Package 'COUNT'

affairs

Description

Data from Fair (1978). Although Fair used a tobit model with the data, the outcome measure can be modeled as a count. In fact, Greene (2003) modeled it as Poisson, but given the amount of overdispersion in the data, employing a negative binomial model is an appropriate strategy. The data is stored in the affairs data set. Naffairs is the response variable, indicating the number of affairs reported by the participant in the past year.

Usage

data(affairs)

Format

A data frame with 601 observations on the following 18 variables.

naffairs

number of affairs within last year

kids

1=have children;0= no children

vryunhap

(1/0) very unhappily married

unhap

(1/0) unhappily married

avgmarr

(1/0) average married

hapavg

(1/0) happily married

vryhap

(1/0) very happily married

antirel

(1/0) anti religious

notrel

(1/0) not religious

slghtrel

(1/0) slightly religious

smerel

(1/0) somewhat religious

vryrel

(1/0) very religious

yrsmarr1

(1/0) >0.75 yrs

yrsmarr2

(1/0) >1.5 yrs

yrsmarr3

(1/0) >4.0 yrs

yrsmarr4

(1/0) >7.0 yrs

yrsmarr5

(1/0) >10.0 yrs

yrsmarr6

(1/0) >15.0 yrs

Details

rwm5yr is saved as a data frame. Count models use naffairs as response variable. 0 counts are included.

Source

Fair, R. (1978). A Theory of Extramarital Affairs, Journal of Political Economy, 86: 45-61. Greene, W.H. (2003). Econometric Analysis, Fifth Edition, New York: Macmillan.

References

Hilbe, Joseph M (2011), Negative Binomial Regression, Cambridge University Press Hilbe, Joseph M (2009), Logistic regression Models, Chapman & Hall/CRC

Examples

data(affairs)
glmaffp <- glm(naffairs ~ kids + yrsmarr2 + yrsmarr3 + yrsmarr4 + yrsmarr5,
               family = poisson, data = affairs)
summary(glmaffp)
exp(coef(glmaffp))

require(MASS)
glmaffnb <- glm.nb(naffairs ~ kids + yrsmarr2 + yrsmarr3 + yrsmarr4 + yrsmarr5,
                   data=affairs)
summary(glmaffnb)
exp(coef(glmaffnb))

---

azcabgptca

Description

Random subset of the 1991 Arizona Medicare data for patients hospitalized subsequent to undergoing a CABG (DRGs 106, 107) or PTCA (DRG 112) cardiovascular procedure.

Usage

data(azcabgptca)

Format

A data frame with 1959 observations on the following 6 variables.

died

systolic blood pressure of subject

procedure

1=CABG; 0=PTCA

gender

1=male; 0=female

age

age of subject

los

hospital length of stay

type

1=emerg/urgent; 0=elective

Details

azcabgptca is saved as a data frame.

Source

Hilbe, Negative Binomial Regression, 2nd ed, Cambridge Univ Press

References

Hilbe, Joseph M (2014), Modeling Count Data, Cambridge University Press

Examples

data(azcabgptca); attach(azcabgptca)
table(los); table(procedure, type); table(los, procedure)
summary(los)
summary(c91a <- glm(los ~ procedure+ type, family=poisson, data=azcabgptca))
modelfit(c91a)
summary(c91b <- glm(los ~ procedure+ type, family=quasipoisson, data=azcabgptca))
modelfit(c91b)
library(sandwich)
sqrt(diag(vcovHC(c91a, type="HC0")))

---

azdrg112

Description

The data set relates to the hospital length of stay for patients having a CABG or PTCA (typel) heart procedure. The data comes from the 1995 Arizona Medicare data for DRG (Diagnostic Related Group) 112. Other predictors include gender(1=female) and age75 (1-age 75+). Type is labeled as 1=emergency or urgent admission; 0= elective. Length of stay (los) ranges from 1 to 53 days.

Usage

data(azdrg112)

Format

A data frame with 1,798 observations on the following 4 variables.

los

hospital length of stay: 1-53 days

gender

1=male; 0=female

type1

1=emergency/urgent admission; 0=elective admission

age75

1=age>75; 0=age<=75

Details

azdrg112 is saved as a data frame. Count models typically use los as response variable. 0 counts are not included

Source

DRG 112 data from the 1995 Arizona Medicare (MedPar) State files

References

Hilbe, Joseph M (2007, 2011), Negative Binomial Regression, Cambridge University Press

Examples

data(azdrg112)
glmazp <- glm(los ~ type1 + gender + age75, family=poisson, data=azdrg112)
summary(glmazp)
exp(coef(glmazp))
library(MASS)
glmaznb <- glm.nb(los ~ type1 + gender + age75, data=azdrg112)
summary(glmaznb)
exp(coef(glmaznb))

---

azpro

Description

Data come from the 1991 Arizona cardiovascular patient files. A subset of the fields was selected to model the differential length of stay for patients entering the hospital to receive one of two standard cardiovascular procedures: CABG and PTCA. CABG is the standard acronym for Coronary Artery Bypass Graft, where the flow of blood in a diseased or blocked coronary artery or vein has been grafted to bypass the diseased sections. PTCA, or Percutaneous Transluminal Coronary Angioplasty, is a method of placing a balloon in a blocked coronary artery to open it to blood flow. It is a much less severe method of treatment for those having coronary blockage, with a corresponding reduction in risk.

