Package 'gamlss.data'

Description

The abdom data frame has 610 rows and 2 columns. The data are measurements of abdominal circumference (response variable) taken from fetuses during ultrasound scans at Kings College Hospital, London, at gestational ages (explanatory variable) ranging between 12 and 42 weeks.

Usage

data(abdom)

Format

This data frame contains the following columns:

y

abdominal circumference: a numeric vector

x

gestational age: a numeric vector

Details

The data were used to derived reference intervals by Chitty et al. (1994) and also for comparing different reference centile methods by Wright and Royston (1997), who also commented that the distribution of Z-scores obtained from the different fitted models 'has somewhat longer tails than the normal distribution'.

Source

Dr. Eileen M. Wright, Department of Medical Statistics and Evaluation, Royal Postgraduate Medical School, Du Cane Road, London, W12 0NN.

References

Chitty, L.S., Altman, D.G., Henderson, A. and Campbell, S. (1994) Charts of fetal size: 3, abdominal measurement. Br. J. Obstet. Gynaec., 101: 125–131

Wright, E. M. and Royston, P. (1997). A comparison of statistical methods for age-related reference intervals. J.R.Statist.Soc. A., 160: 47–69.

Examples

data(abdom)
attach(abdom)
plot(x,y)
detach(abdom)

Description

The data shows the acidity index for 155 lakes in the Northeastern United States (previously analysed as a mixture of gaussian distributions on the log scale by Crawford et al.(1992, 1994)). These 155 observations are the log acidity indices for the lakes.

Usage

data(acidity)

Format

A data frame with 155 observations on the following variable.

y

a numeric vector showing the acidity index for 155 lakes in the Northeastern United States

References

Crawford S.L., DeGroot M.H., Kadane J.B., and Small M.J. (1992), Modeling lake-chemistry distributions: Approximate Bayesian methods for estimating a finite-mixture model, Technometrics, 34, pp 441-450.

Crawford S.L. (1994) An application of the Laplace method to finite mixture distributions, JASA, 89. pp 269-278.

McLachlan G. and Peel D., Finite Mixture Models, Wiley, New York.

Examples

data(acidity)
with( acidity, hist(y))

Description

The data, 1383 observations, are from a study at the Hospital del Mar, Barcelona during the years 1988 and 1990, Gange et al. (1996).

Usage

data(aep)

Format

A data frame with 1383 observations on the following 8 variables.

los

the total number of days patients spent in hospital: a discrete vector

noinap

the number of inappropriate days spent in hospital: a discrete vector

loglos

the log(los/10): a numeric vector

sex

the gender of patient: a factor with levels 1=male, 2=female

ward

the type of ward in the hospital: a factor with levels 1=medical 2=surgical, 3=others

year

the specific year 1988 or 1990: a factor with levels 88 and 90

age

the age of the patient subtracted from 55: a numeric vector

y

the response variable a matrix with 2 columns, the first is noinap the second is equal to (los-noinap)

Details

Gange et al. (1996) used a logistic regression model for the number of inappropriate days (noinap) out of the total number of days spent in hospital (los), with binomial and beta binomial errors and found that the later provided a better fit to the data. They modelled both the mean and the dispersion of the beta binomial distribution (BB) as functions of explanatory variables

Source

Gange, S. J. Munoz, A. Saez, M. and Alonso, J. (1996)

References

Gange, S. J. Munoz, A. Saez, M. and Alonso, J. (1996) Use of the beta-binomial distribution to model the effect of policy changes on appropriateness of hospital stays. Appl. Statist, 45, 371–382

Examples

data(aep)
attach(aep)
pro<-noinap/los
plot(ward,pro)
rm(pro)
detach(aep)

Description

The quarterly reported AIDS cases in the U.K. from January 1983 to March 1994 obtained from the Public Health Laboratory Service, Communicable Disease Surveillance Centre, London.

Usage

data(aids)

Format

A data frame with 45 observations on the following 3 variables.

y

the number of quarterly aids cases in England and Wales: a numeric vector

x

time in months from January 1983, 1:45 : a numeric vector

qrt

the quarterly seasonal effect a factor with 4 levels, [1=Q1 (Jan-March), 2=Q2 (Apr-June), 3=Q3 (July-Sept), 4=Q4 (Oct-Dec)]

Details

The counts y can be modelled using a (smooth) Poisson regression model in time x with the quarterly effects i.e. cs(x,df=7)+qrt. Overdispersion persists, so use a Negative Binomial distribution of type I or II. The data also can be used to find a break point in time, see Rigby and Stasinopoulos (1992).

Source

Public Health Laboratory Service, Communicable Disease Surveillance Centre, London.

References

Stasinopoulos, D.M. and Rigby, R. A. (1992). Detecting break points in generalized linear models. Computational Statistics and Data Analysis, 13, 461–471.

Examples

data(aids)
attach(aids)
plot(x,y,pch=21,bg=c("red","green3","blue","yellow")[unclass(qrt)])
detach(aids)

Description

These data, reported by Proschan (1963, Technometrics 5, 375-383), refer to the intervals, in service-hours, between failures of the air-conditioning equipment in a Boeing 720 aircraft. (Proschan reports data on 10 different aircraft. The data from only one of the aircraft is used here. Cox and Snell (1981, Applied Statistics: principles and examples, Chapman and Hall, London) discuss the analysis of the data on all 10 aircraft.) The dataset consists of a single vector of data. They are used in the book ‘Distributions for location, scale and shape: Using GAMLSS in R’ to demonstrate the likelihood function and maximum likelihood estimation.

Usage

data("aircond")

Format

A data frame with 24 observations on the following variable.

aircond

a numeric vector

Source

The data were taken from the R package rpanel where they refer to as aircon.

References

Cox and Snell (1981, Applied Statistics: principles and examples, Chapman and Hall, London)

rpanel: Simple interactive controls for R functions using the tcltk package. Journal of Statistical Software, 17, issue 9.

Proschan, F. (1963) Theoretical explanation of observed decreasing failure rate. Technometrics, Vol. 5 no. 3, pp 375-383, Taylor & Francis.

Examples

data(aircond)

Description

This data set is a subset of the data used in Judah et. al (2025) for analysis liver function data during pregnacy. This set was used to constact centiles at different gestation age for the variable Alkaike Phosphatate (ALP).

Usage

data("ALP")

Format

A data frame with 3429 observations on the following 2 variables.

ALP

Alkaike Phosphatate, a numeric vector

ga

Gestational Age, a numeric vector

Details

The data come from a bigger data set used to in Judah et. al (2025) to (1) provide reference ranges for liver function tests in a large population of uncomplicated pregnancies after adjusting for the effect of gestational age and maternal demographic characteristics on the median and measures of dispersion and shape (skewness and kurtosis) of the distribution of these variables.

Source

Judah et. al (2025)

References

Judah, H.R., Rigby, R.A., Stasinopoulos, M.D., Pateras, K., Rahim, M.N., Heneghan, M.A., Nicolaides, K.H. and Kametas, N.A., 2025. Reference ranges for liver function tests in pregnancy controlling for maternal characteristics. American Journal of Obstetrics and Gynecology.

Examples

data(ALP)
plot(ALP~ga, data=ALP)

Description

alveolar : alveolar-bronchiolar adenomas data used by Tamura and Young (1987) and also reproduce in Hand et al. (1994), data set 256. The data are the number of mice out of certain number of mice (the binomial denominator) in 23 independent groups, having alveolar-bronchiolar adenomas.

Usage

data(alveolar)

Format

Data frames each with the following variable.

r

a numeric vector showing the number of mice out of n number of mice (the binomial denominator below) in 23 independent groups, having alveolar-bronchiolar adenomas.

n

a numeric vector showing the total number of mice

Details

Data sets usefull for the GAMLSS booklet

References

Hand et al. (1994) A handbook of small data sets. Chapman and Hall, London.

