Likelihood Estimation for Markov Chains

Description

Computes maximum likelihood estimates of transition probabilities for stationary Markov chain models, of order 0 (independence) to 3.

This is intended for use with Practical 6.1 of Davison (2003), not as production code.

Usage

MClik(d)

Arguments

Value

Author(s)

A. C. Davison (Anthony.Davison@epfl.ch)

References

Avery, P. J. and Henderson, D. A. (1999) Fitting Markov chain models to discrete state series such as DNA sequences. Applied Statistics, 48, 53–61.

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Section 6.1.

Examples

data(intron)

fit <- MClik(intron)

Add Exponential Lines in Practical 11.3

Description

Adds lines to density plot used in Practical 11.3

Usage

add.exp.lines(exp.out, i, B = 10)

Arguments

Author(s)

Anthony Davison

Examples

B <-10; I <- 15; S <- 500

exp.out <- exp.gibbs(B=B,I=I,S=S)

hist(exp.out[1,,I],prob=TRUE,nclass=15,xlab="u1",ylab="PDF",xlim=c(0,B),ylim=c(0,1))

add.exp.lines(exp.out,1)

Daily Rainfall at Alofi

Description

Three-state data derived from daily rainfall over three years at Alofi in the Niue Island group in the Pacific Ocean. The states are 1 (no rain), 2 (up to 5mm rain), 3 (over 5mm).

Usage

data(alofi)

Source

Avery, P. J. and Henderson, D. A. (1999) Fitting Markov chain models to discrete state series such as DNA sequences. Applied Statistics, 48, 53–61.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 294.

Examples

data(alofi)
fit <- MClik(alofi)
fit$df
fit$AIC
plot(fit$df,fit$AIC)  # best model has minimal AIC?

Remission Times for Acute Myelogenous Leukaemia

Description

A clinical trial to evaluate the efficacy of maintenance chemotherapy for acute myelogenous leukaemia was conducted by Embury et al. (1977) at Stanford University. After reaching a stage of remission through treatment by chemotherapy, patients were randomized into two groups. The first group received maintenance chemotherapy and the second group did not. The aim of the study was to see if maintenance chemotherapy increased the length of the remission. The data here formed a preliminary analysis which was conducted in October 1974.

Usage

data(aml)

Format

A data frame with 23 observations on the following 3 variables.

time

The length of the complete remission (in weeks).

cens

An indicator of right censoring. 1 indicates that the patient had a relapse and so 'time' is the length of the remission. 0 indicates that the patient had left the study or was still in remission in October 1974, that is the length of remission is right-censored.

group

The group into which the patient was randomized. Group 1 received maintenance chemotherapy, group 2 did not.

Source

Miller, R.G. (1981) Survival Analysis. John Wiley: New York. Page 49.

References

Embury, S.H, Elias, L., Heller, P.H., Hood, C.E., Greenberg, P.L. and Schrier, S.L. (1977) Remission maintenance therapy in acute myelogenous leukaemia. Western Journal of Medicine, 126, 267–272.

Teaching Arithmetic Data

Description

45 school pupils were divided at random into 5 groups of size 9. Groups A and B were taught arithmetic in separate classes by the usual method. Groups C, D, and E were taught together for several days. On each day group C were publically praised, group D were publically reproved, and group E were ignored. The responses are from a standard test taken by all pupils at the end of the period.

Usage

data(arithmetic)

Format

A data frame with 45 observations on the following 2 variables.

group

a factor with levels A B C D E

y

a numeric vector

Source

Unpublished lecture notes, Imperial College, London.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 427.

Examples

data(arithmetic)
attach(arithmetic)
plot(y~group)
anova(lm(y~group,data=arithmetic))
summary(lm(y~group,data=arithmetic))  # two different parametrisations
summary(lm(y~group-1,data=arithmetic)) # for ANOVA

Shakespeare's Word Type Frequencies

Description

These are the frequencies with which Shakespeare used word types. There are 846 word types which appear more than 100 times in his total works, giving an overall total of 31534 word types.

Usage

data(bard)

Format

A data frame with 100 observations on the following 2 variables.

r

Number of times a word type is used

n

Number of word types used r times

Details

The canon of Shakespeare's accepted works contains 884,647 words, with 31,534 distinct word types. A word type is a distinguishable arrangement of letters, so ‘king’ is different from ‘kings’ and ‘alehouse’ different from both ‘ale’ and ‘house’.

Source

Efron, B. and Thisted, R. (1976) Estimating the number of unseen species: How many words did Shakespeare know? Biometrika, 63, 435–448.

Thisted, R. and Efron, B. (1987 ) Did Shakespeare write a newly-discovered poem? Biometrika, 74, 445–455.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 629.

Spring Barley Data

Description

The spatial layout and plot yield at harvest in a final assessment trial of 75 varietes of spring barley. The varieties are sown in three blocks, each with 75 plots, and each variety is replicated thrice. The yield for variety 27 is missing in block 3.

Usage

data(barley)

Format

A data frame with 225 observations on the following 4 variables.

Block

a factor with three levels

Location

a numeric vector with 75 values giving the plot

Variety

a factor with 75 levels giving the variety of barley sown in the plot

y

yield at harvest, standardised to have unit crude variance

Source

Besag, J. E., Green, P. J., Higdon, D. and Mengersen, K. (1995) Bayesian computation and stochastic systems (with Discussion). Statistical Science, 10, 3–66.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Pages 534–535.

Examples

data(barley)

Body Temperatures for a Female Beaver

Description

Data comprise 100 consecutive elemetric measurements of the body temperature of a female beaver, at 10-minute intervals. The animal remained in its lodge for the first 38 recordings, and then went outside.

Usage

data(beaver)

Format

A data frame with 100 observations on the following 4 variables.

day

Day number

time

Time of day (hhmm)

temp

Body temperature (degrees Celsius)

activ

Indicator of activity outside the lodge

Source

Reynolds, P. S. (1994) Time-series analyses of beaver body temperatures. In Case Studies in Biometry, eds N. Lange, L. Ryan, L. Billard, D. R. Brillinger, L. Conquest and J. Greenhouse, pp. 211–228. New York: Wiley.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 266.

Examples

data(beaver)
plot(beaver$temp,type="l",xlab="Time",ylab="Temperature")

Gibbs Sampler for Normal Changepoint Model, Practical 11.7

Description

This function implements a Gibbs sampler for the normal changepoint model applied to the beaver temperature data used in Example 6.22 and Practical 11.7 of Davison (2003), which should be consulted for details.

Usage

beaver.gibbs(init, y, R = 10, a = 1, b = 0.05)

Arguments

Details

This is provided simply so that readers spend less time typing. It is not intended to be robust and general code.

Value

A matrix of size R x 6, whose first four columns contain the values of the parameters for the iterations. Columns 5 and 6 contain the log likelihood and log prior for that iteration.

Author(s)

Anthony Davison (anthony.davison@epfl.ch)

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Practical 11.7.

Examples

## From Example 11.7:
data(beaver)
system.time( gibbs.out <- beaver.gibbs(c(36, 40, 3, 38), beaver$temp, R=1000))
par(mfrow=c(2,3))
plot.ts(gibbs.out[,1],main="mu1") # time series plot for mu1
plot.ts(gibbs.out[,2],main="mu2") # time series plot for mu2
plot.ts(gibbs.out[,3],main="lambda") # time series plot for lambda
plot.ts(gibbs.out[,4],main="gamma") # time series plot for gamma
plot.ts(gibbs.out[,5],main="log likelihood")  # and of log likelihood

Japanese beetle data

Description

Numbers of Japanese beetle larvae per square found in the top foot of soil of an 18 x 8 foot area of a field planted with maize. The columns of the matrix correspond to the direction of cultivation of the field; the maize rows were sown 4 feet apart.

Usage

data(beetle)

Format

The format is: num [1:18, 1:8] 0 2 3 1 5 3 5 3 2 3 ...

Source

Unpublished lecture notes, Imperial College, London

Examples

data(beetle)

Bicycling Times

Description

The times taken to cycle up a hill, as function of the bicycle seat height, use of dynamo, and tyre pressure. 16 runs were made using a factorial design.

Usage

data(bike)

Format

A data frame with 16 observations on the following 11 variables.

day

Day of run

run

Order of run

seat

Seat height: -1 indicates 26 inches, 1 indicates 30 inches

dynamo

Use of dynamo: -1 indicates not used

tyre

Tyre pressure: -1 indicates 40 psi, 1 indicates 55 psi

dayf

factor corresponding to day

runf

factor corresponding to run

seatf

factor corresponding to seat height

dynamof

factor corresponding to use of dynamo

tyref

factor corresponding to tyre pressure

time

Run time (seconds)

Source

Box, G. E. P., Hunter, W. G. and Hunter, J. S. (1978) Statistics for Experimenters. New York: Wiley.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 357.

Examples

data(bike)
anova(lm(time~dayf+runf+seat+dynamo+tyre,data=bike))

Birth Times

Description

Times spent in delivery suite by 95 women giving birth at the John Radcliffe Hospital, Oxford. The data were kindly provided by Ethel Burns.

Usage

data(births)

Format

A data frame with 95 observations on the following 2 variables.

day

Day on which woman arrived

time

Time (hours) spent on delivery suite

Source

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 18.

Examples

data(births)

Blalock–Taussig Shunt Data

Description

The Blalock–Taussig shunt is an operative procedure for infants with congenital cyanotic heart disease. The data are the survival times in months for shunts in 81 infants, divided into two age groups.

Usage

data(blalock)

Format

A data frame with 81 observations on the following 3 variables.

group

1 indicates infants aged over 1 month at time of the operation. 2 indicates those aged 30 or fewer days at time of operation.

months

survival time in months

cens

censoring indicator: 1 indicates observed failure time

Source

Oakes, D. (1991) Life-table analysis. In Statistical Theory and Modelling: In Honour of Sir David Cox, FRS, eds D. V. Hinkley, N. Reid and E. J. Snell, pp. 107–128. London: Chapman and Hall/CRC Press.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 192.