Usage

data(azpro)

Format

A data frame with 3589 observations on the following 6 variables.

los

length of hospital stay

procedure

1=CABG;0=PTCA

sex

1=Male; 0=female

admit

1=Urgent/Emerg; 0=elective (type of admission)

age75

1= Age>75; 0=Age<=75

hospital

encrypted facility code (string)

Details

azpro is saved as a data frame. Count models use los as response variable. 0 counts are structurally excluded

Source

1991 Arizona Medpar data, cardiovascular patient files, National Health Economics & Research Co.

References

Hilbe, Joseph M (2007, 2011), Negative Binomial Regression, Cambridge University Press Hilbe, Joseph M (2009), Logistic Regression Models, Chapman & Hall/CRC

Examples

data(azpro)
glmazp <- glm(los ~ procedure + sex + admit, family=poisson, data=azpro)
summary(glmazp)
exp(coef(glmazp))
#glmaznb < -glm.nb(los ~ procedure + sex + admit, data=azpro)
#summary(glmaznb)
#exp(coef(glmaznb))

---

azprocedure

Description

Data come from the 1991 Arizona cardiovascular patient files. A subset of the fields was selected to model the differential length of stay for patients entering the hospital to receive one of two standard cardiovascular procedures: CABG and PTCA. CABG is the standard acronym for Coronary Artery Bypass Graft, where the flow of blood in a diseased or blocked coronary artery or vein has been grafted to bypass the diseased sections. PTCA, or Percutaneous Transluminal Coronary Angioplasty, is a method of placing a balloon in a blocked coronary artery to open it to blood flow. It is a much less severe method of treatment for those having coronary blockage, with a corresponding reduction in risk.

Usage

data(azprocedure)

Format

A data frame with 3589 observations on the following 6 variables.

los

length of hospital stay

procedure

1=CABG;0=PTCA

sex

1=Male; 0=female

admit

1=Urgent/Emerg; 0=elective (type of admission)

age75

1= Age>75; 0=Age<=75

hospital

encrypted facility code (string)

Details

azprocedure is saved as a data frame. Count models use los as response variable. 0 counts are structurally excluded

Source

1991 Arizona Medpar data, cardiovascular patient files, National Health Economics & Research Co.

References

Hilbe, Joseph M (2014), Modeling Count Data, Cambridge University Press Hilbe, Joseph M (2007, 2011), Negative Binomial Regression, Cambridge University Press Hilbe, Joseph M (2009), Logistic Regression Models, Chapman & Hall/CRC

Examples

library(MASS)
library(msme)

data(azprocedure)

glmazp <- glm(los ~ procedure + sex + admit, family=poisson, data=azprocedure)
summary(glmazp)
exp(coef(glmazp))

nb2 <- nbinomial(los ~ procedure + sex + admit, data=azprocedure)
summary(nb2)
exp(coef(nb2))

glmaznb <- glm.nb(los ~ procedure + sex + admit, data=azprocedure)
summary(glmaznb)
exp(coef(glmaznb))

---

badhealth

Description

From German health survey data for the year 1998 only.

Usage

data(badhealth)

Format

A data frame with 1,127 observations on the following 3 variables.

numvisit

number of visits to doctor during 1998

badh

1=patient claims to be in bad health; 0=not in bad health

age

age of patient: 20-60

Details

badhealth is saved as a data frame. Count models use numvisit as the response variable, 0 counts are included.

Source

German Health Survey, amended in Hilbe and Greene (2008).

References

Hilbe, Joseph M (2011), Negative Binomial Regression, Cambridge University Press Hilbe, J. and W. Greene (2008). Count Response Regression Models, in ed. C.R. Rao, J.P Miller, and D.C. Rao, Epidemiology and Medical Statistics, Elsevier Handbook of Statistics Series. London, UK: Elsevier.

Examples

data(badhealth)
glmbadp <- glm(numvisit ~ badh + age, family=poisson, data=badhealth)
summary(glmbadp)
exp(coef(glmbadp))
library(MASS)
glmbadnb <- glm.nb(numvisit ~ badh + age, data=badhealth)
summary(glmbadnb)
exp(coef(glmbadnb))

---

fasttrakg

Description

Data are from the Canadian National Cardiovascular Disease registry called, FASTRAK. years covered at 1996-1998. They have been grouped by covariate patterns from individual observations.

Usage

data(fasttrakg)

Format

A data frame with 15 observations on the following 9 variables.

die

number died from MI

cases

number of cases with same covariate pattern

anterior

1=anterior site MI; 0=inferior site MI

hcabg

1=history of CABG; 0=no history of CABG

killip

Killip level of cardiac event severity (1-4)age75

1= Age>75; 0=Age<=75

kk1

(1/0) angina; not MI

kk2

(1/0) moderate severity cardiac event

kk3

(1/0) Severe cardiac event

kk4

(1/0) Severe cardiac event; death

Details

fasttrakg is saved as a data frame. Count models use died as response numerator and cases as the demoninator

Source

1996-1998 FASTRAK data, Hoffman-LaRoche Canada, National Health Economics & Research Co.

