Package 'mdhglm'

Description

This package allows different models for multivariate response variables where each response is assumed to follow DHGLMs (Lee and Nelder, 2006; Lee, Nelder and Pawitan, 2006, 2016). With DHGLMs, the mean and dispersion parameters for the variance of random effects and residual variance (overdispersion) can be modeled as random-effect models. Furthermore, the mdhglm package allows various correlation structures among the random effects in DHGLMs of different response variables. Functions are provided to format and summarize the mdhglm results. The estimates of fixed effects, random effects and their variances and correlations are calculated.

Details

This is version 1.4 of the mdhglm package.

Author(s)

Youngjo Lee, Marek Molas, Maengseok Noh

Maintainer: Maengseok Noh <[email protected]>

References

Lee, Y. and Nelder, J.A. (2006). Double hierarchical generalized linear models (with discussion), Applied Statistics 55, 139–185.

Lee, Y., Nelder, J.A. and Pawitan, Y. (2006). Generalized Linear Models with Random Effects. Chapman and Hall, Boca Raton, 1st edition.

Lee, Y., Nelder, J.A. and Pawitan, Y. (2016). Generalized Linear Models with Random Effects (2nd Edition). Chapman and Hall, Boca Raton, 2nd edition.

Description

Both longitudinal and survival data were collected in a recent clinical trial to compare the efficacy and safety of two antiretroviral drugs in treating patients who had failed or were intolerant of zidovudine (AZT) therapy (Rizopoulos, 2015). In this trial, 467 HIV-infected patients were enrolled and randomly assigned to receive either didanosine (ddI) or zalcitabine (ddC). The number of CD4 cells per cubic millimeter of blood were recorded at study entry, and again at the 2, 6, 12, and 18 month visits.

Usage

data("aids")

Format

A data frame with 1405 observations on the following 12 variables.

patient

patients identifier for 467 patients

Time

time to death or censoring

death

status with 0 denoting censoring and 1 death for patient

CD4

CD4 cells count

obstime

time points at which the CD4 cells count was recorded

drug

a factor with levels ddC (zalcitabine) and ddI (didanosine)

gender

a factor with levels female and male

prevOI

a factor with levels noAIDS (previous opportunistic infection at study entry) and AIDS (no previous infection)

AZT

a factor with levels intolerance (AZT intolerance) and failure (AZT failure)

start

start of time in the interval

stop

end of time in the interval

event

status with 0 denoting censoring and 1 death in the interval

References

Rizopoulos, D. (2015). JM: Joint Modeling of Longitudinal and Survival Data. R package version 1.4-2.

Description

In the AIDS data, survival data can be summarized for each of patients. Times to death were also recorded with 40 percent of censoring rate.

Usage

data("aids.id")

Format

A data frame with 467 observations on the following 12 variables.

patient

patients identifier for 467 patients

Time

time to death or censoring

death

status with 0 denoting censoring and 1 death for patient

CD4

CD4 cells count

obstime

time points at which the CD4 cells count was recorded

drug

a factor with levels ddC (zalcitabine) and ddI (didanosine)

gender

a factor with levels female and male

prevOI

a factor with levels noAIDS (previous opportunistic infection at study entry) and AIDS (no previous infection)

AZT

a factor with levels intolerance (AZT intolerance) and failure (AZT failure)

start

start of time in the first interval

stop

end of time in the first interval

event

status with 0 denoting censoring and 1 death in the first interval

References

Rizopoulos, D. (2015). JM: Joint Modeling of Longitudinal and Survival Data. R package version 1.4-2.

Description

Tests of the presence of the bacteria H. influenzae in children with otitis media in the Northern Territory of Australia (Ripley, et al., 2016).

Usage

data("bacteria")

Format

A data frame with 220 observations on the following 6 variables.

y

a factor with levels n (absence of bacteria) and y (preence of bacteria)

ap

a factor with levels a (active) and p (placebo)

hilo

a factor with levels hi (high compliance) and lo (low compliance)

week

week of test

ID

subjects identifier

trt

a factor with levels placebo, drug and drug+

References

Ripley, B., Venables, B., Bates, D.M., Hornik, K., Gebhardt, A. and Firsth, D. (2016). MASS: Support Functions and Datasets for Venables and Ripley's MASS. R package version 7.3-45.

Description

Therneau and Lumley (2015) reported data on recurrences of bladder cancer, which were used to demonstrate methodology for recurrent event modelling (Wei et al., 1989). This is the data set from 85 subjects who were assigned to either thiotepa or placebo, and reports the first four recurrences for any patient. The stop variable is the tumor recurrence or censoring time in month. The event variable is 1 for recurrence and 0 for everything else (including death for any reason).

Usage

data("bladder")

Format

A data frame with 340 observations on the following 7 variables.

id

patients identifier for 85 patients

rx

treatment; 1 (=placebo) and 2 (=thiotepa)

number

initial number of tumours (8=8 or more)

size

size (cm) of largest initial tumour

stop

recurrence or censoring time

event

event variable with 1 for recurrence and 0 for everythis else (including death for any reason)

enum

which recurrence (up to 4)

References

Therneau, T. and Lumley, T. (2015). survival: Survival Analysis. R package version 2.38-3.

Wei, L.J., Lin, D.Y., and Weissfeld, L. (1989). Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. Journal of the Americal Statistical Association, 84, 1065–1073.

