337Chambers, J. M. and
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BIBLIOGRAPHY 339Everitt, B. S. and
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BIBLIOGRAPHY 341Heitjan, D. F. (199
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BIBLIOGRAPHY 343Leisch, F. and Ross
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BIBLIOGRAPHY 345Proudfoot, J., Gold
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BIBLIOGRAPHY 347Stevens, J. (2001),
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