References

Hilbe, Joseph M (2007, 2011), Negative Binomial Regression, Cambridge University Press Hilbe, Joseph M (2009), Logistic Regression Models, Chapman & Hall/CRC Hilbe, Joseph M (2014), Modeling Count Data, Cambridge University Press

Examples

library(MASS)
data(fasttrakg)
glmfp <- glm(die ~ anterior + factor(killip) + offset(log(cases)), family=poisson, data=fasttrakg)
summary(glmfp)
exp(coef(glmfp))

---

fishing

Description

The fishing data is adapted from Zuur, Hilbe and Ieno (2013) to determine whether the data appears to be generated from more than one generating mechanism. The data are originally adapted from Bailey et al. (2008) who were interested in how certain deep-sea fish populations were impacted when commercial fishing began in locations with deeper water than in previous years. Given that there are 147 sites that were researched, the model is of (1) the total number of fish counted per site (totabund); ( 2) on the mean water depth per site (meandepth); (3) adjusted by the area of the site (sweptarea); (4) the log of which is the model offset.

Usage

data(fishing)

Format

A data frame with 147 observations on the following variables.

totabund

total fish counted per site

meandepth

mean water depth per site

sweptarea

adjusted area of site

density

folage density index

site

catch site

year

1977-2002

period

0=1977-1989; 1=2000+

Details

fishing is saved as a data frame. Count models use totabund as response variable. Counts start at 2

Source

Zuur, Hilbe, Ieno (2013), A Beginner's Guide to GLM and GLMM using R,

References

Hilbe, Joseph M (2014), Modeling Count Data, Cambridge University Press Zuur, Hilbe, Ieno (2013), A Beginner's Guide to GLM and GLMM using R, Highlands. Bailey M. et al (2008), "Longterm changes in deep-water fish populations in the North East Atlantic", Proc Roy Soc B 275:1965-1969.

Examples

## Not run: 
library(MASS)
library(flexmix)
data(fishing)
attach(fishing)
fmm_pg <- flexmix(totabund~meandepth + offset(log(sweptarea)), data=rwm1984, k=2,
         model=list(FLXMRglm(totabund~., family="NB1"), 
                    FLXMRglm(tpdocvis~., family="NB1")))
parameters(fmm_pg, component=1, model=1)
parameters(fmm_pg, component=2, model=1)
summary(fmm_pg)

## End(Not run)

---

lbw

Description

The data come to us from Hosmer and Lemeshow (2000). Called the low birth weight (lbw) data, the response is a binary variable, low, which indicates whether the birth weight of a baby is under 2500g (low=1), or over (low=0).

Usage

data(lbw)

Format

A data frame with 189 observations on the following 10 variables.

low

1=low birthweight baby; 0=norml weight

smoke

1=history of mother smoking; 0=mother nonsmoker

race

categorical 1-3: 1=white; 2-=black; 3=other

age

age of mother: 14-45

lwt

weight (lbs) at last menstrual period: 80-250 lbs

ptl

number of false of premature labors: 0-3

ht

1=history of hypertension; 0 =no hypertension

ui

1=uterine irritability; 0 no irritability

ftv

number of physician visits in 1st trimester: 0-6

bwt

birth weight in grams: 709 - 4990 gr

Details

lbw is saved as a data frame. Count models can use ftv as a response variable, or convert it to grouped format

Source

Hosmer, D and S. Lemeshow (2000), Applied Logistic Regression, Wiley

References

Hilbe, Joseph M (2007, 2011), Negative Binomial Regression, Cambridge University Press Hilbe, Joseph M (2009), Logistic Regression Models, Chapman & Hall/CRC

Examples

data(lbw)
glmbwp <- glm(ftv ~ low + smoke + factor(race), family=poisson, data=lbw)
summary(glmbwp)
exp(coef(glmbwp))
library(MASS)
glmbwnb <- glm.nb(ftv ~ low + smoke + factor(race), data=lbw)
summary(glmbwnb)
exp(coef(glmbwnb))

---

lbwgrp

Description

grouped format of the lbw data. The observation level data come to us form Hosmer and Lemeshow (2000). Grouping is such that lowbw is the numerator, and cases the denominator of a binomial model, or cases may be an offset to the count variable, lowbw. Birthweights under 2500g classifies a low birthweight baby.

Usage

data(lbwgrp)

Format

A data frame with 6 observations on the following 7 variables.

lowbw

Number of low weight babies per covariate pattern: 12-60

cases

Number of observations with same covariate pattern: 30-165

smoke

1=history of mother smoking; 0=mother nonsmoker

race1

(1/0): Caucasian

race2

(1/0): Black

race3

(1/0): Other

low

low birth weight (not valid variable in grouped format)

Details

lbwgrp is saved as a data frame. Count models: count response=lowbt; offset=log(cases); Binary: binomial numerator= lowbt; binomial denominator=cases

Source

Hosmer, D and S. Lemeshow (2000), Applied Logistic Regression, Wiley

References

Hilbe, Joseph M (2007, 2011), Negative Binomial Regression, Cambridge University Press Hilbe, Joseph M (2009), Logistic Regression Models, Chapman & Hall/CRC

Examples

data(lbwgrp)
glmgp <- glm(lowbw ~ smoke + race2 + race3 + offset(log(cases)), family=poisson, data=lbwgrp)
summary(glmgp)
exp(coef(glmgp))
library(MASS)
glmgnb <- glm.nb(lowbw ~  smoke + race2 + race3, data=lbwgrp)
summary(glmgnb)
exp(coef(glmgnb))

---

Logistic regression : generic synthetic binary/binomial logistic data and model

Description

logit_syn is a generic function for developing synthetic logistic regression data and a model given user defined specifications.