Description

In an experiment on the preparation of chocolate cakes, conducted at Iowa State College, 3 recipes for preparing the batter were compared (Cochran and Cox, 1957). Recipes I and II differed in that the chocolate was added at 40C and 60C, respectively, while recipe III contained extra sugar. In addition, 6 different baking temperatures were tested: these ranged in 10C steps from 175C to 225C. For each mix, enough batter was prepared for 6 cakes, each of which was baked at a different temperature. Thus the recipes are the whole-unit treatments, while the baking temperatures are the sub-unit treatments. There were 15 replications, and it will be assumed that these were conducted serially according to a randomized blocks scheme: that is, one replication was completed before starting the next, so that differences among replicates represent time differences. A number of measurements were made on the cakes. The measurement presented here is the breaking angle. One half of a slab of cake is held fixed, while the other half is pivoted about the middle until breakage occurs. The angle through which the moving half has revolved is read on a circular scale. Since breakage is gradual, the reading tends to have a subjective element.

Usage

data("cake")

Format

A data frame with 270 observations on the following 5 variables.

Replicate

replication number for 1...15 replicates

Batch

recipes number for 1...3 recipes

Recipe

recipes number for 1...3 recipes

Temperature

baking temperature

Angle

breaking angle

References

Cochran, W.G. and Cox, G.M. (1957). Experimental Designs. John Wiley and Sons, New York, 2nd edition.

Description

The CGD data set presented by Fleming and Harrington (1991) and Therneau and Lumley (2015) consists of a placebo-controlled randomized trial of gamma interferon (rIFN-g) in the treatment of chronic granulomatous disease (CGD). 128 patients from 13 centers were tracked for around 1 year. The number (i.e., cluster size) of patients per center ranged from 4 to 26. The survival times are the recurrent infection times of each patient from the different centers. Censoring occurred at the last observation for all patients, except one, who experienced a serious infection on the data he left the study; in the CGD study about 63 per cent of the data were censored. The recurrent infection times for a given patient are likely to be correlated. However, each patient belongs to one of the 13 centers; hence, the correlation may also be attributed to a center effect.

Usage

data("cgd")

Format

A data frame with 203 observations on the following 16 variables.

id

subjects identifier for 128 patients

center

enrolling center for 13 centers

random

date of randomization

treat

a factor with levels placebo and rIFN-g (gamma interferon)

sex

a factor with levels male and female

age

age in years at study entry

height

height in cm at study entry

weight

weight in kg at study entry

inherit

a factor for pattern of inheritance with levels X-linked and autosomal

steroids

use of steroids at study entry with 1 (=yes) and 0(=no)

propylac

use of prophylactic antibiotics at study entry

hos.cat

a factor for centers into 4 goups with levels US:NIH, US:other, Europe:Amsterdam and Europe:other

tstart

start of each time interval

enum

observation number within subject

tstop

end of each time interval

status

status with 1 for infection and 0 for censoring

References

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

Therneau, T. and Lumley, T. (2015). survival: Survival Analysis. R package version 2.38-3.

Description

An experiment on integrated circuits was reported by Phadke et al. (1983). The width of lines made by a photoresist-nanoline tool were measured in five different locations on silicon wafers, measurements being taken before and after an etching process being treated separately. Here, the pre-etching data are analyzed. The eight experimental factors (A-H) were arranged in an L18 orthogonal array and produced 33 measurements at each of five locations, giving a total of 165 observations. There were no whole-plot (i.e. between-wafer) factors.

Usage

data("circuit")

Format

A data frame with 165 observations on the following 13 variables.

Width

width of lines made by a photoresist-nanoline tool

A

a factor A with levels 1, 2 and 3

B

a factor B with levels 1, 2 and 3

C

a factor C with levels 1, 2 and 3

D

a factor D with levels 1, 2 and 3

E

a factor E with levels 1, 2 and 3

F

a factor F with levels 1, 2 and 3

G

a factor G with levels 1, 2 and 3

H

a factor H with levels 1, 2 and 3

I

a factor I with levels 1, 2 and 3

Wafer

wafers indenfifier

waf

replication number for two replicates

exp

experiment number for differenct array

References

Phadke, M.S., Kacka, R.N., Speeney, D.V. and Grieco, M.J. (1983). Off-line quality control for integrated circuit fabrication using experimental design. Bell System Technical Journal, 62, 1273–1309.

Description

Lee, Nelder, and Pawitan (2016) considered the Vascular Cognitive Impairment (VCI) data. As the elderly population increases, the proportion of stroke, one of main geriatric diseases also rises. The increase of the number of patients with stroke results in the rise of that of patients with the VCI which cognitive function is declined due to stroke. Through an early intervention for the VCI, the cognitive function can be improved. They considered standardized VCI scores for four domains (response variables): executive (y1), memory (y2), visuospatial (y3) and language (y4). The purpose of the study is to examine the effects of ten demographic and ten acute neuroimaging variables on the cognitive function in the ischemic stroke patients.