Examples

data(alveolar)
with(alveolar, hist(r/n))

Description

Brown fat (or brown adipose tissue) is found in hibernating mammals, its function being to increase tolerance to the cold. It is also present in newborn humans. In adult humans it is more rare and is known to vary considerably with ambient temperature. RouthierLabadie2011 analysed data on 4,842 subjects over the period 2007-2008, of whom 328 (6.8%) had brown fat. Brown fat mass and other demographic and clinical variables were recorded. The purpose of the study was to investigate the factors associated with brown fat occurrence and mass in humans.

Usage

data("brownfat")

Format

A data frame with 4842 observations on the following 14 variables.

sex

1=female, 2=male

diabetes

0=no, 1=yes

age

age in years

day

day of observation (1=1 January, ..., 365=31 December)

exttemp

external temperature (degrees Centigrade)

season

Spring=1, Summer=2, Autumn=3, Winter=4

weight

weight in kg

height

height in cm

BMI

body mass index

glycemy

glycemia (mmol/L)

LBW

lean body weight

cancerstatus

0=no, 1=yes, 99=missing

brownfat

presence of brown fat (0=no, 1=yes)

bfmass

brown fat mass (g) (zero if brownfat=0)

Source

Determinants of the Presence and Volume of Brown Fat in Humans (2011), Statistical Society of Canada, https://ssc.ca/en/case-study/determinants-presence-and-volume-brown-fat-human, , Accessed 13 February 2019,

References

Ouellet, V., Routhier-Labadie, A., Bellemare, W., Lakhal-Chaieb, L., Turcotte, E., Carpentier, A.C. and Richard, D., (2011). Outdoor temperature, age, sex, body mass index, and diabetic status determine the prevalence, mass, and glucose-uptake activity of 18F-FDG-detected BAT in humans. The Journal of Clinical Endocrinology & Metabolism, 96(1), pp.192-199.

Examples

data(brownfat)

Description

US election data, at the state level, in the 2000 Presidential Election from Kieschnick and McCullough (2003).

Usage

data("bush2000")

Format

A data frame with 51 observations on the following 10 variables.

state

name of state a factor with levels 51 levels.

bush

proportion of state's vote for George Bush

male

percentage of population male

pop

population

rural

percentage of population living in rural areas

bpovl

percentage of population with income below the poverty level

clfu

unemployment rate (%)

mgt18

percentage of male population older than 18 years

pgt65

percentage of population older than 65 years

numgt75

percentage of population with income greater than 75K

Details

The US election data, at the state level, in the 2000 Presidential Election. The response variable is the proportion of the state that voted for George Bush; and the predictors are state demographic indicators.

Source

Kieschnick and McCullough (2003)

References

Kieschnick, R. and McCullough, B. D. (2003) Regression analysis of variates observed on (0, 1): percentages, proportions and fractions, Statistical Modelling, 3, Vol 3, pp 193-213, Sage Publications Sage CA: Thousand Oaks, CA.

Examples

data(bush2000)
plot(bush~bpovl, data=bush2000)

Description

The penetration of cable television in 283 market areas in the USA.

Usage

data("cable")

Format

A data frame with 283 observations on the following 6 variables.

pen5

proportion of households having cable TV in market area

lin

log median income

child

percentage of households with children

ltv

number of local TV stations

dis

consumer satisfaction index with values 0 and 1

agehe

age of cable TV headend

Details

The cable data set concerns the penetration of cable television in 283 market areas in the USA. The data were collected in a mailed survey questionnaire in 1992 Kieschnick and McCullough (2003). The aim of the study was to explain cable television uptake (the proportion pen5) as a function of area demographics.

Source

Kieschnick and McCullough (2003)

References

Kieschnick, R. and McCullough, B. D. (2003) Regression analysis of variates observed on (0, 1): percentages, proportions and fractions, Statistical Modelling, 3, Vol 3, pp 193-213, Sage Publications Sage CA: Thousand Oaks, CA.

Examples

data(cable)

Description

CD4: The data were given by Wade and Ades (1994) and refer to cd4 counts from uninfected children born to HIV-1 mothers and the age of the child.

Usage

data(CD4)

Format

Data frames each with the following variable.

cd4

a numeric vector showing the CD4 counts

age

the age of the child

Details

Data sets usefull for the GAMLSS booklet

References

Wade, A. M. and Ader, A. E. (1994) Age-related reference ranges : Significance tests for models and confidence intervals for centiles. Statistics in Medicine, 13, pages 2359-2367.

Examples

data(CD4)
with(CD4,plot(cd4~age))

Description

computing: The data relate to DEC-20 computers which operated at the Open University in the 1980. They give the number of computers that broke down in each of the 128 consecutive weeks of operation, starting in late 1983, see Hand et al. (1994) page 109 data set 141.

Usage

data(computer)

Format

Data frames each with the following variable.

failure

a numeric vector showing the number of times computers failed

Details

Data sets usefull for the GAMLSS booklet

References

Hand et al. (1994) A handbook of small data sets. Chapman and Hall, London.

Examples

data(computer)
with(computer, plot(table(failure)))

Description

The cysts data set is a univariate sample of 110 counts of kidney cysts in mice fetuses, Para and Jan (2016).

Usage

data("cysts")

Format

The cysts data frame has 12 observations on the following 2 variables.

y

the counts

f

the frequancy

Source

For systs Para and Jan (2016)

References

Para B. A. and Jan T. R. (2016). On discrete three parameter Burr type XII and discrete Lomax distributions and their applications to model count data from medical science. Biometrics and Biostatistics International Journal, Vol 4, pp 1-15.

Examples

data(cysts)
barplot(cysts$f, names.arg=cysts$y)

Description

The data are comming from the Fourth Dutch Growth Study, Fredriks et al. (2000a, 2000b), which is a cross-sectional study that measures growth and development of the Dutch population between the ages 0 and 21 years. The study measured, among other variables, height, weight, head circumference and age for 7482 males and 7018 females. Here we have the only the head circumference of Dutch boys.

Usage

data(db)

Format

A data frame with 7040 observations on the following 2 variables.

head

head circumference

age

age in years

Source

The data were kindly given by professor Stef. van Buuren.

References

Fredriks, A.M. van Buuren, S. Burgmeijer, R.J.F. Meulmeester, J.F. Beuker, R.J. Brugman, E. Roede, M.J. Verloove-Vanhorick, S.P. and Wit, J. M. (2000a), Continuing positive secular change in The Netherlands, 1955-1997, Pediatric Research, 47, 316–323

Fredriks, A.M. van Buuren, S. Wit, J.M. and Verloove-Vanhorick, S. P. (2000b) Body index measurments in 1996-7 compared with 1980, Archives of Childhood Diseases, 82, 107–112

van Buuren and Fredriks M. (2001) Worm plot: simple diagnostic device for modelling growth reference curves. Statistics in Medicine, 20, 1259–1277

Examples

data(db)
attach(db)
plot(age,head)
detach(db)

Description

The data are comming from the Fourth Dutch Growth Study, Fredriks et al. (2000a, 2000b), which is a cross-sectional study that measures growth and development of the Dutch population between the ages 0 and 21 years. The study measured, among other variables, height, weight, head circumference and age for 7482 males and 7018 females. Here we have the only the BMI of Dutch boys.

Usage

data(dbbmi)

Format

A data frame with 7294 observations on the following 2 variables.

age

a numeric vector

bmi

a numeric vector

Source

The data were kindly given by professor Stef. van Buuren.