Examples

data(blalock)
library(survival)
plot(survfit(Surv(months,cens)~group,data=blalock),conf.int=TRUE,col=c(2,3))

Bliss data on deaths of flour beetles

Description

These are the number of adult flour beetles which died following a 5-hour exposure to gaseous carbon disulphide.

Usage

data(bliss)

Format

A data frame with 8 observations on the following 3 variables.

dose

concentration of carbon disulphide(mg. per litre)

m

Numbers of beetles exposed

r

Numbers of beetles dying

Source

Bliss, C. I. (1935).The calculation of the dosage-mortality curve. Annals of Applied BIology, 22, 134-167.

Examples

data(bliss)
attach(bliss)
plot(log(dose),r/m,ylim=c(0,1),ylab="Proportion dead")
fit <- glm(cbind(r,m-r)~log(dose),binomial)
summary(fit)

Blood Group Data

Description

Data on the incidence of blood groups O, A, B, and AB in 12 studies on people living in Britain or of British origin living elsewhere.

Usage

data(blood)

Format

A data frame with 12 observations on the following 4 variables.

O

Number of persons with blood group O

A

Number of persons with blood group A

B

Number of persons with blood group B

AB

Number of persons with blood group AB

Source

Taylor, G. L. and Prior, A. M. (1938) Blood groups in England. Annals of Eugenics, 8, 343–355.

Breast Cancer Data

Description

Initial and follow-up status for 37 breast cancer patients treated for spinal metastases. The status is able to walk unaided (1), unable to walk unaided (2), dead (3). The follow-up times are 0, 3, 6, 12, 24, and 60 months after treatment began.

Usage

data(breast)

Format

A data frame with 37 observations on the following 8 variables.

j

Case number

init

Initial status

x0

Status immediately after treatment started

x1

Status after 3 months

x2

Status after 6 months

x3

Status after 12 months

x4

Status after 24 months

x5

Status after 60 months

Details

Woman 24 was alive after 6 months but her ability to walk was not recorded (she was in state 1 or 2).

NA indicates that a woman has previously died, or that her status is unknown.

Source

de Stavola, B. L. (1988) Testing departures from time homogeneity in multistate Markov processes. Applied Statistics, 37, 242–250.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 227.

Examples

data(breast)

IQs of identical twins

Description

These are said to be measurements of IQ scores for pairs of identical twins, the first raised by foster parents and the second raised by natural parents, published by Sir Cyril Burt. Cases are divided into groups according to parents' social class, A-C, labelled 1-3. The general objective is to assess the impact of social class, and in particular the effect of environment, on IQ.

Usage

data(burt)

Format

A data frame with 27 observations on the following 3 variables.

y

IQ score for twin raised in foster home

x

IQ score for twin raised by natural parents

class

Social class of twins

Details

Burt used these and similar data to argue that IQ was largely inherited, a view which strongly influenced British education through the creation of the 11+ exam, which was used to decide which children should be given different forms of education. However after his death it was suggested that the data were fake, a view accepted by some and strongly rebutted by others.

Source

Unpublished lecture notes of David Hinkley.

References

For information about Burt, see www.indiana.edu/~intell/burt.shtml

Examples

data(burt)
attach(burt)
par(pty="s")
plot(x,y,type="n",xlim=c(60,140),ylim=c(60,140))
text(x,y,class,cex=0.8)
abline(0,1,lty=2)

Breaking of Chocolate Cakes

Description

Data on breaking angles of chocolate cakes made using different recipes, mixes, and cooking temperatures.

Usage

data(cake)

Format

A data frame with 270 observations on the following 4 variables.

recipe

Recipe used

mix

mix, a factor with 15 levels

temp

temperature (degrees Fahrenheit) at which cake baked

y

breaking angle (degrees)

Details

These are data from an experiment in which six different temperatures for cooking three recipes for chocolate cake were compared. Each time a mix was made using one of the recipes, enough batter was prepared for six cakes, which were then randomly allocated to be cooked at the different temperatures. The response is the breaking angle, found by fixing one half of a slab of cake, then pivoting the other half about the middle until breakage occurs.

Source

Cochran, W. G. and Cox, G. M. (1959) Experimental Designs. Second edition. New York: Wiley.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 454.

Examples

data(cake)

Calcium Uptake Data

Description

These are data on the uptake of calcium by cells suspended in a radioactive solution, as a function of time.

Usage

data(calcium)

Format

A data frame with 27 observations on the following 2 variables.

time

The time (in minutes) that the cells were suspended in the solution

cal

The amount of calcium uptake (nmoles/mg)

Details

Howard Grimes from the Botany Department, North Carolina State University, conducted an experiment for biochemical analysis of intracellular storage and transport of calcium across plasma membrane. Cells were suspended in a solution of radioactive calcium for a certain length of time and then the amount of radioactive calcium that was absorbed by the cells was measured. The experiment was repeated independently with 9 different times of suspension each replicated 3 times.

Source

Rawlings, J.O. (1988) Applied Regression Analysis. Wadsworth and Brooks/Cole Statistics/Probability Series.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 469.

Examples

data(calcium)
summary(nls(cal~beta0*(1-exp(-time/beta1)),data=calcium,start=list(beta0=5,beta1=5)))

Mortality Rates for Cardiac Surgery on Babies at 12 Hospitals

Description

The title should be self-explanatory.

Usage

data(cardiac)

Format

A data frame with 12 observations on the following 2 variables.

r

Number of deaths

m

Number of operations

Source

Spiegelhalter, D. J., Thomas, A., Best, N. G. and W. R. Gilks (1996) BUGS 0.5 Examples Volume 1 (Version ii). Cambridge: MRC Biostatistics Unit. Page 15.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 579.

Cat Heart Data

Description

Data from a Latin square experiment on the potencies of cardiac drugs given to anesthetized cats.

Usage

data(cat.heart)

Format

A data frame with 64 observations on the following 6 variables.

Day

on which experiment performed

Time

morning or afternoon

Observer

four observers took part

Drug

cardiac drug given to cat

y

100 times log dose in micrograms at which cat died

x

100 times log cat heart weight in grams

Details

These are results from an experiment to determine the relative potencies of eight similar cardiac drugs, labelled A–H, where A is a standard. The method used was to infuse slowly a suitable dilution of the drug into an anaesthetized cat. The dose at which death occurred and the weight of the cat's heart were recorded. Four observers each made two determinations on each of eight days, with a Latin square design used to eliminate observer and time differences. The heart weight cannot be known at the start of the experiment, but might be expected to affect comparisons among the treatments; it is assumed that heart weight is unaffected by the treatments.

Source

Unpublished lecture notes, Imperial College, London.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 447.

Examples

data(cat.heart)
anova(lm(y~Observer+Time+Day+Drug+Observer:Time,data=cat.heart))

Hald Cement Data

Description

Heat evolved in setting of cement, as a function of its chemical composition.

Usage

data(cement)

Format

A data frame with 13 observations on the following 5 variables.

x1

percentage weight in clinkers of 3CaO.Al2O3

x2

percentage weight in clinkers of 3CaO.SiO2

x3

percentage weight in clinkers of 4CaO.Al2O3.Fe2O3

x4

percentage weight in clinkers of 2CaO.SiO2

y

heat evolved (calories/gram)

Source

Woods, H., Steinour, H. H. and Starke, H. R. (1932) Effect of composition of Portland cement on heat evolved during hardening. Industrial Engineering and Chemistry, 24, 1207–1214.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 355.

Examples

data(cement)
lm(y~x1+x2+x3+x4,data=cement)

Chick Bone Data

Description

Balanced incomplete block design on the effect of amino acids on growth of chick bones.

Usage

data(chicks)

Format

A data frame with 30 observations on the following 3 variables.

Treat

Treatment with levels All (all amino acids present), Arg-(all acids present except Arg), etc.

Pair

bones were taken in pairs from 15 chicks

y

Log10 dry weight of bones at end of experiment

Details

Bones from 7-day-old chick embryos were cultivated over a nutrient chemical medium. Two bones were available from each chick, and the experiment was set out in a balanced incomplete block design with two units per block. The treatments were growth in the complete medium, with about 30 nutrients in carefully controlled quantities, and growth in five other media, each with a single amino acid omitted. Thus His-, Arg-, and so forth denote media without particular amino acids.

Source

Cox, D. R. and Snell, E. J. (1981) Applied Statistics: Principles and Examples. London: Chapman and Hall/CRC Press. Page 95.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 432.

Chimpanzee Learning Data

Description

These are the times in minutes taken for four chimpanzees to learn each of four words.

Usage

data(chimps)

Format

A data frame with 40 observations on the following 3 variables.

chimp

a factor with levels 1-4

word

a factor with 1-10

y

learning time (minutes)

Source

Brown, B. W. and Hollander, M. (1977) Statistics: A Biomedical Introduction. New York: Wiley.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 485.

Examples

data(chimps)
anova(glm(y~chimp+word,Gamma(log),data=chimps),test="F")
anova(glm(y~word+chimp,Gamma(log),data=chimps),test="F")

Numbers of Flaws in Lengths of Cloth

Description

The data comprise lengths of cloth samples and the numbers of flaws found in them.

Usage

data(cloth)

Format

A data frame with 32 observations on the following 2 variables.

x

The length of the roll of cloth.

y

The number of flaws found in the roll.

Source

Bissell, A. F. (1972) A negative binomial model with varying element size. Biometrika, 59, 435–441.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 515.

Examples

data(cloth)
attach(cloth)
plot(x,y)
# Comparison of Poisson and quasilikelihood fits
summary(glm(y~x-1,family=poisson(identity)))
summary(glm(y~x-1,family=quasipoisson(identity)))

Data on UK coal mining disasters

Description

The 'coal' data frame has 191 rows and 1 column.