Usage

data("cog")

Format

A data frame with 1139 observations on the following 26 variables.

x1

integer of age/10

x2

=1 (male), =0 (female)

x3

=0 (none), =1 (elementary) , =2 (middle), =3 (high), =4 (over college)

x4

=1 (hypertension), =0 (none)

x5

=1 (diabetes mellitus), =0 (none)

x6

=1 (atrial brillation), =0 (none)

x7

=1 (history of stroke), =0 (none)

x8

national institute of health stroke scale score at admission

x9

time interval from stroke onset to rst K-VCIHS-NP

x10

=1 (IQCODE>=3.6), =0 (otherwise)

x11

left or bilateral involvement

x12

lesion multiplicity in acute DWI imaging

x13

cortical involvement of acute lesions

x14

cortical involvement of chronic territorial infarction

x15

Periventricular white matter lesions (PVWM); =0 (PVWN 0, 1), =1 (PVWN 2, 3)

x16

Subcortical white matter lesions (SCWM); = 0 (SCWM 0, 1), = 1 (SCWM 2, 3)

x17

presence of lacunes

x18

presence of cerebral microbleeds

x19

Medial temporal lobe atrophy (MTA); = 1 (MTA 2), = 0 (not 2)

x20

= 1 (MTA 3, 4), = 0 (not 3, 4)

y1

executive

y2

memory

y3

visuospatial

y4

language

id

patients identifier

References

Lee, Y., Nelder, J.A. and Pawitan, Y. (2016). Generalized Linear Models with Random Effects (2nd Edition). Chapman and Hall, Boca Raton, 2nd edition.

Description

Hudak et al. (1978) presented data on crack growth data, which have been listed by Lu and Meeker (1993). There are 21 metallic specimens, each subjected to 120,000 loading cycles, with the crack lengths recorded every 10,000 cycles. We take t=no. cycles/100,000 here, so t(j)=j/1000 for j=1,...,12 coded by cycle. The crack increment sequences look rather irregular. Let l(i,j) be the crack length of the ith specimen at the jth observation and let y(i,j)=l(i,j)-l(i,j-1) be the corresponding increment of crack length, which has always a positive value. l(i,j-1) is coded by crack0 to use as a covariate.

Usage

data("crack_growth")

Format

A data frame with 241 observations on the following 5 variables.

ID

id for each 241 observations

y

increment in crack length, y(i,j)=l(i,j)-l(i,j-1), where l(i,j) is the crack length of the ith specimen at the jth observation

crack0

previous crack length, l(i,j-1)

specimen

specimen number for 21 metallic specimens

cycle

number of cycles/100,000; t(j)=j/100, j=1,...,12

References

Hudak, S.J., Saxena, A. Bucci, R.J. and Malcom, R.C. (1978). Development of standard methods of testing and analyzing fatigue crack growth rate data. Technical report. AFML-TR-78-40. Westinghouse R and D Center, Wesinghouse Electric Corp., Pittsburgh, PA.

Lu, C.J. and Meeker, W.Q. (1993). Using degeneration measurements to estimate a time-to-failure distribution, Technometrics, 35, 161–174.

Description

The DHGLMMODELING specifies a GLM, HGLM, DHGLM model for the mean parameters (mu), and a GLM, HGLM model for the overdispersion parameters (phi). GLM for mu, and GLM for phi are specified by adding only fixed terms to the linear predictors for the mu and phi, respectively. These are extended to HGLM for mu and HGLM for phi by adding some random terms. The DHGLM for mu is specified by allowing random effects for the variance of random effects in HGLM for mu. The LMatrix argument allows correlation structures to be defined for random terms. This is done by setting LMatrix to a matrix L that is used as a post-multiplier for the Z matrix of the corresponding random term.

Usage

DHGLMMODELING(Model="mean",Link=NULL,LinPred="constant",RandDist=NULL,
Offset=NULL,LMatrix=NULL,LinkRandVariance=NULL,LinPredRandVariance=NULL,
RandDistRandVariance="gaussian",
LinkRandVariance2=NULL,LinPredRandVariance2=NULL)

Arguments

Description

Price et al. (1985) presented data from a study on the developmental toxicity, ethylene glycol (EG),in mice. Responses are the malformation (binary response) and fetal weight (continuous response) outcomes for the experiment, which shows clear dose-related trends with respect to both outcomes.

Usage

data("eg")

Format

A data frame with 1028 observations on the following 5 variables.

litter

litter number for 94 mice

dose

dose input

y1

fetal weight (g)

y2

malformation (0; No, 1; Yes)

dose2

dose*dose

References

Price, C.J., Kimmel, C.A., Tyl, R.W. and Marr. M.C. (1985). The developmental toxicity of ethylene glycol in rats and mice. Toxicolal Applied Pharmacology, 81, 113—127.

Description

Thall and Vail (1990) presented longitudinal data from a clinical trial of 59 epileptics, who were randomized to a new drug or a placebo (T=0 or T=1). Baseline data were available at the start of the trial; the trial included the logarithm of the average number of epileptic seizures recorded in the 8-week period preceding the trial (B), the logarithm of age (A), and visit (V: a linear trend, coded (-3,-1,1,3)/10). A multivariate response variable (y) consists of the seizure counts during 2-week periods before each of four visits to the clinic.

Usage

data("epilepsy")

Format

A data frame with 236 observations on the following 7 variables.

y

seizure counts during 2-week periods before each of four visits to the clinic

T

treatment (0=new drug, 1=placebo)

B

average number of epileptic seizures in the 8-week period preceding the trial

A

logarithm of age (in years) of each patient

V

linear trend coded (-3, -1, 1, 3)/10 for four visits of each patient

patient

patient number for 59 epileptics

id

observation number for 236 observations

References

Thall, P.F. and Vail, S.C. (1990). Some covariance models for longitudinal count data with overdispersion, Biometrics, 46, 657–671.