Usage

logit_syn(nobs=50000, d=1,  xv  = c(1, 0.5, -1.5))

Arguments

nobs	number of observations in model, Default is 50000
d	binomial denominator, Default is 1, a binary logistic model. May use a variable containing different denominator values.
xv	predictor coefficient values. First argument is intercept. Use as xv = c(intercept , x1_coef, x2_coef, ...)

Details

Create a synthetic logistic regression model using the appropriate arguments. Binomial denominator must be declared. For a binary logistic model, d=1. A variable may be used as the denominator when values differ. See examples.

Value

by	binomial logistic numerator; number of successes
sim.data	synthetic data set

Author(s)

Joseph M. Hilbe, Arizona State University, and Jet Propulsion Laboratory, California Institute of Technology Andrew Robinson, Universty of Melbourne, Australia.

References

Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press. Hilbe, J.M. (2009), Logistic Regression Models, Chapman & Hall/CRCD

See Also

probit_syn

Examples

# Binary logistic regression (denominator=1)
sim.data <-logit_syn(nobs = 500, d = 1, xv = c(1, .5, -1.5))
mylogit <- glm(cbind(by,dby) ~ ., family=binomial(link="logit"), data = sim.data)
summary(mylogit)
confint(mylogit)

# Binary logistic regression with odds ratios (denominator=1); 3 predictors
sim.data <-logit_syn(nobs = 500, d = 1, xv = c(1, .75, -1.5, 1.15))
mylogit <- glm(cbind(by,dby) ~ ., family=binomial(link="logit"), data = sim.data)
exp(coef(mylogit))
exp(confint(mylogit))

# Binomial or grouped logistic regression with defined denominator, den
den <- rep(1:5, each=100, times=1)*100
sim.data <- logit_syn(nobs = 500, d = den, xv = c(1, .5, -1.5))
gby <- glm(cbind(by,dby) ~ ., family=binomial(link="logit"), data = sim.data)
summary(gby)

## Not run: 
# default
sim.data <- logit_syn(nobs=500, d=1,  xv = c(2, -.55, 1.15))
dlogit <- glm(cbind(by,dby) ~ . , family=binomial(link="logit"), data = sim.data)
summary(dlogit)

## End(Not run)

---

loomis

Description

Data are taken from Loomis (2003). The study relates to a survey taken on reported frequency of visits to national parks during the year. The survey was taken at park sites, thus incurring possible effects of endogenous stratification.

Usage

data(loomis)

Format

A data frame with 410 observations on the following 11 variables.

anvisits

number of annual visits to park

gender

1=male;0=female

income

income in US dollars per year, categorical: 4 levels

income1

<=$25000

income2

>$25000 - $55000

income3

>$55000 - $95000

income4

>$95000

travel

travel time, categorical: 3 levels

travel1

<.25 hrs

travel2

>=.25 - <4 hrs

travel3

>=4 hrs

Details

loomis is saved as a data frame. Count models typically use anvisits as response variable. 0 counts are included

Source

from Loomis (2003)

References

Hilbe, Joseph M (2007, 2011), Negative Binomial Regression, Cambridge University Press Loomis, J. B. (2003). Travel cost demand model based river recreation benefit estimates with on-site and household surveys: Comparative results and a correction procedure, Water Resources Research, 39(4): 1105

Examples

data(loomis)
glmlmp <- glm(anvisits ~ gender + factor(income) + factor(travel), family=poisson, data=loomis)
summary(glmlmp)
exp(coef(glmlmp))
library(MASS)
glmlmnb <- glm.nb(anvisits ~ gender + factor(income) + factor(travel), data=loomis)
summary(glmlmnb)
exp(coef(glmlmnb))

---

mdvis

Description

Data from a subset of the German Socio-Economic Panel (SOEP). The subset was created by Rabe-Hesketh and Skrondal (2005). Only working women are included in these data. Beginning in 1997, German health reform in part entailed a 200 co-payment as well as limits in provider reimbursement. Patients were surveyed for the one year panel (1996) prior to and the one year panel (1998) after reform to assess whether the number of physician visits by patients declined - which was the goal of reform legislation. The response, or variable to be explained by the model, is numvisit, which indicates the number of patient visits to a physician's office during a three month period.

Usage

data(mdvis)

Format

A data frame with 2,227 observations on the following 13 variables.

numvisit

visits to MD office 3mo prior

reform

1=interview yr post-reform: 1998;0=pre-reform:1996

badh

1=bad health; 0 = not bad health

age

Age(yrs 20-60)

educ

education(1:7-10;2=10.5-12;3=HSgrad+)

educ1

educ1= 7-10 years

educ2

educ2= 10.5-12 years

educ3

educ3= post secondary or high school

agegrp

age: 1=20-39; 2=40-49; 3=50-60

age1

age 20-39

age2

age 40-49

age3

age 50-60

loginc

log(household income in DM)

Details

mdvis is saved as a data frame. Count models typically use docvis as response variable. 0 counts are included

Source

German Socio-Economic Panel (SOEP), 1995 pre-reform; 1998 post reform. Created by Rabe-Hesketh and Skrondal (2005).