References

Fredriks, A.M. van Buuren, S. Burgmeijer, R.J.F. Meulmeester, J.F. Beuker, R.J. Brugman, E. Roede, M.J. Verloove-Vanhorick, S.P. and Wit, J. M. (2000a), Continuing positive secular change in The Netherlands, 1955-1997, Pediatric Research, 47, 316–323

Fredriks, A.M. van Buuren, S. Wit, J.M. and Verloove-Vanhorick, S. P. (2000b) Body index measurments in 1996-7 compared with 1980, Archives of Childhood Diseases, 82, 107–112

van Buuren and Fredriks M. (2001) Worm plot: simple diagnostic device for modelling growth reference curves. Statistics in Medicine, 20, 1259–1277

Examples

data(dbbmi)
plot(bmi~age, data=dbbmi)

Description

The data are comming from the Fourth Dutch Growth Study, Fredriks et al. (2000a, 2000b), which is a cross-sectional study that measures growth and development of the Dutch population between the ages 0 and 21 years. The study measured, among other variables, height, weight, head circumference and age for 7482 males and 7018 females. Here we have the only the head circumference and height of Dutch boys.

Usage

data("dbhh")

Format

A data frame with 6885 observations on the following 3 variables.

head

head circumference

age

age in years

ht

height

Source

The data were kindly given by professor Stef. van Buuren.

References

Fredriks, A.M. van Buuren, S. Burgmeijer, R.J.F. Meulmeester, J.F. Beuker, R.J. Brugman, E. Roede, M.J. Verloove-Vanhorick, S.P. and Wit, J. M. (2000a), Continuing positive secular change in The Netherlands, 1955-1997, Pediatric Research, 47, 316–323

Fredriks, A.M. van Buuren, S. Wit, J.M. and Verloove-Vanhorick, S. P. (2000b) Body index measurments in 1996-7 compared with 1980, Archives of Childhood Diseases, 82, 107–112

van Buuren and Fredriks M. (2001) Worm plot: simple diagnostic device for modelling growth reference curves. Statistics in Medicine, 20, 1259–1277

Examples

data(dbhh)
plot(dbhh$age, dbhh$head)
plot(dbhh$age, dbhh$ht)

Description

The purpose of this data is to estimate the importance of labor, capital and useful energy in explaining economic growth (quantified by the GDP) of the EU 15 from 1960 to 2009. The response variable is the GDP while the indepedent variables are the labor, capital and useful energy. The EU 15 includes Austria, Belgium, Benmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembrourg, Netherlands, Portugal, Spain, Sweden and UK. The data was analysed by Voudouris et al.[2015].

Usage

data("eu15")

Format

A data frame with 50 observations on the following 5 variables.

Year

the year from 1960 to 2009

UsefulEnergy

the total amount of useful energy (energy that performs some short of work) for the EU 15 countries

GDP

the sum of the GDP of the EU 15 countries

Labor

the sum of total hours worked of the EU 15 countries.

Capital

the sum of the net capital stock of the EU 15 countries.

Source

Voudouris, V. Ayres, R. Serrenho, A. C. and Kiose, D. (2015) The economic growth enigma revisited: The EU-15 since the 1970s. Energy Policy.

Examples

data(eu15)

Description

The data are 32 observations on faults in rolls of fabric

Usage

data(fabric)

Format

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

leng

the length of the roll : a numeric vector

y

the number of faults in the roll of fabric : a discrete vector

x

the log of the length of the roll : a numeric vector

Details

The data are 32 observations on faults in rolls of fabric taken from Hinde (1982) who used the EM algorithm to fit a Poisson-normal model. The response variable is the number of faults in the roll of fabric and the explanatory variable is the log of the length of the roll.

Source

John Hinde

References

Hinde, J. (1982) Compound Poisson regression models: in GLIM 82, Proceedings of the International Conference on Generalized Linear Models, ed. Gilchrist, R., 109–121, Springer: New York.

Examples

data(fabric)
attach(fabric)
plot(x,y)
detach(fabric)

Description

Moro at al. (2016) present a study on the performance of Facebook posts, with the aim of prediction of a post's performance, or impact, on the basis of its characteristics. The metrics used for post performance (the output) were the number of likes, shares or comments on the post, as well as a number of metrics used by Facebook. All posts on the page of a particular cosmetic brand in 2014 were analyzed (n=495).

Usage

data("fbdata")

Format

A data frame with 495 observations on the following 7 variables.

share

a numeric vector

Type

Type of content a factor with levels Link Photo/Video Status

Category

Content categorization a factor with levels 1 2 3

Post.Month

Month posted, a numeric vector, 1=January,...,12=December

Post.Weekday

Day posted a numeric vector 1=Sunday, ..., 7= Suturday

Post.Hour

Hour posted a numeric vector (0,...,24)

Paid

Paid andertisment a factor with levels 0=no 1=yes

Details

See Stasinopoulos et.al. (2024) for more details.

References

Moro, S., Rita, P. and Vala, B., 2016. Predicting social media performance metrics and evaluation of the impact on brand building: A data mining approach. Journal of Business Research, 69(9), pp.3341-3351.

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in https://www.gamlss.com/.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, https://www.jstatsoft.org/v23/i07/.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Stasinopoulos, M.D., Kneib, T., Klein, N., Mayr, A. and Heller, G.Z., (2024). Generalized Additive Models for Location, Scale and Shape: A Distributional Regression Approach, with Applications (Vol. 56). Cambridge University Press.

(see also https://www.gamlss.com/).

Examples

data(fbdata)
str(fbdata)

Description

Data from film revenues from the 1930s'.

Usage

data(film30)

Format

A data frame with 969 observations on the following 3 variables.

film

a factor with the name of the film

total

a numeric vector

opening

a numeric vector

Source

The data were collected by Prof. John Sedgwick

References

Gilchrist, R., Rigby, R., Sedgwick, J., Stasinopoulos, S., Voudouris, V. (2011) Forecasting film revenues using GAMLSS, in Proceedings of the 26th International Workshop on Statistical Modeling ed: Conesa, D., Forte, A., Lopez-Quilez, A., Munoz, F., 263-268, Valencia, Spain.

Voudouris V., Gilchrist R., Rigby R., Sedgwick J. and Stasinopoulos D. (2011) Modelling skewness and kurtosis with the BCPE density in GAMLSS. Journal of Applied Statistics

Examples

data(film30)
## maybe str(film30) ; plot(film30) ...

Description

Data from film revenues from the 1990s'.

Usage

data(film90)

Format

A data frame with 4031 observations on the following 4 variables.

lnosc

the log of the number of screens

lboopen

the log of box office opening revenues

lborev1

the log of box office revenues after the first week

dist

a factor indicating whether Independent or Major distributor

Details

Those data are data analysed in Voudouris et. al. (2011) suitably anonymised.

Source

Data collected by Prof. John Sedgwick

References

Gilchrist, R., Rigby, R., Sedgwick, J., Stasinopoulos, S., Voudouris, V. (2011) Forecasting film revenues using GAMLSS, in Proceedings of the 26th International Workshop on Statistical Modeling ed: Conesa, D., Forte, A., Lopez-Quilez, A., Munoz, F., 263-268, Valencia, Spain.

Voudouris V., Gilchrist R., Rigby R., Sedgwick J. and Stasinopoulos D. (2011) Modelling skewness and kurtosis with the BCPE density in GAMLSS. Journal of Applied Statistics

Examples

data(film90)

Description

glass: show the strength of glass fibres, measured at the National Physical Laboratory, England, see Smith and Naylor (1987), (the unit of measurement were not given in the paper).

Usage

data(glass)

Format

Data frames each with the following variable.

strength

a numeric vector showing the strength of glass fibres

Details

Data sets usefull for the GAMLSS booklet

References

Smith R. L. Naylor, J. C. (1987) A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distributuion. Appl. Statist. 36, 358-369

Examples

data(glass)
with(glass, hist(strength))

Description

The Blue Mountains Eye Study.

Usage

data("glasses")

Format

A data frame with 1016 observations on the following 3 variables.

age

The age of the participants in the Blue Mountains Eye Study

sex

the gender of the participants, a factor with levels 1=‘male’ 2=‘female’.

ageread

the age in which reading glasses were required.