Description

Harvey et al. (1994) presented daily observations for the weekday closing exchange rates for the U.K. Sterling/U.S. Dollar from 1/10/81 to 28/6/85.

Usage

data("exch")

Format

A data frame with 944 observations on the following 4 variables.

rt

exchange rate at time t

yt

mean-correted returns

yt1

one lag of yt

yt12

yt1*yt1

References

Harvey, A.C., Ruiz, E. and Shephard, N. (1994). Multivariate stochastic variance models. Review of Economic Studies, 61, 247–264.

Description

In the fabric data (Bissell, 1972), the main response is the number of faults in a bolt of fabric of length.

Usage

data("fabric")

Format

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

x

log of length

y

number of faults

rf

obervation number for 32 obervations

References

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

Description

Lee, Nelder and Pawitan considered the binary factor data with six items taking 1 or 0 for 350 subjects.

Usage

data("factor")

Format

A data frame with 350 observations on the following 7 variables.

y1

item 1

y2

item 2

y3

item 3

y4

item 4

y5

item 5

y6

item 6

subject

subjects idenfier

References

Lee, Y., Nelder, J.A. and Pawitan, Y. (2016). Generalized Linear Models with Random Effects (2nd Edition). Chapman and Hall, Boca Raton, 2nd edition.

Description

Durbin and Koopman (2000) considered the lagged quarterly-demand for gas in the UK from 1960 to 1986.

Usage

data("gas")

Format

A data frame with 108 observations on the following 4 variables.

y

lagged quarterly-demand for gas

year

year; 1960...1986

quarter

quarter; 1...4

time

data number for 108 obervations

References

Durbin, J. and Koopman, S.J. (2000). Time series analysis of nongaussian observations based on state space models from both classical and bayesian perspectives (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62, 3–56.

Description

Engel (1992) presented data from an injection-moulding experiment. An industrial Taguchi experiment was performed to study the in uence of several controllable factors on the mean value and the variation in the percentage of shrinkage of products made by injection moulding. The responses y were percentages of shrinkage of products made by injection moulding. There are seven controllable factors (A-G), in a 2^(7-4) fractional factorial design. There are 8 combinations of levels for seven controllable factors (A-G) to allow the estimates of seven main effects for controllable factors. At each setting of the controllable factors, 4 observations were obtained from a 2^(3-1) fractional factorial with three noise factors (M-O).

Usage

data("injection")

Format

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

y

percentages of shrinkage of products

a

a controllable factor A with levels 1 and 2

b

a controllable factor B with levels 1 and 2

c

a controllable factor C with levels 1 and 2

d

a controllable factor D with levels 1 and 2

e

a controllable factor E with levels 1 and 2

f

a controllable factor F with levels 1 and 2

g

a controllable factor G with levels 1 and 2

m

a noise factor M with levels 1 and 2

n

a noise factor N with levels 1 and 2

o

a noise factor O with levels 1 and 2

References

Engel, J. (1992). Modelling variation in industrial experiments. Applied Statistics, 41, 579–593.

Description

The jointfit is used to fit a multivariate double hierarchical generalized linear models (MDHGLMs) allowing different models for multivariate response variables where each response follow DHGLM. A variety of distributions and link functions for both response and the random effects are allowed. Fixed and random effects can also be fitted in both the mean and the dispersion components. To call the fitting function jointfit, models for the mean and dispersion must be specified by DHGLMMODELING object preferably created by calling the DHGLMMODELING function.

Usage

jointfit(RespDist="gaussian",BinomialDen=NULL, DataMain, MeanModel,DispersionModel=NULL,
PhiFix=NULL,LamFix=NULL,structure="correlated",mord=0,dord=1,convergence=1e-05,
Init_Corr=NULL, EstimateCorrelations=TRUE, ZZCorr=NULL, factor=NULL, REML=TRUE,order=1)

Arguments

Examples

data(eg)
eg1<-eg[1:100,] ## using sampled data to have faster results 

jm1<-DHGLMMODELING(Link="identity", LinPred=y1~dose+dose2+(1|litter),RandDist="gaussian")
jm2<-DHGLMMODELING(Link="logit", LinPred=y2~dose+dose2+(1|litter),RandDist="gaussian")

Init_Corr=list(c(0))
SSC=list(as.factor(c(eg1$litter,eg1$litter)),as.factor(c(eg1$litter,eg1$litter)))
EstimateOverDisp=c(TRUE,FALSE)
LaplaceFixed=c(TRUE,TRUE)
ZZ1<-model.matrix(~as.factor(eg1$litter)-1)
ZZCorr=list(ZZ1,ZZ1)

#### independent random-effects model ####
res_ind<-jointfit(RespDist=c("gaussian","binomial"),DataMain=list(eg1,eg1),
    MeanModel=list(jm1,jm2),structure="correlated",
    Init_Corr=Init_Corr,EstimateCorrelations=FALSE,convergence=1,ZZCorr=ZZCorr)

#### correlated random-effects model ####
res_corr<-jointfit(RespDist=c("gaussian","binomial"),DataMain=list(eg1,eg1),
    MeanModel=list(jm1,jm2),structure="correlated",
    Init_Corr=Init_Corr,convergence=1,ZZCorr=ZZCorr)

#### shared random-effects model ####
Init_Corr=c(1,-10)
res_saturated<-jointfit(RespDist=c("gaussian","binomial"),DataMain=list(eg1,eg1),
    MeanModel=list(jm1,jm2),structure="shared",
    Init_Corr=Init_Corr,convergence=1)

Description

This data consist of times until the first and second recurrences of kidney infection in 38 patients using a portable dialysis machine (McGilchrist and Aisbett, 1991; Therneau and Lumley, 2015). Each survival time is the time until infection since the insertion of the catheter.