This data frame gives the dates of 191 explosions in UK coal mines which resulted in 10 or more fatalities. The time span of the data is from March 15, 1851 until March 22 1962.

Usage

data(coal)

Format

This data frame contains the following column:

date

The date of the disaster. The integer part of 'date' gives the year. The day is represented as the fraction of the year that had elapsed on that day.

Source

The data were obtained from

Hand, D.J., Daly, F., Lunn, A.D., McConway, K.J. and Ostrowski, E. (1994) A Handbook of Small Data Sets, Chapman and Hall.

References

Jarrett, R.G. (1979) A note on the intervals between coal-mining disasters. Biometrika, 66, 191–193.

Examples

data(coal)
plot(density(coal$date))
rug(coal$date)

Function for Coin Spinning, Practical 11.1

Description

This function computes the posterior distribution of the success probability theta when a coin is spun on its edge (or tossed), when the prior density for that probability is a mixture of beta densities.

Usage

coin.spin(para, r = 0, n = 0, n.points = 199)

Arguments

Details

This is provided simply so that readers spend less time typing. It is not intended to be robust and general code.

Value

Author(s)

Anthony Davison (anthony.davison@epfl.ch)

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Practical 11.1.

Examples

## From Practical 11.1:
para <- matrix( c(0.5, 10, 20, 0.5, 20, 10), nrow=2, ncol=3, byrow=TRUE)
prior <- coin.spin(para)
plot(prior, xlab="theta",ylab="PDF", type="l",ylim=c(0,6))
post <- coin.spin(para, r=4, n=10)

Danish Fire Insurance Claims

Description

Data on major insurance claims due to fires in Denmark, 1980–1990. The values of the claims have been rescaled for commercial reasons.

Usage

data(beaver)

Format

An irregular time series.

Source

Embrechts, P., Kluppelberg, C. and Mikosch, T. (1997) Modelling Extremal Events for Insurance and Finance. Berlin: Springer.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 278.

Examples

data(danish)
plot(danish,type="h")

Darwin's Maize Data

Description

The heights in eighths of inches of young maize plants put by Charles Darwin in four pots. He planted 15 pairs of plants together, one of each pair being cross-fertilised, and the other being self-fertilised.

Usage

data(darwin)

Format

A data frame with 30 observations on the following 4 variables.

pot

a factor giving the pot

pair

a factor giving the pair

type

a factor giving the type of fertilisation

height

height of plant in eighths of inches

Source

Fisher, R. A. (1935) Design of Experiments. Edinburgh: Oliver and Boyd. Page 30.

References

The original book is reprinted as part of Fisher, R. A. (1990) Statistical Methods, Experimental Design, and Scientific Inference. Oxford University Press.

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 2.

Examples

data(darwin)
attach(darwin)
plot(height~type)
anova(lm(height~pot+pair+type,data=darwin))

Gibbs Sampling for Two Truncated Exponential Variables, Practical 11.3

Description

Performs Gibbs sampling for problem with two truncated exponential variables. See Practical 11.3 of Davison (2003) for details.

Usage

exp.gibbs(u1 = NULL, u2 = NULL, B, I = 100, S = 100)

Arguments

Details

This is provided simply so that readers spend less time typing. It is not intended to be robust and general code.

Value

A 2 x S x I array containing the values of the variables for the successive iterations

Author(s)

Anthony Davison (anthony.davison@epfl.ch)

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press.Practical 11.3.

Examples

add.exp.lines <- function( exp.out, i, B=10)
{
  dexp.trunc <- function( u, lambda, B ) 
     dexp(u, rate=lambda)/(1-exp(-lambda*B))
  S <- dim(exp.out)[2]
  I <- dim(exp.out)[3]
  u <- seq(0.0001,B,length=1000)
  fu <- rep(0,1000)
  for (s in 1:S) fu <- fu + dexp.trunc(u,exp.out[3-i,s,I],B)/S
  lines(u,fu,col="red")
  invisible()
}
par(mfrow=c(3,2))
B <-10; I <- 15; S <- 500
exp.out <- exp.gibbs(B=B,I=I,S=S)
hist(exp.out[1,,I],prob=TRUE,nclass=15,xlab="u1",ylab="PDF",xlim=c(0,B),ylim=c(0,1))
add.exp.lines(exp.out,1)
hist(exp.out[2,,I],prob=TRUE,nclass=15,xlab="u2",ylab="PDF",xlim=c(0,B),ylim=c(0,1))
add.exp.lines(exp.out,2)

Visual Impairment Data

Description

Joint distribution of visual impairment on both eyes, by race and age.

Usage

data(eyes)

Format

A data frame with 32 observations on the following 6 variables.

L

Impairment (+) or not (-) for left eye.

R

Impairment (+) or not (-) for right eye.

age

a factor with levels 40-50 51-60 61-70 70+

colour

White (W) or black (B)

a

mid-point for age groups, as numeric vector

y

Number of individuals in each class

Source

K.-Y. Liang, S. L. Zeger and B. Qaqish (1992) Multivariate regression analyses for categorical data (with Discussion). Journal of the Royal Statistical Society, series B, 54, 3–40.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 505.

Examples

data(eyes)
eyes.glm <- glm(y~age*colour+L*R+(L+R):poly(a,2)+colour:(L+R),poisson,data=eyes)
anova(eyes.glm,test="Chi")   # analysis of deviance for loglinear model

Field Concrete Mixture Data

Description

Data from a 4x4 Latin square experiment on the efficiency of a field concrete mixer.

Usage

data(field.concrete)

Format

A data frame with 16 observations on the following 4 variables.

efficiency

a numeric vector

speed

a factor with levels 4, 8, 12, 16 mph.

run

order in which runs were performed each day

day

day on which runs were performed

Source

Unpublished lecture notes, Imperial College, London.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 435.

Examples

data(field.concrete)
fit <- lm(efficiency~run+day+speed,data=field.concrete)
anova(fit)
summary(fit)
fit <- lm(efficiency~run+day+poly(as.numeric(speed),3),data=field.concrete)
summary(fit)

Counts of Balsam-fir Seedlings

Description

The number of balsam-fir seedlings in each quadrant of a grid of 50 five foot square quadrants were counted. The grid consisted of 5 rows of 10 quadrants in each row.

Usage

data(fir)

Format

A data frame with 50 observations on the following 3 variables.

count

The number of seedlings in the quadrant

row

The row number of the quadrant

col

The quadrant number within the row

Source

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 641.

Atmospheric Pressure and Boiling Point in the Alps

Description

James Forbes measured the atmospheric pressure and boiling point of water at 17 locations in the Alps.

Usage

data(forbes)

Format

A data frame with 17 observations on the following 2 variables.

bp

Boiling point (Fahrenheit)

pres

Pressure (inches of mercury)

Source

Atkinson, A. C. (1985) Plots, Transformations, and Regression. Oxford University Press.

Examples

data(forbes)
plot(forbes)
fit <- lm(bp~pres,data=forbes)
fit
plot(forbes$pres,resid(fit))  # model OK?
# try refitting with transformation
fit <- lm(log(bp)~log(pres),data=forbes)

Head Dimensions in Brothers

Description

The 'frets' data frame has 25 rows and 4 columns.

The data consist of measurements of the length and breadth of the heads of pairs of adult brothers in 25 randomly sampled families. All measurements are expressed in millimetres.

Usage

data(frets)

Format

This data frame contains the following columns:

l1

The head length of the eldest son.

b1

The head breadth of the eldest son.

l2

The head length of the second son.

b2

The head breadth of the second son.

Source

Frets, G.P. (1921) Heredity of head form in man. Genetica, 3, 193.

References

Whittaker, J. (1990) Graphical Models in Applied Multivariate Statistics. John Wiley.

Examples

data(frets)
## maybe str(frets) ; plot(frets) ...

FTSE Daily Returns

Description

Daily returns ( index, 1991–1998.

Usage

data(ftse)

Format

A time series.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 266.

Examples

data(ftse)
plot(ftse,type="l",xlab="Time",ylab="Percent return")
plot(exp(cumsum(ftse/100)),type="l",xlab="Time",ylab="Relative closing value")

Galaxy Velocity Data

Description

Velocities (km/second) of 82 galaxies in a survey of the Corona Borealis region.

Usage

data(galaxy)

Format

The format is: num [1:82] 9.17 9.35 9.48 9.56 9.78 ...

Source

Roeder, K. (1990) Density estimation with confidence sets exemplified by superclusters and voids in galaxies. Journal of the American Statistical Association, 85, 617–624.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 214.

Examples

data(galaxy)
plot(density(galaxy))
rug(galaxy)

Estimate Alpha from Data

Description

Estimate prior value of a parameter from the data.

Usage

get.alpha(d)

Arguments

Value

Prior value of a parameter, estimated from the data.

See Also

poi.beta.laplace

Generalized Linear Model Diagnostics

Description

Calculates jackknife deviance residuals, standardized deviance residuals, standardized Pearson residuals, approximate Cook statistic, leverage and estimated dispersion.

Usage

## S3 method for class 'diag'
glm(glmfit)

Arguments

Value

A list containing the following items:

Note

See the helpfile for glm.diag.plots for an example of the use of glm.diag.

Author(s)

Anthony Davison <anthony.davison@epfl.ch>

References

Davison, A.C. and Snell, E.J. (1991) Residuals and diagnostics. In Statistical Theory and Modelling: In Honour of Sir David Cox. D.V. Hinkley, N. Reid and E.J. Snell (editors), 83-106. Chapman and Hall.

See Also

glm,lm,plot.glm.diag,summary.glm

Haemolytic Uraemic Syndrome

Description

Annual numbers of cases of 'diarrhoea-associated haemolytic uraemic syndrome' treated in clinics in Birmingham and Newcastle from 1970–1989.