References

Attebo, Karin, Paul Mitchell, and Wayne Smith (1996). "Visual acuity and the causes of visual loss in Australia: the Blue Mountains Eye Study." Ophthalmology 103.3:pp 357-364.

Examples

data(glasses)
plot(ageread~sex, data=glasses)

Description

The data is a subset (only boys) from the data analysyed by Cohen et al. (2010).

Usage

data("grip")

Format

A data frame with 3766 observations on the following 2 variables.

age

the age of the participant

grip

the handgrip strength

Details

Cohen et al. (2010) analysed the of hand grip (HG) strength in relation to gender and age in English schoolchildren. Here there are 3766 observations of the boys.

References

Cohen, D.D.,Voss, C., Taylor, M.J.D., Stasinopoulos, D.M., Delextrat, A. and Sandercock, G.R.H. (2010) Handgrip strength in English schoolchildren, Acta Paediatrica, 99, 1065-1072.

Examples

data(grip)

Description

There two data sets contain data used in Hodges (1998). In addition to the data used in that manuscript, it contains other data items.

The original data consists of two matrices of dimensions of 341x6 and a 45x4 respectively.

The first matrix hodges describes plans. The information for each plan is: the state, a two-character code that identifies plans within state, the total premium for an individual, the total premium for a family, the total enrollment of federal employees as individuals, and the total enrollment of federal employees as families.

The second matrix, hodges, describes states. The information for each state is: its two-letter abbreviation, the state average expenses per admission (from American Medical Association 1991 Annual Survey of Hospitals), population (1990 Census), and the region (from the Marion Merrill Dow Managed Care Digest 1991).

The Hodges manuscript used these variables: Plan level: individual premium, individual enrollment. State level: expenses per admission, region.

Usage

data(hodges)

Format

Two data frames the first with 341 observations on the following 6 variables.

state

a factor with 45 levels AL AZ CA CO CT DC DE FL GA GU HI IA ID IL IN KS KY LA MA MD ME MI MN MO NC ND NE NH NJ NM NV NY OH OK OR PA PR RI SC TN TX UT VA WA WI

plan

a two-character code that identifies plans within state declared here as factor with 325 levals.

prind

a numeric vector showing the total premium for an individual

prfam

a numeric vector showing the total premium for a family

enind

a numeric vector showing the total enrollment of federal employees as individuals

enfam

a numeric vector showing the total enrollment of federal employees as families.

and the second with 45 observations on the following 4 variables

State

a factor with levels same as state above

expe

a numeric vector showing the state average expenses per admission (from American Medical Association 1991 Annual Survey of Hospitals)

pop

a numeric vector shoing the population (1990 Census)

region

the region (from the Marion Merrill Dow Managed Care Digest 1991), a factor with levels MA MT NC NE PA SA SC

Source

http://www.biostat.umn.edu/~hodges/

References

Hodges, J. S. (1998). Some algebra and geometry for hierarchical models, applied to diadnostics. J. R. Statist. Soc. B., 60 pp 497:536.

Examples

data(hodges)
attach(hodges)
plot(prind~state, cex=1, cex.lab=1.5, cex.axis=1, cex.main=1.2)
str(hodges)
data(hodges1)
str(hodges1)

Description

The following data set is not real data set but it is created for the purpose of demonstrating a binomial type response variable. The data set is based on some real data obtained from the Parana State in Brazil in 2010.

Usage

data("InfMort")

Format

A data frame with 399 observations on the following 11 variables.

x

the x-coordinate

y

the y-coordinate

dead

the number of dead infants

bornalive

the number of infants born alive

IFDM

FIRJAN index of city development

illit

the illiteracy index

lGDP

the logarithm of the gross national product

cli

the proportion of children living in a household with half the basic salary

lpop

the logarithm of the number of people living in each city

PSF

the proportion covered by the family health program

poor

the proportion of individuals low household income per capita

Details

There is geographical information given by the x and y coordidates and also several social-economics variables.

References

Rigby, R. A. and Stasinopoulos D. M.(2005). Generalized additive models for location, scale and shape, (with discussion),Appl. Statist., 54, part 3, pp 507-554.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in https://www.gamlss.com/.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, doi:10.18637/jss.v023.i07.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

(see also https://www.gamlss.com/).

Examples

data(InfMort)

Description

The data set, kinkly provided to us by Dr Maria Durban, is based on a study conducted at Harvard University with girls afected by Acute lymphoblastic leukaemia. The obesity and short stature are common effcts on teens who have or have had the disease, and the treatments applied trying to minimize this type of side effects without compromising its effctiveness. In one of the clinical trials conducted, 618 children were studied between the years 1987 and 1995 and three diffrent treatments were applied: intracranial therapy without radiation, conventional intracranial radiation therapy and intracranial radiation therapy twice a day. Approximately every 6 months the children height was measured. For children the height increases smoothly along the years. In this example, (the data have been changed for confidentiality) 197 girls diagnosed with Acute lymphoblastic leukaemia between 2 and 9 years old are measured. The height of the children was measured at different times and in total 1988 observations were collected. The number of observations per child varies between 1 and 21.

Usage

data("Leukemia")

Format

A data frame with 1988 observations on the following 4 variables.

case

a factor with levels 1 to 197 indicating the participant

treatment

a factor with levels 1 2 3

height

the height of the participants

age

the age of the participants

Source

Dr Maria Durban

References

Durban M. (2016) Splines con Penalizaciones: Teoria y aplicaciones, https://halweb.uc3m.es/esp/Personal/personas/durban/esp/web/cursos/Psplines/Psplines.html

Examples

data(Leukemia)

Description

LGAclaims: the data were given by Gillian Heller and can be found in de Jong and Heller (2007). This data set records the number of third party claims, Claims, in a twelve month period between 1984-1986 in each of 176 geographical areas (local government areas) in New South Wales, Australia. Areas are grouped into thirteen statistical divisions (SD). Other recorded variables are the number of accidents, Accidents, the number of people killed or injured and population with all variables classified according to area.

Usage

data(LGAclaims)

Format

Data frames each with the following variable.

Claims

the number of third party claims

LGA

Local government areas in New South Wales

SD

statistical divisions

Pop_density

population density

KI

the number of people killed or injured

Accidents

the number of accidents

Population

population size

L_KI

log of KI

L_Accidents

the log of the number of accidents

L_Population

log Population

Details

Data sets usefull for the GAMLSS booklet

References

de Jong, P. and Heller G. (2007) Generalized Linear Models for Insurance Data , Cambridge University Press

Examples

data(LGAclaims)
with(LGAclaims, plot(data.frame(Claims, Pop_density, KI, Accidents, Population)))

Description

lice : The data come from Williams (1944) (also used by Stein and Juritz (1988).) and they are lice per head of Hindu male prisoners in Cannamore, South India, 1937-1939.

Usage

data(lice)

Format

Data frames each with the following variable.

head

a numeric vector showing the number lice per head of Hindu male prisoners in Cannamore, South India, 1937-1939.

freq

a numeric vector showing the frequency of lice per head

Details

Data sets usefull for the GAMLSS booklet

References

Stein, G. Z. and Juritz, J. M. (1988). Linear models with an inverse Gaussian-Poisson error distribution. Communications in Statistics- Theory and Methods, 17, 557-571.

Examples

data(lice)

Description

3164 male observations of lung function data previously analysed by Stanojevic et al. 2008 and Hossain et al. 2016.

Usage

data("lungFunction")

Format

A data frame with 3164 observations on the following 3 variables.

slf

the spirometric lung function, FEV_1 / FVC, which is an established index for diagnosing airway obstruction (males only)

height

the height in centimetres

age

the age

Details

The response variable is slf=FEV_1/FVC and the explanatory variable is height. The response variable slf is a ratio of forced expiratory volume in 1 second, FEV_1, to forced vital capacity, FVC. Spirometric lung function slf is an established index for diagnosing airway obstruction, e.g. Quanjer et al. 2010. The purpose here is to create centile curves of slf against height. More details about the analysis using GAMLSS of the FEV_1/FVC data can be found in Hossain et al. 2016.