Usage

data("kidney")

Format

A data frame with 76 observations on the following 7 variables.

id

patients identifier for 38 patients

time

time until infection since the insertion of the catheter

status

event stuatus (=1; infection, =0; censoring)

age

age of patients in years

sex

1=male, 2=female

disease

a factor for disease type with levels Other, GN, AN and PKD

frail

frailty estimate from original paper

References

McGilchrist, C.A. and Aisbett, C.W. (1991). Regression with frailty in survival analysis. Biometrics, 47, 461–466.

Therneau, T. and Lumley, T. (2015). survival: Survival Analysis. R package version 2.38-3.

Description

Clayton and Kaldor (1987) analyzed observed and expected numbers of lip cancer cases in the 56 administrative areas of Scotland with a view to produce a map that would display regional variations in cancer incidence and yet avoid the presentation of unstable rates for the smaller areas. The expected numbers had been calculated allowing for the different age distributions in the areas by using a fixed-effects multiplicative model; these were regarded for the purpose of analysis as (Intercept)s based on an external set of standard rates. Presumably the spatial aggregation is due in large part to the effects of environmental risk factors. Data were available on the percentage of the work force in each area employed in agriculture, fishing, or forestry. This covariate exhibits spatial aggregation paralleling that for lip cancer itself. Because all three occupations involve outdoor work, exposure to sunlight, the principal known risk factor for lip cancer, might be the explanation.

Usage

data("lip")

Format

A data frame with 56 observations on the following 4 variables.

y

observed number of lip cancer

n

expected number of lip cancer

x

percentage of the work force in each area employed in agriculture, fishing, or forestry

county

county number for 56 areas

References

Clayton, D.G. and Kaldor, J. (1987). Empirical bayes estimates of agestandardized relative risks for use in disease mapping. Biometrics, 43, 671–681.

Description

Rousset et al. (2016) presented the loaloa data set which describes prevalence of infection by the nematode Loa loa in North Cameroon, 1991- 2001. The study investigated the relationship between altitude, vegetation indices, and prevalence of the parasite.

Usage

data("Loaloa")

Format

A data frame with 197 observations on the following 11 variables.

longitude

longitude, in degrees

latitude

latitude, in degrees

ntot

sample size per location

npos

number of infected individuals per location

maxNDVI

maximum normalised-difference vegetation index (NDVI) from repeated satellite scans

seNDVI

standard error of NDVI

elev1

altitude, in m

elev2

additional altitude variables derived from the previous one, provided for convenience respectively, positive values of altitude-650,

elev3

positive values of altitude-1000

elev4

positive values of altitude-1300

maxNDVI1

a copy of maxNDVI modified as maxNDVI1 (maxNDVI1=0.8 if maxNDVI>0.8, maxNDVI1=maxNDVI otherwise)

References

Rousset, F., Ferdy, J.B. and Courtiol, A. (2016). spaMM: Mixed Models, Particularly Spatial GLMMs. R package version 1.7.2.

Description

Asar and Ilk (2014) considered the longitudinal data set from mother's stress and children's morbidity study (MSCM). In MSCM study, 167 mothers and their preschool children were enrolled for 28 days. Investigation of the serial dependence structures of the two longitudinal responses suggested a weak correlation structure for the period of days 1~16. Therefore, only the period of days 17~28 is considered in this data set.

Usage

data("motherStress")

Format

A data frame with 2004 observations on the following 14 variables.

id

subjects identifier for 167 mothers

stress

mother's stress (0=absence, 1=presence)

illness

children's illness status (0=absence, 1=presence)

married

mother's marriage status (0=other, 1=married)

education

mother's highest education level (0=less than high school, 1=more than high school)

employed

mother's employment status (0=unemployed, 1=employed)

chlth

health status of children at baeline (0=very poor/poor, 1=fair, 2=good, 3=very good)

mhlth

health status of mother at baeline (0=very poor/poor, 1=fair, 2=good, 3=very good)

race

children's race (0=white, 1=non-white)

csex

children's gender (0=male, 1=female)

housize

household size (0=2-3 people, 1=more than 3 people)

bstress

the average mother's stress of the 1~16 days

billness

the average children's illnes of the 1~16 days

week

study time (=(day-22)/7)

References

Asar, O. and Ilk, O. (2013). mmm: An R package for analyzing multivariate longitudinal data with multivariatemarginal models. Computer Methods and Programs in Biomedicine, 112, 649–654.

Description

Loehlin and Nichols (1976) presented the national merit twins data including extensive questionnaires from 839 adolescent twins. The twins were identified among the roughly 600,000 US high school juniors who took the national merit scholarship qualifying test (NMSQT) in 1962. They were diagnosed as identical (509 pairs) or same-sex fraternal (330 pairs) by a brief mail questionnaire and later completed a 1082-item questionnaire covering a variety of behaviors, attitudes, personality, life experiences, health, vocational preferences, etc., plus the 480-item California psychological inventory. Twins' scores on the NMSQT and their five subscales are also included. The 285-item questionnaire filled out by the parent was mainly focused on the life histories and experiences of the twins.