Usage

data(hus)

Format

A data frame with 20 observations on the following 3 variables.

year

a numeric vector

birmingham

Number of cases treated in Birmingham

newcastle

Number of cases treated in Newcastle

Source

Henderson, R. and Matthews, J. N. S. (1993) An investigation of changepoints in the annual number of cases of haemolytic uraemic syndrome. Applied Statistics, 42, 461–471.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 142.

Examples

data(hus)
plot(hus$year,hus$birmingham,ylab="Annual number of cases",type="s")

Gibbs Sampler for Poisson Changepoint Model, Practical 11.6

Description

This function implements a Gibbs sampler for the Poisson changepoint model applied to the HUS data used in Example 4.40 and Practical 11.6 of Davison (2003), which should be consulted for details.

Usage

hus.gibbs(init, y, R = 10, a1 = 1, a2 = 1, c = 0.01, d = 0.01)

Arguments

Details

This is provided simply so that readers spend less time typing. It is not intended to be robust and general code.

Value

A matrix of size R x 7, whose first five columns contain the values of the parameters for the iterations. Columns 6 and 7 contain the log likelihood and log prior for that iteration.

Author(s)

Anthony Davison (anthony.davison@epfl.ch)

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Practical 11.6.

Examples

## From Example 11.6:
hus <- c(1,5,3,2,2,1,0,0,2,1,1,7,11,4,7,10,16,16,9,15)
system.time( gibbs.out <- hus.gibbs(c(5, 5, 1, 1, 2), hus, R=1000))
plot.ts(gibbs.out[,1], main="lambda1") # time series plot for lam1
plot.ts(gibbs.out[,2], main="lambda1") # time series plot for lam2
plot.ts(gibbs.out[,6], main="log lik") # and of log likelihood
table(gibbs.out[,5])  # tabulate observed values of tau
rm(hus)

Inverse Hessian

Description

Inverse Hessian matrix, useful for obtaining standard errors

Usage

ihess(f, x, ep = 1e-04, ...)

Arguments

Value

Matrix of dimension dim(x) times dim(x), containing inverse Hessian matrix of f at x.

Note

This is not needed in R, where hessian matrices are obtained by setting hessian=T in calls to optimisation functions.

Author(s)

Anthony Davison

References

Based on code written by Stuart Coles of Padova University

Examples

# ML fit of t distribution
nlogL <- function(x, data) # negative log likelihood
{ mu <- x[1]
  sig <- x[2]
  df <- x[3]
  -sum(log( dt((data-mu)/sig, df=df)/sig )) }
y <- rt(n=100, df=10) # generate t data
# this is Splus code.....so remove the #'s for it to work in R
# fit <- nlminb(c(1,1,4), nlogL, upper=c(Inf,Inf,Inf), lower=c(-Inf,0,0),
#               data=y)
# fit$parameters # maximum likelihood estimates
# J <- ihess(nlogL, fit$parameters, data=y)
#  sqrt(diag(J)) # standard errors based on observed information
# 
# In this example the standard error can be a bad measure of
# uncertainty for the df.

Intron Gene Sequence

Description

Sequence of 1572 bases from first human preproglucagon gene

Usage

data(intron)

Format

This is a factor with 4 levels, "A","C","G","T"

Source

Avery, P. J. and Henderson, D. A. (1999) Fitting Markov chain models to discrete state series such as DNA sequences. Applied Statistics, 48, 53–61.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 226.

Examples

data(intron)
## maybe str(intron) ; plot(intron) ...

Jacamar Learning Ability Data

Description

Response of a rufous-tailed jacamar to butterflies, by not attacking them, by attacking but not eating them, and by attacking and eating them.

Usage

data(jacamar)

Format

A data frame with 48 observations on the following 5 variables.

species

Butterfly species: Aphrissa boisduvalli (Ab), Phoebis argante (Pa), Dryas iulia (Di), Pierella luna (Pl), Consul fabius (Cf), Siproeta stelenes (Ss)

colour

colour butterfly wings were painted: Unpainted, Brown, Yellow, Blue, Green, Red, Orange, Black

N

Number not attacked

S

Number attacked but rejected

E

Number eaten

Details

As part of a study of the learning ability of tropical birds, Peng Chai of the University of Texas at Austin collected data on the response of a rufous-tailed jacamar to butterflies. He used marker pens to paint the underside of the wings of eight species of butterflies, and then released each butterfly in the cage where the bird was confined. The bird responded in three ways: by not attacking the butterfly (N); by attacking the butterfly, then sampling but rejecting it (S); or by attacking and eating the butterfly, usually after removing some or all of the wings (E).

Source

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 470.

Examples

data(jacamar)

Jelinski and Moranda Data on Software Failures

Description

These are times in days between sucessive failures of a piece of software developed as part of a large data system. The software was released after the first 31 failures. The last three failures occurred after release.

Usage

data(jelinski)

Format

The format is: num [1:34] 9 12 11 4 7 2 5 8 5 7 ...

Source

Jelinski, Z. and Moranda, P. B. (1972) Software reliability research. In W. Freiberger (ed), Statistical Computer Performance Evaluation. London: Academic Press. Pages 465–484.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 299.

Survival Times and White Blood Counts for Leukaemia Patients

Description

A data frame of data from 33 leukaemia patients.

Usage

data(leuk)

Format

A data frame with 33 observations on the following 3 variables.

wbc

white blood cell count

ag

a test result, '"present"' or '"absent"'

time

survival time in weeks

Details

Survival times are given for 33 patients who died from acute myelogenous leukaemia. Also measured was the patient's white blood cell count at the time of diagnosis. The patients were also factored into 2 groups according to the presence or absence of a morphologic characteristic of white blood cells. Patients termed AG positive were identified by the presence of Auer rods and/or significant granulation of the leukaemic cells in the bone marrow at the time of diagnosis.

Source

Feigl, P. and Zelen, M. (1965) Estimation of exponential survival probabilities with concomitant information. Biometrics, 21, 826–838.

References

Cox, D. R. and Oakes, D. (1984) Analysis of Survival Data. Chapman & Hall, p. 9.

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 542.

Examples

data(leuk)
library(survival)
plot(survfit(Surv(time) ~ ag, data = leuk), lty = 2:3, col = 2:3)
# fit of exponential model
summary(glm(time~ag+log10(wbc),data=leuk,family=Gamma(log)),dispersion=1)
# now Cox models
leuk.cox <- coxph(Surv(time) ~ ag + log(wbc), leuk)
summary(leuk.cox)

Likelihood Confidence Intervals for Scalar Parameter

Description

A simple function for computing confidence intervals from the values of a likelihood function for a scalar parameter. It prints the maximum likelihood estimate (MLE) and its standard error, and confidence intervals based on normal approximation to the distribution of the MLE and on the chi-squared approximation to the distribution of the likelihood ratio statistic.

Usage

lik.ci(psi, logL, conf = c(0.975, 0.025))

Arguments

Value

See above

Note

This uses the spline functions in library(modreg).

Author(s)

Anthony Davison (Anthony.Davison@epfl.ch)

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Sections 4.4.2, 4.5.1.

Examples

# likelihood analysis for mean of truncated Poisson data
y <- c(1:6)
n <- c(1486,694,195,37,10,1)
logL <- function(x, y, n.obs)      # x is theta
{  f <- dpois(y,x)/(1-dpois(0,x))  # dpois is Poisson PDF
   sum(n*log(f))  }                # log likelihood
theta <- seq(from=0.8, to=1, length=200)
L <- rep(NA, 200)
for (i in 1:200) L[i] <- logL(theta[i], y, n)
plot(theta, L, type="l", ylab="Log likelihood")
lik.ci(theta, L)

Swedish Speed Limit Data

Description

The data are numbers of traffic accidents with personal injuries, reported to the police, on Swedish roads on 92 days in 1961 and 92 matching days in 1962. On some of these days a general speed limit of 90 or 100 km/hour was imposed.

Usage

data(limits)

Format

A data frame with 92 observations on the following 5 variables.

day

A factor indicating the day, coded 1-92.

lim1

1 indicates a limit imposed in 1961, 0 not.

lim2

1 indicates a limit imposed in 1962, 0 not.

y1

Number of accidents on this day in 1961.

y2

Number of accidents on this day in 1962.

Source

Svensson, A. (1981) On a goodness-of-fit test for multiplicative Poisson models. Annals of Statistics, 9, 697–704.

Examples

data(limits)
## maybe str(limits) ; plot(limits) ...

Lizard Count Data

Description

These are data on the structural habitat of two species of lizards in Whitehouse, Jamaica. They comprise observed counts for perch height, perch diameter, insolation, and time of day, for both species. The data can be represented as a 2 x 2 x 2 x 3 x 2 contingency table.

Usage

data(lizards)

Format

A data frame with 48 observations on the following 6 variables.

height

high indicates perch at height 5 or more feet, low indicates perch below 5 feet.

diameter

large indicates perch diameter 2 inches or more, small indicates perch diameter less than 2 inches.

sun

Is the perch in a shady or a sunny location?

time

Time of day when lizard observed: early, late or midday.

species

Species of lizard: grahami or opalinus.

y

Number of lizards seen.

Source

Bishop, Y. M. M., Fienberg, S. E. and Holland, P. W. (1975) Discrete Multivariate Analysis. Cambridge, Mass.: MIT Press. Page 164.

Examples

data(lizards)
## maybe str(lizards) ; plot(lizards) ...

Lung Cancer Deaths among UK Physicians

Description

The data give the number of deaths due to lung cancer in British male physicians, as a function of years of smoking and cigarette consumption.