Source

The data were kindly provided by Dr Sanja Stanojevic.

References

Hossain, A., Rigby, R.A., Stasinopoulos, D.M. and Enea, M. (2016), Centile estimation for a proportion response variable, Statistics in Medicine, 6, Vol. 35, pp 895-904,

Quanjer, P.H., Stanojevic, S. and Stocks, J. and Hall, G.L. and Prasad, K.V.V. and Cole, T.J. and Rosenthal, M. and Perez-Padilla, R. and Hankinson, J.L. and Falaschetti, E. and others, (2010) Changes in the FEV1 /FVC ratio during childhood and adolescence: an intercontinental study, European Respiratory Journal, 6, Vol 36, page 1391, European Respiratory Society.

Stanojevic, S., Wade, A., Stocks, J., Hankinson, J., Coates, A. L., Pan, H., Rosenthal, M., Corey, M., Lebecque, P., and Cole, T. J. (2008), Reference ranges for spirometry across all ages: a new approach, American Journal of Respiratory and Critical Care Medicine, Vol 177, pp. 253-260.

Examples

data(lungFunction)
plot(lungFunction)

Description

margolin: Margolin et al. (1981) present data from an Ames Salmonella assay, where y is the number of revertant colonies observed on a plate given a dose y of quinoline. The data were subsequently analysed by Breslow (1984), Lawless (1987) and Saha and Paul (2005).

Usage

data(margolin)

Format

Data frames each with the following variable.

y

a numeric vector showing the number of revertant colonies observed on a plate given a dose x of quinoline.

x

a numeric vector showing a a dose x of quinoline.

Details

Data sets usefull for the GAMLSS booklet

References

Breslow, N. (1984) Extra-Poisson variation in log-linear models. Applied Statistics, 33, 38-44.

Hand et al. (1994) A handbook of small data sets. Chapman and Hall, London.

Lawless, J.F. (1987) Negative binomial and mixed Poisson regression. The Canadian Journal of Statistics, 15, 209-225.

Margolin, B.H., Kaplan, N. and Zeiger, E. (1981) Statistical analysis of the Ames salmonella/microsome test. Proceedings of the National Academy of Science, U.S.A., 76, 3779-3783.

Saha, K. and Paul, S. (2005) Bias-Corrected Maximum Likelihood Estimator of the Negative Binomial Dispersion Parameter. Biometrics, 61, 179-185

Examples

data(margolin)
with(margolin, plot(y~x))

Description

The data here are coming from a statistical meta analysis problem. In meta analysis we combine the evidence from different studies to obtain an overall treatment effect. The data from Silagy et al. (2003) consist of different clinical trials of nicotine replacement therapy for smoking cessation. In each trial the patient was randomized into a treatment or control group. The treatment group were given a nicotine gum. In the majority of studies the control group receive the same appearance gum but without the ingredients but in some they were given no gum. The outcome, whether the participant is smoking or not, was observed after six months. The data were previously analysed by Aitkin (1999) and by Skrondal and Rabe-Hesketh (2004).

Usage

data("meta")

Format

A data frame with 54 observations on the following 6 variables.

studyname

a factor the name of the place of the different studies (note that the values of studyname is the same for studies at the same place in different years)

year

the year of the study

d

the number of quitters (non-smokers) after six months

n

the total number of participants in the study

fac

a factor with two levels indicating whether control, 1 or treatment 2

study

a factor with levels from 1 to 27 indicating the different studies (that is, the interaction of studyname and year

References

Aitkin. M. Meta-analysis by random effect modelling in generalised linear models. Statistics in Medicine, 18, 2343-2351, 1999

Skrondal A. and Rabe-Hesketh S. Generalized Latent Variable modelling. Chapman & Hall, (2004).

Examples

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

Description

Mothers encouragement for participation in Higher Education. The response variable is mums a three level factor which can be used in a multinomial Logistic model or mumsB a two level factor suitable for binary logistic model.

Usage

data(Mums)

Format

A data frame with 871 observations on the following 7 variables.

mums

mothers encouragement: factor with levels 1 is for strong encouragement, 2 is for some encouragement and 3 for no encouragement/discouragement

class

social class: a factor with levels 1is C1, 2 is C2, 3 is D and 4 is E

age

age of the participants: a factor with levels 1 is 16-18, 2 is 19-20 and 3 is 20-30

gender

a factor with levels 1 is male and 2 is female

ethn

ethnicity of the participants: a factor with levels 1 is white, 2 is black, 3 is asian and 4 is other

qual

qualifications of the participants: a factor with levels, 1 is greater or equal to 2 A levels, 2 is HND or more than 5 GCSE's, 3 is less than 5 GSCSE's ar none above and 4 no formal qualification

mumsb

mothers encouragement: a factor with levels, 0 is no encouragement or some encouragement 1 is for strong encouragement

Details

The data were collected as part of the Social Class and widening Participation in Higher Education Project based at the University of North London (now London Metropolitan University) and supported by the University's Development and Diversity Fund over the period 1998-2000.

Source

Professor Robert Gilchrist director of STORM at London Metropolitan

References

Collier T., Gilchrist R. and Phillips D. (2003), Who Plans to Go to University? Statistical Modelling of potential Working-Class Participants, Education Research and Evaluation, Vol 9, No 3, pp 239-263.

Examples

data(Mums)
MM<-xtabs(~mums+qual, data=Mums)
mosaicplot(MM, color=TRUE)
MM<-xtabs(~mums+ethn+gender, data=Mums)
mosaicplot(MM, color=TRUE)

Description

The motor vehicle insurance data are motor vehicle insurance policies. mvi is a sample of 2000 observations from mviBig which has 67143 observartions

Usage

data(mvi)
data(mviBig)

Format

Two data frames with 2000 or 67143 observations on the following 14 variables.

retval

a numeric vector showing the value of the vehicle

whetherclm

a numeric vector showing whether a claim is made, 0 no claim, 1 at least one claim

numclaims

a nuneric vactor showing the number of claims

claimcst0

a numeric vector showing the total amount of claim, i.e. for numclaims=0 is zero.

vehmake

a factor showing the make of the car with levels BMW DAEWOO FORD MITSUBISHI

vehbody

a factor showing the type of the cat, with levels BUS CONT COUPE HACK HDTOP HRSE MCARA MIBUS PANVN RDSTR SEDAN STNWG TRUCK UTE

vehage

a numeric vector showing the age of the car

gender

a factor showing the gender of the policy holder with levels F M

area

a factor showing the Area of residence of the policy holder with levels A B C D E F

agecat

a factor showing the age band of the policy holder with levels 1 2 3 4 5 6 one is youngest

exposure

a numeric vector showing the time of exposure with values from zero to one

Details

The motor vehicle insurance data are motor vehicle insurance policies from an insurance company over a twelve-month period in 2004-05. The original data are 67143 observation but here we also include a random sample of 2000.

References

Heller, G. Stasinopoulos M and Rigby R.A. (2006) The zero-adjusted Inverse Gaussian distribution as a model for insurance claims. in Proceedings of the 21th International Workshop on Statistial Modelling, eds J. Hinde, J. Einbeck and J. Newell, pp 226-233, Galway, Ireland.

Heller G. Z., Stasinopoulos M.D., Rigby R. A. and de Jong P. (2007) Mean and dispersion modeling for policy claims costs. To be published in the Scandinavian Actuarial Journal.

Examples

data(mvi)
## a histogram of claims with fitted gamma disteibution
## library(gamlss)
## with(mvi, histDist(claimcst0[whetherclm==1&claimcst0<15000], family=GA, main="Claims"))

Description

The Oil data: Using model selection to discover what affects the price of oil. The data s contains the daily prices of front month WTI (West Texas Intermediate) oil price traded by NYMEX (New York Mercantile Exchange). The front month WTI oil price is a futures contract with the shortest duration that could be purchased in the NYMEX market. The idea is to use other financially traded products (e.g., gold price) to discover what might affect the daily dynamics of the price of oil.