References

Hilbe, Joseph M (2007, 2011), Negative Binomial Regression, Cambridge University Press Hilbe, Joseph M (2009), Logistic Regression Models, Chapman & Hall/CRC Rabe-Hesketh, S. and A. Skrondal (2005). Multilevel and Longitudinal Modeling Using Stata, College Station: Stata Press.

Examples

data(mdvis)
glmmdp <- glm(numvisit ~ reform + factor(educ) + factor(agegrp), family=poisson, data=mdvis)
summary(glmmdp)
exp(coef(glmmdp))
library(MASS)
glmmdnb <- glm.nb(numvisit ~ reform + factor(educ) + factor(agegrp), data=mdvis)
summary(glmmdnb)
exp(coef(glmmdnb))

---

medpar

Description

The US national Medicare inpatient hospital database is referred to as the Medpar data, which is prepared yearly from hospital filing records. Medpar files for each state are also prepared. The full Medpar data consists of 115 variables. The national Medpar has some 14 million records, with one record for each hospilitiztion. The data in the medpar file comes from 1991 Medicare files for the state of Arizona. The data are limited to only one diagnostic group (DRG 112). Patient data have been randomly selected from the original data.

Usage

data(medpar)

Format

A data frame with 1495 observations on the following 10 variables.

los

length of hospital stay

hmo

Patient belongs to a Health Maintenance Organization, binary

white

Patient identifies themselves as Caucasian, binary

died

Patient died, binary

age80

Patient age 80 and over, binary

type

Type of admission, categorical

type1

Elective admission, binary

type2

Urgent admission,binary

type3

Elective admission, binary

provnum

Provider ID

Details

medpar is saved as a data frame. Count models use los as response variable. 0 counts are structurally excluded

Source

1991 National Medpar data, National Health Economics & Research Co.

References

Hilbe, Joseph M (2014), Modeling Count Data, Cambridge University Press Hilbe, Joseph M (2007, 2011), Negative Binomial Regression, Cambridge University Press Hilbe, Joseph M (2009), Logistic Regression Models, Chapman & Hall/CRC first used in Hardin, JW and JM Hilbe (2001, 2007), Generalized Linear Models and Extensions, Stata Press

Examples

library(MASS)
library(msme)
data(medpar)
glmp <- glm(los ~ hmo + white + factor(type), family=poisson, data=medpar)
summary(glmp)
exp(coef(glmp))
nb2 <- nbinomial(los ~ hmo + white + factor(type), data=medpar)
summary(nb2)
exp(coef(nb2))
glmnb <- glm.nb(los ~ hmo + white + factor(type), data=medpar)
summary(glmnb)
exp(coef(glmnb))

---

NB1: maximum likelihood linear negative binomial regression

Description

ml.nb1 is a maximum likelihood function for estimating linear negative binomial (NB1) data. Output consists of a table of parameter estimates, standard errors, z-value, and confidence intervals.

Usage

ml.nb1(formula, data, offset=0, start=NULL, verbose=FALSE)

Arguments

formula	an object of class '"formula"': a symbolic description of the model to be fitted. The details of model specification are given under 'Details'.
data	a mandatory data frame containing the variables in the model.
offset	this can be used to specify an _a priori_ known component to be included in the linear predictor during fitting. The offset should be provided on the log scale.
start	an optional vector of starting values for the parameters.
verbose	a logical flag to indicate whether the fit information should be printed.

Details

ml.nb1 is used like glm.nb, but without saving ancillary statistics.

Value

The function returns a dataframe with the following components:

Estimate	ML estimate of the parameter
SE	Asymptotic estimate of the standard error of the estimate of the parameter
Z	The Z statistic of the asymptotic hypothesis test that the population value for the parameter is 0.
LCL	Lower 95% confidence interval for the parameter estimate.
UCL	Upper 95% confidence interval for the parameter estimate.

Author(s)

Andrew Robinson, Universty of Melbourne, Australia, and Joseph M. Hilbe, Arizona State University, and Jet Propulsion Laboratory, California Institute of Technology

References

Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press.

See Also

glm.nb, ml.nbc, ml.nb2

Examples

# Table 10.8, Hilbe. J.M. (2011), Negative Binomial Regression, 
#   2nd ed. Cambridge University Press (adapted)
data(medpar)
medpar$type <- factor(medpar$type)
med.nb1 <- ml.nb1(los ~ hmo + white + type, data = medpar)
med.nb1

---

NB2: maximum likelihood linear negative binomial regression

Description

ml.nb2 is a maximum likelihood function for estimating linear negative binomial (NB2) data. Output consists of a table of parameter estimates, standard errors, z-value, and confidence intervals.

Usage

ml.nb2(formula, data, offset=0, start=NULL, verbose=FALSE)

Arguments

formula	an object of class '"formula"': a symbolic description of the model to be fitted. The details of model specification are given under 'Details'.
data	a mandatory data frame containing the variables in the model.
offset	this can be used to specify an _a priori_ known component to be included in the linear predictor during fitting. The offset should be provided on the log scale.
start	an optional vector of starting values for the parameters.
verbose	a logical flag to indicate whether the fit information should be printed.

Details

ml.nb2 is used like glm.nb, but without saving ancillary statistics.