Usage

data(lung.cancer)

Format

A data frame with 63 observations on the following 4 variables.

years.smok

a factor giving the number of years smoking

cigarettes

a factor giving cigarette consumption

Time

man-years at risk

y

number of deaths

Source

Frome, E. L. (1983) The analysis of rates using Poisson regression models. Biometrics, 39, 665–674.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 8.

Examples

data(lung.cancer)

Magnesium Treatment for Heart Attack Patients

Description

Data from 11 clinical trials to compare magnesium treatment for heart attacks with control.

Usage

data(magnesium)

Format

A data frame with 22 observations on the following 4 variables.

trial

a factor with levels 1–11

group

Treatment indicator (factor)

m

Total patients in group

r

Number of deaths in group

Source

Copas, J. B. (1999) What works?: Selectivity models and meta-analysis. Journal of the Royal Statistical Society series A, 162, 96–109.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 208.

Examples

data(magnesium)
fit <- glm(cbind(r,m-r)~trial+group,binomial,data=magnesium[1:20,])
anova(fit,test="Chi")
summary(fit)

Average Heights of the Rio Negro river at Manaus

Description

The 'manaus' time series is of class '"ts"' and has 1080 observations on one variable, which is the monthly average of the daily stages (heights) of the Rio Negro at Manaus, from January 1903 until December 1992. The units are metres.

Usage

data(manaus)

Format

A time series

Details

The data values are monthly averages of the daily stages (heights) of the Rio Negro at Manaus. Manaus is 18km upstream from the confluence of the Rio Negro with the Amazon but because of the tiny slope of the water surface and the lower courses of its flatland affluents, they may be regarded as a good approximation of the water level in the Amazon at the confluence. The data here cover 90 years from January 1903 until December 1992.

The Manaus gauge is tied in with an arbitrary bench mark of 100m set in the steps of the Municipal Prefecture; gauge readings are usually referred to sea level, on the basis of a mark on the steps leading to the Parish Church (Matriz), which is assumed to lie at an altitude of 35.874 m according to observations made many years ago under the direction of Samuel Pereira, an engineer in charge of the Manaus Sanitation Committee Whereas such an altitude cannot, by any means, be considered to be a precise datum point, observations have been provisionally referred to it. The measurements are in metres.

Source

The data were kindly made available by Professors H. O'Reilly Sternberg and D. R. Brillinger of the University of California at Berkeley.

References

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

Sternberg, H. O'R. (1987) Aggravation of floods in the Amazon river as a consequence of deforestation? Geografiska Annaler, 69A, 201-219.

Sternberg, H. O'R. (1995) Waters and wetlands of Brazilian Amazonia: An uncertain future. In The Fragile Tropics of Latin America: Sustainable Management of Changing Environments, Nishizawa, T. and Uitto, J.I. (editors), United Nations University Press, 113-179.

Examples

data(manaus)
plot(manaus)
acf(manaus)
pacf(manaus)

Examination Marking Data

Description

The data are from an experiment to compare how different markers assess examination scripts, some of which were original and others of which were photocopies.

Usage

data(marking)

Format

A data frame with 32 observations on the following 5 variables.

Exam

Two exams were marked

Script

Scripts from 8 persons were marked, coded 1-8.

Marker

Coded 1-4

Original

Is the script an original (1) or a photocopy (0)?

y

The mark out of 80 attributed by the marker.

Details

Normally each marker had a different batch of scripts, but for the experiment one script was taken at random from each batch and replaced after three copies of it had been made. The three copies were sent to the other three markers who assessed them, while the original was replaced and assessed in the usual way. Each of the four copies was therefore assessed by a single marker, but the three markers who had a copy knew that the script was part of the experiment, while the person marking the original did not know it to be part of the experiment. The experiment was repeated at another examination, with the same examiners, but different scripts.

Source

Lindley, D. V. (1961) An experiment in the marking of an examination (with Discussion). Journal of the Royal Statistical Society, series A, 124, 285–313.

Examples

data(marking)
## maybe str(marking) ; plot(marking) ...

Math Marks Data

Description

Marks out of 100 for 88 students taking examinations in mechanics (C), vectors (C), algebra (O), analysis (O), statistics (O), where C indicates closed and O indicates open book examination.

Usage

data(mathmarks)

Format

A data frame with 88 observations on the following 5 variables.

mechanics

mark out of 100 for mechanics

vectors

mark out of 100 for vectors

algebra

mark out of 100 for algebra

analysis

mark out of 100 for analysis

statistics

mark out of 100 for statistics

Source

Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979) Multivariate Analysis. London: Academic Press. Pages 3–4.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 256.

Examples

data(mathmarks)
pairs(mathmarks)
var(mathmarks)

Mice Deaths from Radiation

Description

RFM male mice were exposed to 300 rads of x-radiation at 5–6 weeks of age. The causes of death were thymic lymphoma, reticulum cell sarcoma, and other. Some of the mice were kept in a conventional environment, and the others in a germ-free environment.

Usage

data(mice)

Format

A data frame with 177 observations on the following 4 variables.

type

Environment type (factor)

cause

Cause of death

status

Censoring indicator, with 1 indicating death

y

Age at death (weeks)

Source

Hoel, D. G. and Walburg, H. E. (1972) Statistical analysis of survival experiments. Journal of the National Cancer Institute, 49, 361–372.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 200.

Examples

data(mice)
library(survival)
fit <- survfit(Surv(y,status)~cause,data=mice[1:95,]) # first group
plot(fit,lty=c(3,2,1))

Millet Data

Description

Data from an experiment conducted to determine the optimal planting distance between plants in rows of millet. The rows were 1 foot apart. The design was a 5 x 5 Latin square.

Usage

data(millet)

Format

A data frame with 25 observations on the following 4 variables.

row

Row label, coded 1-5.

col

Column label, coded 1-5.

dist

distances between plants:2, 4, 6, 8, or 10 inches.

y

Average yield (grams) of three central rows, 15 feet long after allowing for discards, from each plot.

Source

Unpublished lecture notes, Imperial College, London.

Examples

data(millet)
## maybe str(millet) ; plot(millet) ...

Motorette Failure Data

Description

Times to failure of motorettes tested at different temperatures.

Usage

data(motorette)

Format

A data frame with 40 observations on the following 3 variables.

x

Temperature in degrees Fahrenheit

cens

Censoring indicator

y

Failure time in hours

Source

Nelson, W. D. and Hahn, G. J. (1972) Linear estimation of a regression relationship from censored data. Part 1 — simple methods and their application (with Discussion). Technometrics, 14, 247–276.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 615.

Examples

data(motorette)
library(survival)
motor.fit <- survreg(Surv(y,cens)~log(x),dist="weibull",data=motorette)
summary(motor.fit)

Nematode Data

Description

Numbers of nematodes invading individual fly larvae for various numbers of initial challengers.

Usage

data(nematode)

Format

A data frame with 29 observations on the following 3 variables.

m

Number of challengers

r

Number of invading nematodes

y

Number of fly larvae

Source

Faddy, M. J. and Fenlon, J. S. (1999) Stochastic modelling of the invasion process of nematodes in fly larvae. Applied Statistics, 48, 31–37.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 295.

Examples

data(nematode)

Nodal Involvement in Prostate Cancer

Description

The ‘nodal’ data frame has 53 rows and 7 columns.

The treatment strategy for a patient diagnosed with cancer of the prostate depend highly on whether the cancer has spread to the surrounding lymph nodes. It is common to operate on the patient to get samples from the nodes which can then be analysed under a microscope but clearly it would be preferable if an accurate assessment of nodal involvement could be made without surgery.

For a sample of 53 prostate cancer patients, a number of possible predictor variables were measured before surgery. The patients then had surgery to determine nodal involvement. It was required to see if nodal involvement could be accurately predicted from the predictor variables and which ones were most important.

Usage

data(nodal)

Format

A data frame with 53 observations on the following 7 variables.

m

A column of ones.

r

An indicator of nodal involvement.

aged

The patients age dichotomized into less than 60 (‘0’) and 60 or over ‘1’.

stage

A measurement of the size and position of the tumour observed by palpatation with the fingers via the rectum. A value of ‘1’ indicates a more serious case of the cancer.

grade

Another indicator of the seriousness of the cancer, this one is determined by a pathology reading of a biopsy taken by needle before surgery. A value of ‘1’ indicates a more serious case of the cancer.

xray

A third measure of the seriousness of the cancer taken from an X-ray reading. A value of ‘1’ indicates a more serious case of the cancer.

acid

The level of acid phosphatase in the blood serum.

Source

Brown, B.W. (1980) Prediction analysis for binary data. In Biostatistics Casebook. R.G. Miller, B. Efron, B.W. Brown and L.E. Moses (editors), 3-18. John Wiley.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 491.

Examples

data(nodal)
nodal.glm <- glm(r~aged+stage+grade+xray+acid,binomial,data=nodal)
summary(nodal.glm,correlation=FALSE)

Nuclear Power Station Construction Data

Description

The data relate to the construction of 32 light water reactor (LWR) plants constructed in the U.S.A in the late 1960's and early 1970's. The data was collected with the aim of predicting the cost of construction of further LWR plants. 6 of the power plants had partial turnkey guarantees and it is possible that, for these plants, some manufacturers' subsidies may be hidden in the quoted capital costs.

Usage

data(nuclear)

Format

A data frame with 32 observations on the following 11 variables.

cost

The capital cost of construction in millions of dollars adjusted to 1976 base.

date

The date on which the construction permit was issued. The data are measured in years since January 1 1990 to the nearest month.

t1

The time between application for and issue of the construction permit.

t2

The time between issue of operating license and construction permit.

cap

The net capacity of the power plant (MWe).

pr

A binary variable where ‘1’ indicates the prior existence of a LWR plant at the same site.

ne

A binary variable where ‘1’ indicates that the plant was constructed in the north-east region of the U.S.A.

ct

A binary variable where ‘1’ indicates the use of a cooling tower in the plant.

bw

A binary variable where ‘1’ indicates that the nuclear steam supply system was manufactured by Babcock-Wilcox.

cum.n

The cumulative number of power plants constructed by each architect-engineer.

pt

A binary variable where ‘1’ indicates those plants with partial turnkey guarantees.