Usage

data("nmsqt")

Format

A data frame with 1536 observations on the following 11 variables.

number

data number for 1536 obervations

pairnum

twin number for 768 pairs

x1

=0 (male), =1 (female)

x2

mother's educational level; =1 (less than or equal to 8th grade), =2 (part high school), =3 (high school grad), =4 (part college), =5 (college grad), =6 (graduate degree)

x3

father's educational level; =1 (less than or equal to 8th grade), =2 (part high school), =3 (high school grad), =4 (part college), =5 (college grad), =6 (graduate degree)

x4

family income level; =1 (less than equal to $5000), =2 ($5000 to $7499), =3 ($7500 to $9999), =4 ($10000 to $14999), =5 ($15000 to $19999), =6 ($20000 to $24999), =7 (more than $25000).

y1

NMSQT score for English (0-100)

y2

NMSQT score mathematics (0-100)

y3

NMSQT score social science (0-100)

y4

NMSQT score natural science (0-100)

x5

zygosity; =0 (identical), =1 (fraternal)

References

Loehlin, J.C. and Nichols, R.C. (1976). Heredity, Environments and Personality: A Study of 850 Twins. University of Texas Press, Austin.

Description

The orthodontic growth data (Pinheiro and Bates, 2000) contain the growth measurements of 27 children for 11 girls and 16 boys from age 8 until age 14. Every two years, the distance between the pituitary and the pterygomaxillary fissure was recorded at ages 8, 10, 12 and 14.

Usage

data("Orthodont")

Format

A data frame with 108 observations on the following 4 variables.

distance

distance between the pituitary and the pterygomaxillary fissure

age

age in year (8, 10, 12 and 14 for each subject)

Subject

subjects indenfier for 11 girs and 16 boys

Sex

Gender (Male and Female)

References

Pinheiro, J.C. and Bates, D. (2000). Mixed-Effects Models in S and S-PLUS. Springer, New York.

Description

Komarek (2015) presented a longitudinal data set from a Mayo Clinic trial on 312 patients with primary biliary cirrhosis (PBC) conducted in 1974-1984. There are 1 to 5 visits per subject performed at time of months. At each visit, measurements of three response variables are observed: continuous logarithmic bilirubin, discrete platelet count and dichotomous indication of blood vessel malformations.

Usage

data("PBC910")

Format

A data frame with 918 observations on the following 9 variables.

subject

patients idenfier

day

visiting time in day

month

visiting time in month

lbili

continuous logarithmic bilirubin

platelet

discrete platelet count

spiders

dichotomous indication of blood vessel malformation

References

Komarek, A. (2015). mixAK: Multivariate Normal Mixture Models and Mixtures of Generalized Linear Mixed Models Including Model Based Clustering. R package version 4.2.

Description

Fox, et al. (2016) considered an additive non-parametric regression model with the prestige data.

Usage

data("Prestige")

Format

A data frame with 102 observations on the following 6 variables.

education

average education of occupational incumbents, years, in 1971

income

average income of incumbents, dollars, in 1971

women

percentage of incumbents who are women

prestige

Pineo-Porter prestige score for occupation, from a social survey conducted in the mid- 1960s

census

Canadian Census occupational code

type

a factor for type of occupation with levels bc (Blue Collar), prof (Professional, Managerial and Technical) and wc (White Collar)

References

Fox, J., Weisberg, S., Adler, D., Bates, D., Baud-Bovy, G., Ellison, S., Firth, D., Friendly, M., Gorjanc, G., Graves, S., Heiberger, R., Monette, G., Murdoch, D., Nilsson, H., Ogle, D., Riply, B., Venables, W., Winsemius, D. and Zeileis, A. (2016). car: Companion to Applied Regression. R package version 2.1-2.

Description

The Rheumatoid Arthritis Patients rePort Onset Re-activation sTudy (RAPPORT study) is a longitudinal study that aims to identify an increase in disease activity by self-reported questionnaires. A cohort of 159 patients is followed throughout one year. Self-reported questionnaires are provided for patients every three months together with clinical evaluations of patients disease status. Health assessment questionnaires (HAQ) (20 questions from eight categories) and the Rheumatoid Arthritis Disease Activity Index (RADAI) (five items, e.g., todays disease activity in terms of swollen and tender joints) were used for patients to self-report their functional status. We use binarized versions of HAQ and RADAI, with cut-off points of 0.5 (HAQ) and 2.2 (RADAI). Lower values indicate disease stability, while higher values show increased disease activity. A clinical examination was recorded using the disease activity score with 28 joint counts (DAS28), which is a composite score that includes for example the swollen joints count. The DAS28 score varies between 0 and 10, and we assume Gaussian model to approximate its distribution. Information about DAS28, RADAI, and HAQ taken at months 0, 3, 6, 9, and 12 were considered in this example. The analysis include gender and baseline age of the patients as covariates.