Usage

data("oil")

Format

A data frame with 1000 observations on the following 25 variables.

OILPRICE

the log price of front month WTI oil contract traded by NYMEX - in financial terms, this is the CL1. This is the response variable.

CL2_log, CL3_log, CL4_log, CL5_log, CL6_log, CL7_logCL8_log, CL9_log, CL10_log, CL11_log, CL12_log, CL13_log, CL14_log, CL15_log

numeric vectors which are the log prices of the 2 to 15 months ahead WTI oil contracts traded by NYMEX. For example, for the trading day of 2nd June 2016, the CL2 is the WTI oil contract for delivery in August 2016.

BDIY_log

the Baltic Dry Index, which is an assessment of the price of moving the major raw materials by sea.

SPX_log

the S&P 500 index

DX1_log

the US Dollar Index.

GC1_log

he log price of front month gold price contract traded by NYMEX

HO1_log

the log price of front month heating oil contract traded by NYMEX

USCI_log

the United States Commodity Index

GNR_log

the S&P Global Natural Resources Index

SHCOMP_log

the Shanghai Stock Exchange Composite Index.

FTSE_log

the FTSE 100 Index

respLAG

the lag 1 of OILPRICE - lagged version of the response variable.

Source

The dataset was downloaaded from https://data.nasdaq.com/.

Examples

data(oil)
plot(OILPRICE~SPX_log, data=oil)

Description

Parzen: Parzen (1979) and also contained in Hand et al. (1994), data set 278. The data give the annual snowfall in Buffalo, NY (inches) for the 63 years, from 1910 to 1972 inclusive.

Usage

data(parzen)

Format

Data frames each with the following variable.

snowfall

the annual snowfall in Buffalo, NY (inches) for the 63 years, from 1910 to 1972 inclusive, 63 observations

Details

Data sets usefull for the GAMLSS booklet

References

Hand et al. (1994) A handbook of small data sets. Chapman and Hall, London.

Parzen E. (1984) Nonparamemetric statistical daya modelling. JASA, 74, 105-131.

Examples

data(parzen)
with(parzen, hist(snowfall))

Description

A cross-sectional study to investigate the relationship between personal characteristics and dietary factors, and plasma concentrations.

Usage

data("plasma")

Format

A data frame with 315 observations on the following 14 variables.

age

age (years)

sex

sex, 1=male, 2=female

smokstat

smoking status 1=never, 2=former, 3=current Smoker

bmi

body mass index weight/(height^2)

vituse

vitamin use 1=yes, fairly often, 2=yes, not often, 3=no

calories

number of calories consumed per day

fat

grams of fat consumed per day

fiber

grams of fiber consumed per day

alcohol

number of alcoholic drinks consumed per week

cholesterol

cholesterol consumed (mg per day)

betadiet

dietary beta-carotene consumed (mcg per day)

retdiet

dietary retinol consumed (mcg per day)

betaplasma

plasma beta-carotene (ng/ml)

retplasma

plasma retinol (ng/ml)

Details

“Observational studies have suggested that low dietary intake or low plasma concentrations of retinol, beta-carotene, or other carotenoids might be associated with increased risk of developing certain types of cancer \ ... We designed a cross-sectional study to investigate the relationship between personal characteristics and dietary factors, and plasma concentrations of retinol, beta-carotene and other carotenoids." Harrell (2002)

Source

Harrell (2002)

References

Harrell, F. E. (2002), Plasma Retinol and Beta-Carotene Dataset, https://hbiostat.org/data/repo/plasma.html

Examples

data(plasma)

Description

Poliomyelitis cases reported to the U.S. Centers for Disease Control for the years 1970 to 1983, that is, 168 observations.

Usage

data(polio)

Format

The format is: Time-Series [1:168] from 1970 to 1984: 0 1 0 0 1 3 9 2 3 5 ...

Details

The data were originally modelled by Zeger (1988) who used a parameter driven approach, in which a first order autoregressive model was used for the latent process, to conclude that there is evidence of a decrease in the polio infection rate. The data were analysed also by Li (1994), Zeger and Qaqish (1988), Davis et al. (1999), and by Benjamin et al (2003).

Source

Zeger (1988) w

References

Benjamin M. A., Rigby R. A. and Stasinopoulos D.M. (2003) Generalised Autoregressive Moving Average Models. J. Am. Statist. Ass., 98, 214-223.

Davis, R. A., Dunsmuir, W. T. M. and Wang, Y. (1999), “Modelling Time Series of Count Data,” in Asymptotics, Nonparametrics and Time Series (ed Subir Ghosh): Marcel Dekker

Zeger, S. L. (1988), “A Regression Model for Time Series of Counts,” Biometrika, 75, 822-835.

Zeger, S. L. and Qaqish, B. (1988), “Markov Regression Models for Time Series: A Quasi-likelihood Approach,” Biometrics, 44, 1019-1032.

Examples

data(polio)
plot(polio)

Description

A survey was conducted in April 1993 by Infratest Sozialforschung. A random sample of accommodation with new tenancy agreements or increases of rents within the last four years in Munich was selected including: i) single rooms, ii) small apartments, iii) flats, iv) two-family houses. Accommodation subject to price control rents, one family houses and special houses, such as penthouses, were excluded because they are rather different from the rest and are considered a separate market. For the purpose of this study, 1967 observations of the variables listed below were used, i.e. the rent response variable R followed by the explanatory variables found to be appropriate for a regression analysis approach by Fahrmeir et al. (1994, 1995):

Usage

data(rent)

Format

A data frame with 1969 observations on the following 9 variables.

R

: rent response variable, the monthly net rent in DM, i.e. the monthly rent minus calculated or estimated utility cost

Fl

: floor space in square meters

A

: year of construction

Sp

: a variable indicating whether the location is above average, 1, (550 observations) or not, 0, (1419 observations)

Sm

: a variable indicating whether the location is below, 1, average (172 obs.) or not, 0, (1797 obs.)

B

: a factor with levels indicating whether there is a bathroom, 1, (1925 obs.) or not, 0, (44 obs.)

H

: a factor with levels indicating whether there is central heating, 1, (1580 obs.) or not, 0, (389 obs.)

L

: a factor with levels indicating whether the kitchen equipment is above average, 1, (161 obs.) or not, 0, (1808 obs.)

loc

: a factor (combination of Sp and Sm) indicating whether the location is below, 1, average, 2, or above average 3

Details

This set of data were used by Stasinopoulos et al. (2000) to fit a model where both the mean and the dispersion parameter of a Gamma distribution were modelled using the explanatory variables.

Source

Provide by Prof. L. Fahrmeir

References

Fahrmeir L., Gieger C., Mathes H. and Schneeweiss H. (1994) Gutachten zur Erstellung des Mietspiegels fur Munchen 1994, Teil B: Statistiche Analyse der Nettomieten. Hrsg: Landeshaupttstadt Munchen, Sozialreferat-Amt fur Wohnungswesen.

Fahrmeir L., Gieger C., and Klinger, A. (1995) Additive, dynamic and multiplicative regression. In Applied Statistics: Recent Developments, Vandenhoeck and Ruprecht, Gottingen.

Stasinopoulos, D. M., Rigby, R. A. and Fahrmeir, L., (2000), Modelling rental guide data using mean and dispersion additive models, Statistician, 49 , 479-493.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, doi:10.18637/jss.v023.i07.

Examples

data(rent)
attach(rent)
plot(Fl,R)

Description

The Munich rent data and boundaries files of of 1999 survey.