Source

Cox, D.R. and Snell, E.J. (1981) Applied Statistics: Principles and Examples. Chapman and Hall.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 401.

Examples

data(nuclear)
pairs(nuclear)
fit <- lm(log(cost)~date+t1+t2+cap+pr+ne+ct+bw+cum.n+pr,data=nuclear)
step(fit)  # stepwise model selection

Estimates of Hazard Function for Old Age

Description

Historical estimates of the force of mortality (hazard function) averaged for 5-year age groups. The data are taken from various historical sources.

Usage

data(old.age)

Format

A data frame with 14 observations on the following 8 variables.

age

Age group (5-year intervals)

hungary

Data estimated from Hungarian graveyards, 900–1100

eng.1640

Data estimated from England, 1640–1689

breslau

Data estimated from Breslau, 1687–1691

engm.1841

Data from England and Wales, males, 1841

engf.1841

Data from England and Wales, females, 1841

engm.1980

Data from England and Wales, males, 1980–1982

engf.1980

Data from England and Wales, females, 1980–1982

Details

The estimated numbers of people on which the data in the columns are based are 2300, 3133, 2675, 71,000, 74,000, 834,0000, and 828,000.

Source

Thatcher, A. R. (1999) The long-term pattern of adult mortality and the highest attained age (with Discussion). Journal of the Royal Statistical Society series A, 16, 5–43.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 194.

Examples

data(old.age)

Modified Scatterplot Matrix

Description

Plots a scatterplot matrix in which panels below the diagonal show ordinary scatterplots of pairs of variables, and those above the diagonal show scatterplots of residuals after regression on all the other variables.

Usage

## S3 method for class 'mod'
pairs(x, format = "MC", labelnames = names(x), highlight = NULL, level = 0.9, ...)

Arguments

Details

The diagonal shows histograms of the original data, and (in black) histograms of the partial residuals after adjustment on all the other variables, shifted to have the same mean as the original data. Also given are the original

The below-diagonal panels contain the numerical value of the correlation, and those above the diagonal contain the partial correlation, that is, the correlation of the residuals after linear regression on the remaining variables. The panels show ellipses which would contain 90 percent of the observations in a large normal sample with the same mean and covariance matrix as the data.

Value

Produces the scatterplot matrix, and prints the marginal and partial standard deviations of the variables.

Note

pairs.mod calls library(ellipse) and will give an error if this is unavailable.

Author(s)

Sylvain Sardy (Sylvain.Sardy@epfl.ch)

References

Davison, A. C. and Sardy, S. (2000) The partial scatterplot matrix. Journal of Computational and Graphical Statistics, 9, 750–758.

Examples

library(ellipse)
data(mathmarks)
pairs.mod(mathmarks)

Neurotransmission in Guinea Pig Brains

Description

The 'paulsen' data frame has 346 rows and 1 columns.

Sections were prepared from the brain of adult guinea pigs. Spontaneous currents that flowed into individual brain cells were then recorded and the peak amplitude of each current measured. The aim of the experiment was to see if the current flow was quantal in nature (i.e. that it is not a single burst but instead is built up of many smaller bursts of current). If the current was indeed quantal then it would be expected that the distribution of the current amplitude would be multimodal with modes at regular intervals. The modes would be expected to decrease in magnitude for higher current amplitudes.

Usage

data(paulsen)

Format

This data frame contains the following column:

y

The current flowing into individual brain cells. The currents are measured in pico-amperes.

Source

The data were kindly made available by Dr. O. Paulsen of the Department of Pharmacology, University of Oxford.

Paulsen, O. and Heggelund, P. (1994) The quantal size at retinogeniculate synapses determined from spontaneous and evoked EPSCs in guinea-pig thalamic slices. Journal of Physiology, 480, 505-511.

Examples

data(paulsen)
hist(paulsen$y,prob=TRUE)

Mayo Clinic Primary Biliary Cirrhosis Data

Description

Followup of 312 randomised and 108 unrandomised patients with primary biliary cirrhosis, a rare autoimmune liver disease, at Mayo Clinic.

Usage

data(pbc)

Format

A data frame with 418 observations on the following 20 variables.

age

in years

alb

serum albumin

alkphos

alkaline phosphotase

ascites

presence of ascites

bili

serum bilirubin

chol

serum cholesterol

edema

presence of edema

edtrt

0 no edema, 0.5 untreated or successfully treated 1 unsuccessfully treated edema

hepmeg

enlarged liver

time

survival time

platelet

platelet count

protime

standardised blood clotting time

sex

1=male

sgot

liver enzyme (now called AST)

spiders

blood vessel malformations in the skin

stage

histologic stage of disease (needs biopsy)

status

censoring status

trt

1/2/-9 for control, treatment, not randomised

trig

triglycerides

copper

urine copper

Source

Fleming, T. R. and Harrington, D. P. (1991) Counting Processes and Survival Analysis. Wiley: New York.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 549.

Examples

data(pbc)  
# to make version of dataset used in book
pbcm <- pbc[(pbc$trt!=-9),]
pbcm$copper[(pbcm$copper==-9)] <- median(pbcm$copper[(pbcm$copper!=-9)])
pbcm$platelet[(pbcm$platelet==-9)] <- median(pbcm$platelet[(pbcm$platelet!=-9)])
attach(pbcm)

library(survival)
par(mfrow=c(1,2),pty="s")
plot(survfit(Surv(time,status)~trt),ylim=c(0,1),lty=c(1,2),
   ylab="Survival probability",xlab="Time (days)")
plot(survfit(coxph(Surv(time,status)~trt+strata(sex))),ylim=c(0,1),lty=c(1,2),
   ylab="Survival probability",xlab="Time (days)")
lines(survfit(coxph(Surv(time,status)~trt)),lwd=2)
# proportional hazards model fit
fit <- coxph(formula = Surv(time, status) ~ age + alb + alkphos + ascites + 
      bili + edtrt + hepmeg + platelet + protime + sex + spiders, data=pbcm)
summary(fit)
step.fit <- step(fit,direction="backward")

Homing Pigeon Data

Description

Bearings (degrees) of 29 homing pigeons 30, 60, 90 after their release, and on vanishing from sight.

Usage

data(pigeon)

Format

A data frame with 29 observations on the following 4 variables.

s30

Bearing after 30 seconds

s60

Bearing after 60 seconds

s90

Bearing after 90 seconds

van

Bearing on vanishing from sight

Source

Artes, R. (1997) Extensoes da Teoria das Equacoes de Estimacao Generalizadas a Dados Circulares e Modelos de Dispersao. Ph.D. thesis, University of Sao Paulo.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 173.

Examples

data(pigeon)
plt <- function( ang, r=c(1,2,3,4), lty=1,... )
{
  si <- sin(2*pi*ang/360)
  co <- cos(2*pi*ang/360)
  points( r*si,r*co )
  lines( c(0,r*si),c(0,r*co),...)
}
par(pty="s")
plot(c(0,0),c(0,0),xlim=c(-4,4),ylim=c(-4,4),
    xlab="Easting",ylab="Northing")
for (i in 1:nrow(pigeon)) plt( pigeon[i,],col=i )

Pig Diet Data

Description

Data on weight gains in 32 pigs, divided into eight groups of four, and with 4 different diets allocated to the group members.

Usage

data(pigs)

Format

A data frame with 32 observations on the following 3 variables.

group

a factor with 8 levels

diet

a factor with levels I–IV

gain

weight gain (units unknown)

Source

Unpublished lecture notes, Imperial College, London

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 431.

Examples

data(pigs)
anova(lm(gain~group+diet,data=pigs))

Red Blood Cell Data

Description

Numbers of red blood cells counted by five doctors using ten sets of apparatus.

Usage

data(pipette)

Format

A data frame with 50 observations on the following 3 variables.

apparatus

Factor with ten levels

doctor

Factor with five levels

y

Number of red blood cells

Source

Unpublished lecture notes, Imperial College, London.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 462.

Diagnostic plots for generalized linear models

Description

Makes plot of jackknife deviance residuals against linear predictor, normal scores plots of standardized deviance residuals, plot of approximate Cook statistics against leverage/(1-leverage), and case plot of Cook statistic.

Usage

## S3 method for class 'glm.diag'
plot(x, glmdiag = glm.diag(x), subset = NULL, iden = FALSE, 
                        labels = NULL, ret = FALSE, ...)

Arguments

Details

The plot on the top left is a plot of the jackknife deviance residuals against the fitted values.

The plot on the top right is a normal QQ plot of the standardized deviance residuals. The dotted line is the expected line if the standardized residuals are normally distributed, i.e. it is the line with intercept 0 and slope 1.

The bottom two panels are plots of the Cook statistics. On the left is a plot of the Cook statistics against the standardized leverages. In general there will be two dotted lines on this plot. The horizontal line is at 8/(n-2p) where n is the number of observations and p is the number of parameters estimated. Points above this line may be points with high influence on the model. The vertical line is at 2p/(n-2p) and points to the right of this line have high leverage compared to the variance of the raw residual at that point. If all points are below the horizontal line or to the left of the vertical line then the line is not shown.

The final plot again shows the Cook statistic this time plotted against case number enabling us to find which observations are influential.

Use of iden=T is encouraged for proper exploration of these four plots as a guide to how well the model fits the data and whether certain observations have an unduly large effect on parameter estimates.

Value

If ret is TRUE then the value of glmdiag is returned otherwise there is no returned value.