Usage

data("ra_data")

Format

A data frame with 2089 observations on the following 13 variables.

id

subjects idenfier

sex

a factor for gender with levels M and V

age

age in year

yearsRA

years of RA

ethnic

a factor with levels Dutch and Other

edu

a factor with levels Master/Bachelor and Other than Master/Bachelor

X_NAME_

a factor with levels das0, das12, das3, das6, das9, haq0, haq12, haq3, haq6, haq9, radai0, radai12, radai3, radai6 and radai9

X_LABEL_

a factor with levels Das score (clinical) T=0, Das score (clinical) T=12, Das score (clinical) T=3, Das score (clinical) T=6, Das score (clinical) T=9, HAQ T=0, HAQ T=12, HAQ T=3, HAQ T=6, HAQ T=9, RADAI T=0, RADAI T=12, RADAI T=3, RADAI T=6 and RADAI T=9

outcome

outcome responses

outno

number for outcomes

outbin

outbin

outlabel

a factor with levels remission and stable

time

time in month

Description

The data set presented by Mantel, et al. (1977) is based on a tumorigenesis study of 50 litters of female rats. For each litter, one rat was selected to receive the drug and the other two rats were placebo-treated controls. Here each litter is treated as a cluster. The survival time is the time to development of tumor, measured in weeks. Death before occurrence of tumor yields a right-censored observation; forty rats developed a tumor, leading to censoring of about 73 percent.

Usage

data("rats")

Format

A data frame with 300 observations on the following 5 variables.

litter

cluster number for 50 litters

rx

tratment (1=drug, 0=placebo)

time

time to development of tumor, measured in weeks

status

status (1=occurrence of event, 0=censoring)

sex

a factor with levels f (female) and m (male)

References

Mantel, N., Bohidar, N.R. and Ciminera, J.L. (1977). Mantel-haenszel analyses of litter-matched time-to-response data, with modifications for recovery of interlitter information. Cancer Research, 37, 3863–3868.

Description

This example is from a clinical trial comparing two treatments for a respiratory illness (Strokes et al., 1995). In each of two centers, eligible patients were randomly assigned to active treatment or placebo. During treatment, respiratory status was determined at four visits. Potential explanatory variables were centre, sex, and baseline respiratory status (all dichotomous), as well as age(in years) at the time of study entry. There were 111 patients (54 active, 57 placebo).

Usage

data("respiratory")

Format

A data frame with 444 observations on the following 8 variables.

patient

patients identifier for 111 patients

treatment

a factor for treatment with levels active and placebo

sex

a factor for gender with levels female and male

age

age in years

center

center number for two centers

baseline

baseline respiratory status (0 or 1)

past

respiratory status in the previous visit

y

respiratory status (0=poor, 1=good)

References

Strokes, M.E., Davis, C.S., and Koch, G.G. (1995). Categorical Data Analysis using the SAS System. SAS Institute, Cary, NC.

Description

McCullagh and Nelder (1989) presented a data set on salamander mating. Three experiments were conducted: two were done with the same salamanders in the summer and autumn and another one in the autumn of the same year using different salamanders. The response variable is binary, indicating success of mating. In each experiment, 20 females and 20 males from two populations called whiteside, denoted by W, and rough butt, denoted by R, were paired six times for mating with individuals from their own and the other population, resulting in 120 observations in each experiment.

Usage

data("salamander")

Format

A data frame with 360 observations on the following 7 variables.

Season

a factor with levels Fall and Summer

Experiment

experiment number

TypeM

a factor for male with levels R and W

TypeF

a factor for female with levels R and W

Male

males identifier for 20 males

Female

females idenfier for females

Mate

1=success of mating, 0=failness of mating

Source

McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models. Chapman and Hall, London.

Description

Rubin andWu (1997) analyzed schizophrenic behaviour data from an eye-tracking experiment with a visual target moving back and forth along a horizontal line on a screen. The outcome measurement is called the gain ratio, which is eye velocity divided by target velocity, and it is recorded repeatedly at the peak velocity of the target during eye-tracking under three conditions. The first condition is plain sine (PS), which means the target velocity is proportional to the sine of time and the colour of the target is white. The second condition is colour sine (CS), which means the target velocity is proportional to the sine of time, as for PS, but the colours keep changing from white to orange or blue. The third condition is triangular (TR), in which the target moves at a constant speed equal to the peak velocity of PS, back and forth, but the colour is always white. There are 43 nonschizophrenic subjects, 22 females and 21 males, and 43 schizophrenic subjects, 13 females and 30 males. In the experiment, each subject is exposed to five trials, usually three PS, one CS, and one TR. During each trial, there are 11 cycles, and a gain ratio is recorded for each cycle. However, for some cycles, the gain ratios are missing because of eye blinks, so that there are, on average, 34 observations out of 55 cycles for each subject. In this paper, we show how to analyze the data, assuming missing at random which means the probability of being missing does not depend on the values of missing data.s

Usage

data("sch")

Format

A data frame with 2906 observations on the following 7 variables.

y

Gain Ratios for the each measurements of the subject

x1

Effect of PS versus CS (-0.5=CS, 0.5=PS, 0=TR)

x2

Effect of TR versus CS and PS (-1/3=CS, -1/3=PS, 2/3=TR)

sex

Gender of subjects (1=male, 0=female)

time

Linear trend coded -5, ..., 5 for 11 measurement times of each subject

schiz

Indicator of schizophrenic subjects (=1) or not (=0)

v1

Subject number for 43 non-schizophrenic and 43 schizophrenic subjects

References

Rubin, D.B. and Wu, Y.N. (1997) Modeling schizophrenic behavior using general mixture components. Biometrics 53, 243–261.