Usage

data(rent99)

Format

A data frame with 3082 observations on the following 9 variables.

rent

the monthly net rent per month (in Euro).

rentsqm

the net rent per month per square meter (in Euro).

area

Living area in square meters.

yearc

year of construction.

location

quality of location: a factor indicating whether the location is average location, 1, good location, 2, and top location, 3.

bath

quality of bathroom: a a factor indicating whether the bath facilities are standard, 0, or premium, 1.

kitchen

Quality of kitchen: 0 standard 1 premium.

cheating

central heating: a factor 0 without central heating, 1 with central heating.

district

District in Munich.

Details

See Fahrmeir et. al., (2013) page 5, for more details about the data.

Source

Thanks to Thomas Kneib who provide us with the data.

References

Fahrmeir, Ludwig and Kneib, Thomas and Lang, Stefan and Marx, Brian (2013) Regression: models, methods and applications, Springer.

Examples

data(rent99)
plot(rent~area, data=rent99)

Description

The boundaries files of of 1999 Munich survey.

Usage

data(rent99.polys)

Format

This data frame contains the boundaries of the Munich data.

Details

See Fahrmeir et. al., (2013) page 5, for more details about the data.

Source

Thanks to Thomas Kneib who provide us with the data.

References

Fahrmeir, Ludwig and Kneib, Thomas and Lang, Stefan and Marx, Brian (2013) Regression: models, methods and applications, Springer.

Examples

data(rent99.polys)
## library(gamlss.spatial); draw.polys(rent99.polys)

Description

This is cohort study of 275 Indonesian preschool children, ($J=1,2, ...,275$), examined on up to six, consecutive quarters for the presence of respiratory infection. Sommer et al. (1983) describe the study, while Zeger and Karim (1991) and Diggle et al (2002) among others analyzed it. The data were also analyzed by Skrondal and Rabe-Hesketh (2004).

Usage

data("respInf")

Format

A data frame with 1200 observations on the following 14 variables.

id

a factor with 275 levels identifying the individual children

time

the binary response variable identifying the presence of respiratory infection

resp

a vector of ones (not used further)

age

the age in months (centered around 36)

xero

a factor variable for the present of xerophthalmia with levels 0 1

cosine

a cosine term of the annual cycle

sine

a sin term of the annual cycle

female

a gender factor with levels 0 is male 1 is female

height

height for age as percent of the National Center for health Statistics standard centered at 90%

stunted

a factor whether below 85% in height for age 0 1

time.1

the time that the children has been examine, 1 to 6

age1

he age of the child at the fist time of examination

season

a variable taking the values 1,2,3,4 indicating the season

time2

the time in months

References

Diggle, P. J., Heagerty, P., Liang, K. Y. and Zeger S. L.Analysis of Longitudinal Data, 2nd ed. Oxford University Press, Oxford, 2002.

Sommer, Alfred, et al. Increased mortality in children with mild vitamin A deficiency. The Lancet 322 83:50 (1983): 585-588.

Skrondal A. and Rabe-Hesketh S. Genaralized Latent Variable modelling. Chapman & Hall, (2004).

Zeger S. L and Karim M. R. Generalized linear models with random effects: a gibbs sampling approach. J. Am. Statist. Ass., 86, 79-95, 1991.

Examples

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

Description

Data from a study conducted on 133 patients thought to have the condition Obstructive Sleep Apnea (OSA). These patients have undergone a sleep study at a Canadian sleep clinic Ahmadi at al. (2008). While the focus on the study was the relationship between the Berlin Questionnaire for sleep apnea to polysomnographic measurements of respiratory disturbance, in particular the arousal index, we will analyse the proportion of sleep time that is REM sleep (REM). This variable is in the interval [0,1), so necessitates the use of zero-inflated models. We have removed patients with missing values, giving n=106 observations.

Usage

data("sleep")

Format

A data frame with 106 observations on the following 9 variables.

age

age in years

gender

1=female, 0=male

BMI

body mass index

necksize

neck circumference (cm)

sbp

systolic blood pressure (mmHg)

alcohol

alcohol usage (1=yes, 0=no)

caffeine

caffeine usage (1=yes, 0=no)

REM

proportion of rapid eye movement (REM) sleep time

AI

arousal index (number of arousals from sleep per hour of sleep

Source

see references

References

Ahmadi, N., Chung, S. A., Gibbs, A., and Shapiro, C. M. (2008), The Berlin questionnaire for sleep apnea in a sleep clinic population: relationship to polysomnographic measurement of respiratory disturbance. Sleep and Breathing, Vol. 12, pp 39-45.

Examples

data(sleep)

Description

species: The number of different fish species (y=fish) was recorded for 70 lakes of the world together with explanatory variable x=log(lake) area. The data are given and analyzed by Stein and Juritz (1988).

Usage

data(species)

Format

Data frames each with the following variable.

fish

a numeric vector showing the number of different species in 70 lakes in the word

lake

a numeric vector showing the lake area

Details

Data sets usefull for the GAMLSS booklet

References

Stein, G. Z. and Juritz, J. M. (1988). Linear models with an inverse Gaussian-Poisson error distribution. Communications in Statistics- Theory and Methods, 17, 557-571.

Examples

data(species)
with(species, plot(fish~log(lake)))

Description

Speech intelligibility tests are conducted on hearing-impaired people, for the purpose of evaluating the performance of hearing devices under controlled listening conditions in a sound laboratory. The simplest version is that the subject listens to a pre-recorded word, mixed with noise, and repeats it back. Here the stimulus is the signal-to-noise ratio (SNR) and the subject's response is either correct or incorrect. More common usage is for the subject to listen to a short sentence (of length N words) and repeat it back. The number of correctly identified words w is recorded and the proportion correct (y=w/N) is the response of interest. Typically data are collected in tracks of 20 sentences each, in which experimental conditions are the same but the SNR is varied over its range. Using the sentence as the unit of observation, an obvious model for the proportion correct is the binomial distribution; however, the assumption of independent recognition of words in a sentence is unlikely to be satisfied.

Usage

data("speech")

Format

A data frame with 6720 observations on the following 8 variables.

N

Number of words in a sentence

w

Number of words correctly identified

y

proportion correct (w/N)

snr

Signal to noise ratio

algorithm

Sound processing algorithm a factor with levels ("A", "B", "C")

noise_dir

noise direction, a factor with levels ("F" = front, "S" =side)

noise_gender

noice gender a factor with levels ("M","F")

subject

subject identifier a factor

Details

The data were analysed in Stasinopoulos at al. (2024 )

Source

See for more detailts Chapter 9 of Stasinopoulos at al. (2024)

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in https://www.gamlss.com/.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, https://www.jstatsoft.org/v23/i07/.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Stasinopoulos, M.D., Kneib, T., Klein, N., Mayr, A. and Heller, G.Z., (2024). Generalized Additive Models for Location, Scale and Shape: A Distributional Regression Approach, with Applications (Vol. 56). Cambridge University Press.

(see also https://www.gamlss.com/).

Examples

data(speech)
str(speech)

Description

stylo : the data were given by Dr Mario Corina-Borja, see Chappas and Corina-Borja (2006), and has the number of a word appearing in a text.

Usage

data(stylo)

Format

Data frames each with the following variable.

word

a numeric vector showing the number a word appearing in a text

freq

a numeric vector showing the frequency of the number a word appearing in a text

Details

Data sets usefull for the GAMLSS booklet

References

Chappas C. and Corina-Borja M. A Stylometric analysis of newspapers periodical and news scriprs, Journal of Quantitative Linguistics, 13, 285-312

Examples

data(stylo)
plot(freq~word, type="h", data=stylo)

Description

tensile: These data come from Quesenberry and Hales (1980) and were also reproduced in Hand et al. (1994), data set 180, page 140. They contain measurements of tensile strength of polyester fibres and the authors were trying to check if they were consistent with the lognormal distribution. According to Hand et al. (1994) "these data follow from a preliminary transformation. If the lognormal hypothesis is correct, these data should have been uniformly distributed".