Author(s)

Angelo Canty

References

Davison, A.C. and Snell, E.J. (1991) Residuals and diagnostics. In Statistical Theory and Modelling: In Honour of Sir David Cox. D.V. Hinkley, N. Reid, and E.J. Snell (editors), 83-106. Chapman and Hall.

See Also

glm,glm.diag,identify

Examples

  # leukaemia data
require(MASS)
data(leuk, package="MASS")
leuk.mod <- glm(time~ag-1+log10(wbc),family=Gamma(log),data=leuk)
leuk.diag <- glm.diag(leuk.mod)
plot.glm.diag(leuk.mod,leuk.diag)

Pneumoconiosis amongst Coalminers

Description

This gives the degree of pneumoconiosis (normal, present, or severe) in a group of coalminers as a function of the number of years worked at the coalface. The degree of the disease was assessed radiologically and is qualitative.

Usage

data(pneu)

Format

A data frame with 8 observations on the following 4 variables.

Years

Period of exposure (years worked at the coalface)

Normal

Number of miners with normal lungs

Present

Number of miners with disease present

Severe

Number of miners with severe disease

Source

Ashford, J. R. (1959) An approach to the analysis of data for semi-quantal responses in biological assay. Biometrics, 15, 573–581.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 509.

Examples

data(pneu)
summary(glm(cbind(Present+Severe,Normal)~log(Years),data=pneu,binomial))
summary(glm(cbind(Severe,Normal+Present)~log(Years),data=pneu,binomial))

Laplace Approximation for Posterior Density, Practical 11.2

Description

This function computes the Laplace approximation to the posterior density of the parameter beta in a Poisson regression model. For more details see Practical 11.2 of Davison (2003).

Usage

poi.beta.laplace(data, alpha = get.alpha(data), phi = 1, nu = 0.1, 
                 beta = seq(from = 0, to = 7, length = 1000))

Arguments

Details

This is provided simply so that readers spend less time typing. It is not intended to be robust and general code.

Value

Author(s)

Anthony Davison (anthony.davison@epfl.ch)

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Practical 11.2.

Examples

## From Practical 11.2:
get.alpha <- function(d)
{  # estimate alpha from data
  rho <- d$y/d$x
  n <- length(d$y)
  mean(rho)^2/( (n-1)*var(rho)/n - mean(rho)*mean(1/d$x) )
}
data(cloth)
attach(cloth)
plot(x,y)
beta <- seq(from=0,to=10,length=1000)
beta.post <- poi.beta.laplace(cloth,beta=beta,nu=1)
plot(beta.post,type="l",xlab="beta",ylab="Posterior density")
beta.post <- poi.beta.laplace(cloth,beta=beta,nu=5)
lines(beta.post,lty=2)

Gibbs Sampler for Hierarchical Poisson Model, Practical 11.5

Description

This function implements Gibbs sampling for the hierarchical Poisson model described in Example 11.19 and Practical 11.5 of Davison (2003), which should be consulted for more details.

Usage

poi.gibbs(d, alpha, gamma, delta, I, S)

Arguments

Details

This is provided simply so that readers spend less time typing. It is not intended to be robust and general code.

Value

An I x S x (n+1) array containing the successive iterations of the samplers, for the I iterations, S independent replicates, and n rate parameters plus the parameter beta of the prior distribution.

Author(s)

Anthony Davison (anthony.davison@epfl.ch)

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Practical 11.5.

Examples

 ## From Practical 11.5:
data(pumps)
system.time( pumps.sim <- poi.gibbs(pumps, alpha=1.8, delta=0.1, gamma=1, 
             I=1000, S=5) )
par(mfrow=c(2,3))
plot.ts(pumps.sim[,1,1])
acf(pumps.sim[,1,1])
pacf(pumps.sim[,1,1])
plot.ts(pumps.sim[,1,11])
acf(pumps.sim[,1,11])
pacf(pumps.sim[,1,11])

Survival Times for Poisoned Animals

Description

In an experiment to assess the usefulness of treatments for poisons, 48 animals were split randomly into 12 groups of 4. Each group was administered one of three poisons, and one of four treatments, giving a 3x4 factorial design with 4 replicates.

Usage

data(poisons)

Format

A data frame with 48 observations on the following 3 variables.

time

Survival time (units of 10 hours)

poison

Factor giving poison

treat

Factor giving treatment

Source

Box, G. E. P. and Cox, D. R. (1964) An analysis of transformations (with Discussion). Journal of the Royal Statistical Society series B, 26, 211–246.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 391.

Examples

data(poisons)
fit <- lm(time~poison+treat,data=poisons)
library(MASS)
boxcox(time~poison+treat,data=poisons)

Air Pollution and Mortality

Description

Data on the relation between weather, socioeconomic, and air pollution variables and mortality rates in 60 Standard Metropolitan Statistical Areas (SMSAs) of the USA, for the years 1959-1961. Some of the variables are highly collinear.

Usage

data(pollution)

Format

A data frame with 60 observations on the following variables.

prec

Average annual precipitation in inches

jant

Average January temperature in degrees F

jult

Average July temperature in degrees F

ovr95

Percentage of 1960 SMSA population aged 65 or older

popn

Average household size

educ

Median school years completed by those over 22

hous

percentage of housing units which are sound and with all facilities

dens

Population per square mile in urbanized areas, 1960

nonw

Percentage non-white population in urbanized areas, 1960

wwdrk

Percentage employed in white collar occupations

poor

Percentage of families with income < 3000 dollars

hc

Relative hydrocarbon pollution potential

nox

Same for nitric oxides

so

Same for sulphur dioxide

humid

Annual average percentage relative humidity at 1pm

mort

Total age-adjusted mortality rate per 100,000

Source

McDonald, G. C. and Schwing, R. C. (1973) Instabilities of regression estimates relating air pollution to mortality, Technometrics, 15, 463-482.

Examples

data(pollution)
## maybe str(pollution) ; plot(pollution) ...

Pump Failure Data

Description

The data give numbers of failures of ten pumps from several systems in the nuclear plant Farley 1. Pumps 1, 3, 4, and 6 operate continuously, while the rest operate only intermittantly or on standby.

Usage

data(pumps)

Format

A data frame with 10 observations on the following 2 variables.

x

Operating time (in thousands of operatin hours)

y

Number of failures

Source

Gaver, D. P. and O'Muircheartaigh, I. G. (1987) Robust empirical Bayes analysis of event rates. Technometrics, 29, 1–15.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 600.

Exponential Quantile-Quantile Plots

Description

Exponential probability plot of data.

Usage

qqexp(y, line = FALSE, ...)

Arguments

Value

A exponential probablity plot of the data in y; that is, a plot of the ordered values of y against the quantiles of the standard exponential distribution.

See Also

qqnorm

Examples

qqexp(rexp(50))
qqexp(rgamma(50,shape=2),line=TRUE)

Japanese Earthquake Data

Description

Times and magnitudes (Richter scale) of 483 shallow earthquakes in an offshore region east of Honshu and south of Hokkaido, for the period 1885–1980.

Usage

data(quake)

Format

An irregular time series with earthquake

time

in days since start of 1885

mag

magnitude (Richter scale)

Source

Ogata, Y. (1988) Statistical models for earthquake occurrences and residual analysis for point processes. Journal of the American Statistical Association, 83, 9–27.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 289.

Rat Growth Data

Description

Data on the weights of 30 rats each week for 5 weeks.

Usage

data(rat.growth)

Format

A data frame with 150 observations on the following 3 variables.

rat

a factor with levels 1-30

week

takes values 0-4

y

rat weight (units unspecified)

Source

Gelfand, A. E., Hills, S. E., Racine-Poon, A. and Smith, A. F. M. (1990) Illustration of Bayesian inference in normal data models using Gibbs sampling. Journal of the American Statistical Association, 85, 972–985.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 460.

Examples

data(rat.growth)
library(nlme)
rat.fit <- groupedData( y~poly(week,2) | rat,
                   data = rat.growth,
                   labels = list( x = "Week",
                     y = "Weight" ),
                   units = list( x = "", y = "(?)") )

summary(lme(rat.fit))

Water Salinity and River Discharge

Description

The 'salinity' data frame has 28 rows and 4 columns.

Biweekly averages of the water salinity and river discharge in Pamlico Sound, North Carolina were recorded between the years 1972 and 1977. The data in this set consists only of those measurements in March, April and May.

Usage

data(salinity)

Format

This data frame contains the following columns:

sal

The average salinity of the water over two weeks.

lag

The average salinity of the water lagged two weeks. Since only spring is used, the value of 'lag' is not always equal to the previous value of 'sal'.

trend

A factor indicating in which of the 6 biweekly periods between March and May, the observations were taken. The levels of the factor are from 0 to 5 with 0 being the first two weeks in March.

dis

The amount of river discharge during the two weeks for which 'sal' is the average salinity.

Source

The data were obtained from

Ruppert, D. and Carroll, R.J. (1980) Trimmed least squares estimation in the linear model. Journal of the American Statistical Association, 75, 828–838.

Examples

data(salinity)
## maybe str(salinity) ; plot(salinity) ...

Germination of seeds

Description

These are the number of seeds germinating when subjected to extracts of certain roots.

Usage

data(seeds)

Format

A data frame with 21 observations on the following 4 variables.

r

Number of seeds germinating

m

Total number of seeds

seed

Seed type: O. aegyptiaco 75 or O. aegyptiaco 73

root

Root extract

Source

Crowder, M. J. (1978) Beta-binomial ANOVA for proportions. Applied Statistics, 27, 34–37.

References

Cox, D. R. and Snell, E. J. (1989) Analysis of Binary Data, second edition. London: Chapman and Hall. Section 3.2.

Examples

data(seeds)
## maybe str(seeds) ; plot(seeds) ...

Shoe Wear Data

Description

Amount of wear in a paired comparison of two materials used for soling the shoes of 10 boys. The materials were allocated randomly to the left and right feet.