Value

The function returns a dataframe with the following components:

Estimate	ML estimate of the parameter
SE	Asymptotic estimate of the standard error of the estimate of the parameter
Z	The Z statistic of the asymptotic hypothesis test that the population value for the parameter is 0.
LCL	Lower 95% confidence interval for the parameter estimate.
UCL	Upper 95% confidence interval for the parameter estimate.

Author(s)

Andrew Robinson, Universty of Melbourne, Australia, and Joseph M. Hilbe, Arizona State University, and Jet Propulsion Laboratory, California Institute of Technology

References

Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press.

See Also

glm.nb, ml.nbc, ml.nb1

Examples

# Table 8.7, Hilbe. J.M. (2011), Negative Binomial Regression, 
#   2nd ed. Cambridge University Press (adapted)
data(medpar)
medpar$type <- factor(medpar$type)
med.nb2 <- ml.nb2(los ~ hmo + white + type, data = medpar)
med.nb2

---

NBC: maximum likelihood linear negative binomial regression

Description

ml.nbc is a maximum likelihood function for estimating canonical linear negative binomial (NB-C) data.

Usage

ml.nbc(formula, data, start=NULL, verbose=FALSE)

Arguments

formula	an object of class '"formula"': a symbolic description of the model to be fitted. The details of model specification are given under 'Details'.
data	a mandatory data frame containing the variables in the model.
start	an optional vector of starting values for the parameters.
verbose	a logical flag to indicate whether the fit information should be printed.

Details

ml.nbc is used like glm.nb, but without saving ancillary statistics.

Value

The function returns a dataframe with the following components:

Estimate	ML estimate of the parameter
SE	Asymptotic estimate of the standard error of the estimate of the parameter
Z	The Z statistic of the asymptotic hypothesis test that the population value for the parameter is 0.
LCL	Lower 95% confidence interval for the parameter estimate.
UCL	Upper 95% confidence interval for the parameter estimate.

Author(s)

Andrew Robinson, Universty of Melbourne, Australia, and Joseph M. Hilbe, Arizona State University, and Jet Propulsion Laboratory, California Institute of Technology

References

Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press.

See Also

glm.nb, ml.nb1, ml.nb2

Examples

# Table 10.12, Hilbe. J.M. (2011), Negative Binomial Regression, 
#   2nd ed. Cambridge University Press (adapted)

## Not run: 
data(medpar)
nobs <- 50000
x2 <- runif(nobs)
x1 <- runif(nobs)
xb <- 1.25*x1 + .1*x2 - 1.5
mu <- 1/(exp(-xb)-1)
p <- 1/(1+mu)
r <- 1
gcy <- rnbinom(nobs, size=r, prob = p)
test <- data.frame(gcy, x1, x2)
nbc <- ml.nbc(gcy ~ x1 + x2, data=test)
nbc

## End(Not run)

---

NB2: maximum likelihood Poisson regression

Description

ml.pois is a maximum likelihood function for estimating Poisson data. Output consists of a table of parameter estimates, standard errors, z-value, and confidence intervals. An offset may be declared as an option.

Usage

ml.pois(formula, data, offset=0, start=NULL, verbose=FALSE)

Arguments

formula	an object of class '"formula"': a symbolic description of the model to be fitted.
data	a mandatory data frame containing the variables in the model.
offset	this can be used to specify an _a priori_ known component to be included in the linear predictor during fitting. The offset should be provided on the log scale.
start	an optional vector of starting values for the parameters.
verbose	a logical flag to indicate whether the fit information should be printed.

Details

ml.pois is used like glm, but does not provide ancillary statistics.

Value

The function returns a dataframe with the following components:

Estimate	ML estimate of the parameters
SE	Asymptotic estimate of the standard error of the estimate of the parameter
Z	The Z statistic of the asymptotic hypothesis test that the population value for the parameter is 0.
LCL	Lower 95% confidence interval for the parameter estimates.
UCL	Upper 95% confidence interval for the parameter estimates.

Author(s)

Andrew Robinson, Universty of Melbourne, Australia, and Joseph M. Hilbe, Arizona State University, and Jet Propulsion Laboratory, California Institute of Technology

References

Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press.

See Also

glm.nb, ml.nbc, ml.nb1

Examples

# Table 8.7, Hilbe. J.M. (2011), Negative Binomial Regression, 
#   2nd ed. Cambridge University Press (adapted)
data(medpar)
medpar$type <- factor(medpar$type)
med.pois <- ml.pois(los ~ hmo + white + type, data = medpar)
med.pois

data(rwm5yr)
lyear <- log(rwm5yr$year)
rwm.poi <- ml.pois(docvis ~ outwork + age + female, offset=lyear, data =
rwm5yr)
rwm.poi
exp(rwm.poi$Estimate)
exp(rwm.poi$LCL)
exp(rwm.poi$UCL)

---

Fit Statistics for generalized linear models

Description

modelfit is used following a glm() or glm.nb() model to produce a list of model fit statistics.

Usage

modelfit(x)

Arguments

x	the only argument is the name of the fitted glm or glm.nb function model

Details

modelfit is to be used as a post-estimation function, following the use of glm() or glm.nb().

Value

obs	number of model observatiions
aic	AIC statistic
xvars	number of model predictors
rdof	residial degrees of freedom
aic_n	AIC, 'aic'/'obs'
ll	log-likelihood
bic_r	BIC - Raftery parameterization
bic_l	BIC - log-likelihood Standard definition (Stata)
bic_qh	Hannan-Quinn IC statistic (Limdep)

Note

modelfit.r must be loaded into memory in order to be effectve. Users may past modelfit.r into script editor to run, as well as load it.