Usage

data(tensile)

Format

Data frames each with the following variable.

str

a numeric vector showing the tensile strength

Details

Data sets usefull for the GAMLSS booklet

References

Hand et al. (1994) A handbook of small data sets. Chapman and Hall, London.

Quesenberry, C. and Hales, C. (1980). Concentration bands for uniformily plots. Journal of Statistical Computation and Simulation, 11, 41:53.

Examples

data(tensile)
with(tensile,hist(str))

Description

The dataset tidal, McArdle and Anderson (2004), gives counts of the organism "intertidal bivalve A. Stutchburyi" in three tidal areas in the Bay of Plenty, New Zealand.

Usage

data("tidal")

Format

A data frame with 90 observations on the following 3 variables.

number

count of A. Stutchburyi organisms

vertht

vertical tidal height (m)

ht

tidal area, a factor with three level

Details

The dataset gives counts of the organism "intertidal bivalve A. Stutchburyi" in three tidal areas in the Bay of Plenty, New Zealand. Each observation is the count of the number of these organisms in a 0.25 m quadrat, as well as the vertical tidal height of the quadrat. The vertical heights have been classified into three tidal areas: upper (vertical height > 0.66m), middle (0.33- 0.66 m) and lower (<0.33 m). Ecologists are interested in the effect of tidal height (either raw or classified) on the number of organisms.

Source

McArdle and Anderson (2004)

References

McArdle, B. H. and Anderson, M. J. (2004), Variance heterogeneity, transformations, and models of species abundance: a cautionary tale, Canadian Journal of Fisheries and Aquatic Sciences, 7, vol 61, pp 1294-1302, NRC Research Press.

Examples

str(tidal)
plot(number~vertht, data=tidal)
plot(number~ht, data=tidal)

Description

Data from an anthropometry survey of 892 girls and women aged 0-50 years from three Gambian villages in West Africa.

Usage

data("triceps")

Format

A data frame with 892 observations on the following 2 variables.

Age

the age in years

tricep

triceps skinfold in mm

Details

Data from an anthropometry survey of 892 girls and women aged 0-50 years from three Gambian villages in West Africa first analysed by Cole and Green (1992).

Source

Cole and Green (1992)

References

Cole, T. J. and Green, P. J. (1992) Smoothing reference centile curves: the LMS method and penalized likelihood, Statist. Med. 11, 1305–1319

Examples

data(triceps)
head(triceps)

Description

The Turkish stock exchange index, was recorded daily from 1/1/1988 to 31/12/1998. The daily returns, ret=log(I_(i+1)/I_(i)), were obtained for i = 1,2,...,2868.

Usage

data(tse)

Format

A data frame with 2868 observations on the following 4 variables.

year

the year

month

the month

day

the day

ret

day returns ret[t]=ln(currency[t])-ln(currency[t-1])

currency

the currency exchange rate

tl

day return ret[t]=log10(currency[t])-log10(currency[t-1])

References

Ricard D. F. Harris and C. Coskun Kucukozen The Empirical Distribution of Stock returns: Evidence from a Emerging European Market, Applied Economic Letters, 2001,8, pages 367-371.

Examples

data(tse)
plot(ts(tse$ret))

Description

The use of ultrasound during pregnancy for the purpose of identification of fetal abnormalities and prediction of birthweight is a feature of standard obstetric care. The data were analysed in Stasinopoulos et. al. (2024).

Usage

data("ultra")

Format

A data frame with 1038 observations on the following 8 variables.

AC

abdominal circumference

BPD

biparietal diameter

HC

head circumference

FL

femur length

parity

number of previous births, a factor with levels 0 1 2 3+

age

the age of the mother

birthweight

the response variable

DBD

date of birth

Details

Each fetus was scanned twice, the first a median 60 days before delivery, and the second a median 24 days before delivery. As the purpose of this analysis is the prediction of birthweight, we base our analysis on the second scans with 1,038 births at the Royal Hospital for Women, Sydney, Australia, between 2008 and 2013.

Source

Personal communication.

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, doi:10.1201/9780429298547. An older version can be found in https://www.gamlss.com/.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, doi:10.18637/jss.v023.i07.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/b21973

Stasinopoulos M.D., Kneib T, Klein N, Mayr A, Heller GZ. (2024) Generalized Additive Models for Location, Scale and Shape: A Distributional Regression Approach, with Applications. Cambridge University Press.

(see also https://www.gamlss.com/).

Examples

data(ultra)
plot(ultra)

Description

US air pollution data set taken from Hand et al. (1994) data set 26, USAIR.DAT, originally from Sokal and Rohlf (1981).

Usage

data(usair)

Format

A data frame with 41 observations on the following 7 variables.

y

a numeric vector: sulpher dioxide concentration in air mgs. per cubic metre in 41 cities in the USA

x1

a numeric vector: average annual temperature in degrees F

x2

a numeric vector: number of manufacturers employing >20 workers

x3

a numeric vector: population size in thousands

x4

a numeric vector: average annual wind speed in miles per hour

x5

a numeric vector: average annual rainfall in inches

x6

a numeric vector: average number of days rainfall per year

Source

Hand et al. (1994) data set 26, USAIR.DAT, originally from Sokal and Rohlf (1981)

References

Hand, D. J., Daly, F., Lunn, A. D., McConway, K. J. and Ostrowski, E. (1994), A handbook of small data sets, Chapman and Hall, London.

Examples

data(usair)
str(usair) 
plot(usair)
# a possible gamlss model
# gamlss(library)
#ap<-gamlss(y~cs(x1,2)+x2+x3+cs(x4,2)+x5+cs(x6,3)+x4:x5, 
#               data=usair, family=GA(mu.link="inverse"))
#

Description

In the original data 368 patients, measured at 18 times after treatment with one of 7 drug treatments (including placebo), plus a baseline measure (time=0) and one or more pre-baseline measures (time=-1). Here for illustration we will ignore the repeated measure nature of the data and we shall use data from time 5 only (364 observations). The VAS scale response variable, Y, is assumed to be distributed as BEINF(mu,sigma,nu,tau) where any of the distributional parameters mu, sigma, nu and tau are modelled as a constant or as a function of the treatment,

Usage

data(vas5)

Format

A data frame with 364 observations on the following 3 variables.

patient

a factor indicationg the patient

treat

the treatment factor with levels 1 2 3 4 5 6 7

vas

the response variable

Details

The Visual analog scale is used to measure pain and quality of life. For example patients are required to indicate in a scale from 0 to 100 the amount of discomfort they have. This can be easily translated to a value from 0 to 1 and consequently analyzed using the beta distribution. Unfortunately if 0's or 100's are recorded the beta distribution is not appropriate since the values 0 and 1 are not allowed in the definition of the beta distribution. Note that the inflated beta distribution allows values at 0 and 1. This is a mixed distribution (continuous and discrete) having four parameters, nu for modelling the probability at zero p(Y=0) relative to p(0<Y<1), tau for modelling the probability at one p(Y=1) relative to p(0<Y<1), and mu and sigma for modelling the between values, $0<Y<1$, using a beta distributed variable BE(mu,sigma) with mean mu and variance sigma*mu*(1-mu).

Source

The data were provided by Dr. Peter Lane

Examples

data(vas5)

Description

The data shows whether victims of crime were reported in the local media.

Usage

data(VictimsOfCrime)

Format

A data frame with 10590 observations on the following 2 variables.

reported

Whether the crime was reported in local media.

age

the age of the victim

Details

Whether the crime was reported in local media.

Source

The data were given by Prof Brian Francis of Lancaster University. They can be used to demonstrate the usefulness of smoothing techniques with a binary response variable.

References

Rigby, R. A. and Stasinopoulos D. M.(2005). Generalized additive models for location, scale and shape, (with discussion),Appl. Statist., 54, part 3, pp 507-554.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in https://www.gamlss.com/.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.

Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, doi:10.18637/jss.v023.i07.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

(see also https://www.gamlss.com/).

Examples

data(VictimsOfCrime)