Usage

data(shoe)

Format

A data frame with 20 observations on the following 4 variables.

material

factor giving the shoe sole material

boy

factor with 10 levels

foot

factor giving left or right foot

y

amount of shoe wear

Source

Box, G. E. P., Hunter, W. G. and Hunter, J. S. (1978) Statistics for Experimenters. New York: Wiley. Page 100.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 422.

Examples

data(shoe)
attach(shoe)
d <- y[material=="B"]-y[material=="A"]  # difference
t.test(d)  # t test of hypothesis that B wears quicker 

O-ring Thermal Distress Data for Space Shuttle

Description

Data on the number of rubber O-rings showing thermal distress for 23 flights of the space shuttle, with the ambient temperature and pressure at which tests on the putty next to the rings were performed.

Usage

data(shuttle)

Format

A data frame with 23 observations on the following 4 variables.

m

Number of rings

r

Number of rings showing thermal distress

temperature

ambient temperature (degrees Fahrenheit)

pressure

pressure (pounds per square inch)

Source

Dalal, S. R., Fowlkes, E. B. and Hoadley, B. (1989) Risk analysis of the space shuttle: Pre-Challenger prediction of failure. Journal of the American Statistical Association, 84, 945–957.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 7.

Examples

data(shuttle)
attach(shuttle)
plot(temperature, r/m,ylab="Proportion of failures")

Survival and Smoking

Description

Twenty-year survival and smoking status for 1314 women from Whickham, near Newcastle-upon-Tyne.

Usage

data(smoking)

Format

A data frame with 14 observations on the following 4 variables.

age

Age group (factor)

smoker

Smoking status (1=smoker, 0=non-smoker)

alive

Number alive after 20 years

dead

Number dead after 20 years

Source

Appleton, D. R., French, J. M. and Vanderpump, M. P. J. (1996) Ignoring a covariate: An example of Simpson's paradox. The American Statistician, 50, 340–341.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 258.

Examples

data(smoking)
summary(glm(cbind(dead,alive)~smoker,data=smoking,binomial))
# note sign change for smoker covariate, due to Simpson's paradox
summary(glm(cbind(dead,alive)~age+smoker,data=smoking,binomial))

Soccer Scores from English Premier League, 2000-2001 Season

Description

These are scores for the 380 fixtures in the English Premier League, 2000–2001.

Usage

data(soccer)

Format

A data frame with 380 observations on the following 7 variables.

month

Month of match

day

Day of match

year

Year of match

team1

Home team

team2

Away team

score1

Goals scored by home team

score2

Goals scored by away team

Source

http://www.soccerbase.com/footballlive/

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 499.

Spring Failure Data

Description

Failure times of 60 springs divided into 6 groups of 10, with each group subject to a different level of stress. Some of the times are right-censored.

Usage

data(springs)

Format

A data frame with 60 observations on the following 3 variables.

cycles

failure times (in units of $10^3$ cycles of loading)

cens

censoring indicator, with 0 indicating right-censoring

stress

a factor giving the stress (N/mm$^3$)

Source

Cox, D. R. and Oakes, D. (1984) Analysis of Survival Data. London: Chapman and Hall/CRC Press.

Examples

data(springs)
attach(springs)
plot(cycles~stress)
plot(cycles~stress,log="y")

Stickiness of blood data

Description

Data on stickiness of blood for six subjects

Usage

data(sticky)

Format

A data frame with 42 observations on the following 2 variables.

subject

factor with levels 1–6

y

measurement of a property related to stickiness of blood

Source

Unpublished lecture notes, Imperial College London.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 450.

Examples

data(sticky)
anova(lm(y~subject,data=sticky))

Survival of Rats After Radiation Doses

Description

The ‘survival’ data frame has 14 rows and 2 columns.

The data measured the survival percentages of batches of rats who were given varying doses of radiation. At each of 6 doses there were two or three replications of the experiment.

Usage

data(survival)

Format

A data frame with 14 observations on the following 2 variables.

dose

The dose of radiation administered (rads).

surv

The survival rate of the batches expressed as a percentage.

Source

Efron, B. (1988) Computer-intensive methods in statistical regression. SIAM Review, 30, 421-449.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 376.

Examples

data(survival)
plot(survival$dose,survival$surv,log="y")  # note the obvious outlier
lm(log(surv)~dose,data=survival)

Teak Plant Data

Description

These are data from an experiment on the growth of teak plants after one season, using two planting methods and three root lengths. Plants were laid out in four randomised blocks, each consisting of 6 plots with 50 plants in each plot.

Usage

data(teak)

Format

A data frame with 24 observations on the following 4 variables.

Block

Block labels.

Plant

A indicates planting using pits, B using crowbar.

Root

length, 4, 6 or 8 inches.

y

mean height (inches) of the 50 plants grown on each plot.

Source

Unpublished lecture notes, Imperial College, London.

Examples

data(teak)
anova(lm(y~Block*Plant*Root,data=teak),test="F")

Annual Maximum Sea Levels

Description

Annual maximum sea levels (m) at seven locations near to or in south-east England, between 1819–1986. There are many missing values.

Usage

data(tide)

Format

A data frame with 168 observations on the following 8 variables.

year

Year

Yarmouth

Annual maximum high tide at Yarmouth

Lowestoft

Annual maximum high tide at Lowestoft

Harwich

Annual maximum high tide at Harwich

Walton

Annual maximum high tide at Walton

Holland

Annual maximum high tide at a site in Holland

Southend

Annual maximum high tide at Southend

Sheerness

Annual maximum high tide at Sheerness

Source

The data were kindly provided by Professor Jonathan Tawn of Lancaster University.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 281.

Examples

data(tide)
plot(tide$year,tide$Yarmouth,type="l")

Toxoplasmosis Data

Description

Data on the relation between rainfall and the numbers of people testing positive for toxoplasmosis in 34 cities in El Salvador.

Usage

data(toxo)

Format

A data frame with 34 observations on the following 3 variables.

rain

Annual rainfall (mm)

m

Number of persons tested

r

Number of persons testing positive for toxoplasmosis

Source

Efron, B. (1986) Double exponential families and their use in generalized linear regression. Journal of the American Statistical Association, 82, 171–200.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 516.

Examples

data(toxo)
anova(glm(cbind(r,m-r)~poly(rain,3),data=toxo,family=binomial),test="Chi")
fit <- glm(cbind(r,m-r)~poly(rain,3),data=toxo,family=quasibinomial)
anova(fit,test="F")
summary(fit)

Recurrent Bleeding from Ulcers

Description

Data from 40 experiments to compare a new surgery for stomach ulcer with an older surgery.

Usage

data(ulcer)

Format

A data frame with 80 observations on the following 9 variables.

author

Author of study from which data taken

year

Year of publication

quality

Assessment of quality of trial on which data based

age

Mean age of patients

r

Number of patients without recurrent bleeding

m

Total number of patients

bleed

a numeric vector

treat

Factor giving control (C) or variants of new treatment

table

Factor giving 2x2 table corresponding to each trial

Source

Efron, B. (1996) Empirical Bayes methods for combining likelihoods (with Discussion). Journal of the American Statistical Association, 91, 538–565.

Errors in the data given in the paper have been corrected here.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 496.

Examples

data(ulcer)
glm(cbind(r,m-r)~table+treat,data=ulcer,family=binomial)

Urine Analysis Data

Description

The 'urine' data frame has 79 rows and 7 columns.

79 urine specimens were analyzed in an effort to determine if certain physical characteristics of the urine might be related to the formation of calcium oxalate crystals. Cases 1 and 55 have missing covariates.

Usage

data(urine)

Format

This data frame contains the following columns:

r

Indicator of the presence of calcium oxalate crystals.

gravity

The specific gravity of the urine.

ph

The pH reading of the urine.

osmo

The osmolarity of the urine. Osmolarity is proportional to the concentration of molecules in solution.

cond

The conductivity of the urine. Conductivity is proportional to the concentration of charged ions in solution.

urea

The urea concentration in millimoles per litre.

calc

The calcium concentration in millimoles per litre.

Source

Andrews, D.F. and Herzberg, A.M. (1985) Data: A Collection of Problems from Many Fields for the Student and Research Worker. Springer-Verlag. Pages 249–251.

Examples

data(urine)
glm(r~gravity+ph+osmo+cond+urea+calc,binomial,data=urine,subset=-c(1,55))

Extreme Sea Levels at Venice

Description

The ten highest annual sea levels (cm) at Venice, from 1887–1981.

Usage

data(venice)

Format

A data frame with 95 observations on the following 11 variables.

year

1887–1981

y1

Annual maximum sea level (cm)

y2

Second largest sea level (cm)

y3

Third largest sea level (cm)

y4

Fourth largest sea level (cm)

y5

Fifth largest sea level (cm)

y6

Sixth largest sea level (cm)

y7

Seventh largest sea level (cm)

y8

Eighth largest sea level (cm)

y9

Ninth largest sea level (cm)

y10

Tenth largest sea level (cm)

Details

There are missing values in 1922 and 1935.

Source

Pirazzoli, P. A. (1982) Maree estreme a Venezia (periodo 1872–1981). Acqua Aria, 10, 1023–1039.

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Page 162.

Examples

data(venice)
attach(venice)
y <- y1[year>1930]  # for analysis in Section 5 of Davison (2003)
x <- year[year>1930]-1956
plot(x+1956,y,ylab="Sea level (cm)",xlab="Year")
lm(y~x)

Yahoo Closing Prices

Description

Daily closing prices (US dollars) of Yahoo.com shares from 12 April 1996 to 26 April 2000.

Usage

data(yahoo)

Format

An irregular time series with 1017 values.

Examples

data(yahoo)
plot(yahoo,type="l",ylab="Yahoo closing prices")
plot(diff(100*log(yahoo)),type="l",ylab="Yahoo log returns (percent)")