Author(s)

Joseph M. Hilbe, Arizona State University, and Jet Propulsion Laboratory, California Institute of technology

References

Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press.

Hilbe, J.M. (2009), Logistic Regression Models, Chapman Hall/CRC

See Also

glm, glm.nb

Examples

## Hilbe (2011), Table 9.17
library(MASS)
data(lbwgrp)
nb9_3 <- glm.nb(lowbw ~ smoke + race2 + race3 + offset(log(cases)), data=lbwgrp)
summary(nb9_3)
exp(coef(nb9_3))
modelfit(nb9_3)

---

Frequency table

Description

mytable is used to produce a table of frequencies, proportion and cumulative proportions for a count variable

Usage

myTable(x)

Arguments

x	the only argument is the name of the count variable

Details

myTable is used as either a diagnostic to view the distribution of a count variable, or as a frequency distribution display in its own right. myTable is given in Table 9.40 in Hilbe (2011).

Value

x	count value
Freq	Frequency of count
Prop	Proportion
CumProp	Cumulative proportion

Author(s)

Joseph M. Hilbe, Arizona State University, and Jet Propulsion Laboratory, California Institute of Technology

References

Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press. Hilbe, J.M. (2009), Logistic Regression Models, Chapman Hall/CRC

See Also

modelfit

Examples

data(medpar)
myTable(medpar$los)

---

Negative binomial (NB1): generic synthetic linear negative binomial data and model

Description

nb1_syn is a generic function for developing synthetic NB1 data and a model given user defined specifications.

Usage

nb1_syn(nobs=50000, delta=1, xv = c(1, 0.75, -1.25))

Arguments

nobs	number of observations in model, Default is 50000
delta	NB1 heterogeneity or ancillary parameter
xv	predictor coefficient values. First argument is intercept. Use as xv = c(intercept , x1_coef, x2_coef, ...)

Details

Create a synthetic linear negative binomial (NB1) regression model using the appropriate arguments. Model data with predictors indicated as a group with a period (.). See examples.

Data can be modeled using the ml.nb1.r function in the COUNT package, or by using the gamlss function in the gamlss package, using the "family=NBII" option.

Value

nb1y	Negative binomial (NB1) response; number of counts
sim.data	synthetic data set

Author(s)

Joseph M. Hilbe, Arizona State University, and Jet Propulsion Laboratory, California Institute of Technology Andrew Robinson, Universty of Melbourne, Australia.

References

Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press.

See Also

nb2_syn, nbc_syn

Examples

sim.data <- nb1_syn(nobs = 5000, delta = .5, xv = c(.5, 1.25, -1.5))
mynb1 <- ml.nb1(nb1y ~ . , data = sim.data)
mynb1

## Not run: 
# use gamlss to model NB1 data
library(gamlss)         
sim.data <- nb1_syn(nobs = 5000, delta = .5, xv = c(.5, 1.25, -1.5))
mynb1 <- gamlss( nb1y ~ . , family=NBII, data = sim.data)
mynb1

## End(Not run)

## Not run: 
# default
sim.data <- nb1_syn()
dnb1 <- ml.nb1(nb1y ~ . , data = sim.data)
dnb1

## End(Not run)

---

Negative binomial (NB2): generic synthetic negative binomial data and model

Description

nb2_syn is a generic function for developing synthetic NB2 data and a model given user defined specifications.

Usage

nb2_syn(nobs = 50000, off = 0, alpha = 1, xv = c(1, 0.75, -1.5))

Arguments

nobs	number of observations in model, Default is 50000
alpha	NB2 heterogeneity or ancillary parameter
off	optional: log of offset variable
xv	predictor coefficient values. First argument is intercept. Use as xv = c(intercept , x1_coef, x2_coef, ...)

Details

Create a synthetic negative binomial (NB2) regression model using the appropriate arguments. Model data with predictors indicated as a group with a period (.). Offset optional. If no offset is desired, drop "off= loff" from nb2_syn function call and "+ loff" from glm.nb function call. See examples.

Data can be estimated using the glm.nb() function, or the ml.nb2() function in the COUNT package, or by using the gamlss function in the gamlss package, with "family=NBI" option.

Value

nby	Negative binomial response; number of counts
sim.data	synthetic data set

Author(s)

Andrew Robinson, Universty of Melbourne, Australia, and Joseph M. Hilbe, Arizona State University, Jet Propulsion Laboratory, California Institute of Technology

References

Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press.