Description

In clinical trials, various response variables of interest are measured repeatedly over time on the same subject, which can be analysed by using the mdhglm package. At the same time, an event time representing recurrent or terminating time is also obtained. For example, consider a clinical study to investigate the chronic renal allograft dysfunction in renal transplants (Sung et al., 1998). The renal function was evaluated from the serum creatinine (sCr) values. Since the time interval between the consecutive measurements differs from patient to patient, we focus on the mean creatinine levels over six months. In addition, a single terminating survival time (graft-loss time), measured by month, is observed from each patient. During the study period, there were 13 graft losses due to the kidney dysfunction. For other remaining patients, we assumed that the censoring occurred at the last follow-up time. Thus, the censoring rate is about 88 percent.

Usage

data("scr")

Format

A data frame with 1395 observations on the following 9 variables.

id

subjects identifier

month

visiting time in months

cr

serum creatinine value

sex

gender (1=male, 0=female)

age

age in years

icr

1/cr

sur_time

graft loss time

status

=1 for occurrence of event, 0=censoring

first

indicator first visit or not (1=first visit, 0=oterwise)

References

Sung, K.H., Kang, K.W., Kang, C.M., Kwak, J.Y., Park, T.S. and Lee, S.Y. (1998). Study on the factors affecting the chronic renal allograft dysfunction. The Korean Journal of Nephrology, 17, 483–493.

Description

This example is taken from Myers et al. (2002). It involves a designed experiment in a semiconductor plant. Six factors are employed, and it is of interest to study the curvature or camber of the substrate devices produced in the plant. There is a lamination process, and the camber measurement is made four times on each device produced. The goal is to model the camber taken in 10E-04 in. as a function of the design variables. Each design variable is taken at two levels and the design is a 2^(6-2) fractional factorial. The camber measurement is known to be nonnormal.

Usage

data("semicon")

Format

A data frame with 64 observations on the following 8 variables.

Device

Devise number

x1

a x1 variable with two values -1 and 1

x2

a x2 variable with two values -1 and 1

x3

a x3 variable with two values -1 and 1

x4

a x4 variable with two values -1 and 1

x5

a x5 variable with two values -1 and 1

x6

a x6 variable with two values -1 and 1

y

camber measurement

References

Myers, P.H., Montgomery, D.C., and Vining, G.G. (2002). Generalized Linear Models with Applications in Engineering and the Sciences. John Wiley & Sons, New York.

Description

For 1,556 students in the Los Angels area, onset of smoking are observed at each of three timepoints a1; a2 and a3 where a1 is starting time for investigation, a2 is the 1 year follow-up and a3 is the 2 year follow-up (Hedeker, et al., 2015). These event times are grouped at the three intervals [0, a1), [a1, a2) and [a2, a3).

Usage

data("SmokeOnset")

Format

A data frame with 1556 observations on the following 10 variables.

school

schools identifier in the Los Angels area

class

classrooms identifier

student

students identifier

smkonset

coded by i when the event occurs in the ith time interval

event

=1 (smoked), =0 (otherwise)

int

vector of ones representing intercept

SexMale

gender of the student (0=Female, 1=Male)

cc

indicating whether the school was randomized to a social-resistance classroom curriculum (1=Yes, 0=No)

tv

indicating whether the school was randomized to a media (television) intervention (1=Yes, 0=No)

cctv

indicating whether the school was randomized to CC combined with TV

References

Hedeker, D., Archer, K.J., Nordgren, R. and gibbons, R.D. (2015). mixor: Mixed-Effects Ordinal Regression Analysis. R package version 1.0.3.

Description

Agresti (2007) presented the data on an epidemiological survey of 2,484 subjects to investigate snoring as a possible risk factor for heart disease. The subjects were classified according to their snoring level, as reported by their spouses.

Usage

data("snoring")

Format

A data frame with 4 observations on the following 3 variables.

yes

number of subjects for occurrence of heart disease

no

number of subjects for non-occurrence of heart diease

x

snoring level (0, 2, 4, 5)

References

Agresti, A. (2007). An Introduction to Categorical Data Analysis. John Wiley & Sons, New York, 2nd edition.

Description

Approximate 30 percent of hospitalized patients due to acute ischemic stroke are placed in the risk of early neurologic deterioration (END) at their hospital stay. About the patients with acute ischemic stroke, real-time tracking of END would be actualized with monitoring the individual risk assumption with continuous blood pressure (BP). This data-set has systolic BP (SBP) observed repeatedly after arriving at emergency room for two stroke patients (one is END; the other is non-END).

Usage

data("stroke")

Format

A data frame with 72 observations on the following 3 variables.

time

observed time

y1

SBP for END patient

y2

SBP for non-END patient

Description

Agresti (2007) presented the train accident data in the UK between 1975 and 2003. The respone variable y is annual number of collisions between trains and road vehicles, for t million kilometers of train travel. The covariate x is number of years since 1975.

Usage

data("train")

Format

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

x

number of years since 1975

y

annual number of collisions between trains and road vehicles

t

million kilometers of annual train travel

id

oberservations identifier

References

Agresti, A. (2007). An Introduction to Categorical Data Analysis. John Wiley & Sons, New York, 2nd edition.