See Also

poisson_syn, nb1_syn, nbc_syn

Examples

library(MASS)           

sim.data <- nb2_syn(nobs = 500, alpha = .5, xv = c(2, .75, -1.25))
mynb2 <- glm.nb(nby ~ . , data = sim.data)
summary(mynb2)
confint(mynb2)

# with offset
oset <- rep(1:5, each=100, times=1)*100 
loff <- log(oset)   
sim.data <- nb2_syn(nobs = 500, off = loff, alpha = .5, xv = c(1.2, -.75, .25, -1.3))
mypof <- glm.nb(nby ~ . + loff, data = sim.data)
summary(mypof)
confint(mypof)

# without offset, exponentiated coefficients, CI's
sim.data <- nb2_syn(nobs = 500, alpha = .75, xv = c(1, .5, -1.4))
mynbf <- glm.nb(nby ~ . , data = sim.data)
exp(coef(mynbf))
exp(confint(mynbf))

## Not run: 
# default, without offset
sim.data <- nb2_syn()
dnb2 <- glm.nb(nby ~ . , data = sim.data)
summary(dnb2)

## End(Not run)

# use ml.nb2.r function
sim.data <- nb2_syn(nobs = 500, alpha = .5, xv = c(2, .75, -1.25))
mynb2x <- ml.nb2(nby ~ . , data = sim.data)
mynb2x

## Not run: 
# use gamlss function for modeling data after sim.data created
library(gamlss)
sim.data <- nb2_syn(nobs = 500, alpha = .5, xv = c(2, .75, -1.25))
gamnb <- gamlss(nby ~ ., family=NBI, data = sim.data)
gamnb

## End(Not run)

---

Table of negative binomial counts: observed vs predicted proportions and difference

Description

nb2.obs.pred is used to produce a table of a negative binomial model count response with mean observed vs mean predicted proportions, and their difference.

Usage

nb2.obs.pred(len, model)

Arguments

len	highest count for the table
model	name of the negative binomial model created

Details

nb2.obs.pred is used to determine where disparities exist in the mean observed and predicted proportions in the range of model counts. nb2.obs.pred is used in Table 9.28 and other places in Hilbe (2011). nb2.obs.pred follows glm.nb(), where both y=TRUE and model=TRUE options must be used.

Value

Count	count value
obsPropFreq	Observed proportion of counts
avgp	Predicted proportion of counts
Diff	Difference in observed vs predicted

Author(s)

Joseph M. Hilbe, Arizona State University, and Jet Propulsion Laboratory, California Institute of Technology Andrew Robinson, University of Melbourne, Australia

References

Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press.

See Also

myTable

Examples

library(MASS)

data(medpar)
mdpar <- glm.nb(los ~ hmo+white+type2+type3, data=medpar, y=TRUE, model=TRUE)
nb2.obs.pred(len=25, model=mdpar)

---

Negative binomial (NB-C): generic synthetic canonical negative binomial data and model

Description

nbc_syn is a generic function for developing synthetic NB-C data and a model given user defined specifications.

Usage

nbc_syn(nobs=50000, alpha=1.15, xv = c(-1.5, -1.25, -.1))

Arguments

nobs	number of observations in model, Default is 50000
alpha	NB-C heterogeneity or ancillary parameter
xv	predictor coefficient values. First argument is intercept. Use as xv = c(intercept , x1_coef, x2_coef, ...)

Details

Create a synthetic canonial negative binomial (NB-C) regression model using the appropriate arguments. Model data with predictors indicated as a group with a period (.). Data can be modeled using the ml.nbc.r function in the COUNT package. See examples.

Value

nbcy	Canonical negative binomial (NB-C) response; number of counts
sim.data	synthetic data set

Author(s)

Joseph M. Hilbe, Arizona State University, and Jet Propulsion Laboratory, California Institute of Technology Andrew Robinson, Universty of Melbourne, Australia.

References

Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press.

See Also

nb2_syn, nb1_syn

Examples

## Not run: 
sim.data <- nbc_syn(nobs = 50000, alpha = 1.15, xv = c(-1.5, -1.25, -.1))
mynbc <- ml.nbc(nbcy ~ . , data = sim.data)
mynbc

# default
sim.data <- nbc_syn()
dnbc <- ml.nbc(nbcy ~ . , data = sim.data)
dnbc

## End(Not run)

---

nuts

Description

Squirrel data set (nuts) from Zuur, Hilbe, and Ieno (2013). As originally reported by Flaherty et al (2012), researchers recorded information about squirrel behavior and forest attributes across various plots in Scotland's Abernathy Forest. The study focused on the following variables. response cones number of cones stripped by red squirrels per plot predictor sntrees standardized number of trees per plot sheight standardized mean tree height per plot scover standardized percentage of canopy cover per plot The stripped cone count was only taken when the mean diameter of trees was under 0.6m (dbh).

Usage

data(nuts)

Format

A data frame with 52 observations on the following 8 variables.

cones

number cones stripped by squirrels

ntrees

number of trees per plot

dbh

number DBH per plot

height

mean tree height per plot

cover

canopy closure (as a percentage)

sntrees

standardized number of trees per plot

sheight

standardized mean tree height per plot

scover

standardized canopy closure (as a percentage)

Details

nuts is saved as a data frame. Count models use ntrees as response variable. Counts start at 3

Source

Zuur, Hilbe, Ieno (2013), A Beginner's Guide to GLM and GLMM using R, Highlands

References

Hilbe, Joseph M (2014), Modeling Count Data, Cambridge University Press Zuur, Hilbe, Ieno (2013), A Beginner's Guide to GLM and GLMM using R, Highlands. Flaherty, S et al (2012), "The impact of forest stand structure on red squirrels habitat use", Forestry 85:437-444.

Examples

data(nuts)
nut <- subset(nuts, dbh < 0.6)
# sntrees <- scale(nuts$ntrees)
# sheigtht <- scale(nuts$height)
# scover <- scale(nuts$cover)
summary(PO <- glm(cones ~ sntrees + sheight + scover, family=quasipoisson, data=nut))

---

Table of Poisson counts: observed vs predicted proportions and difference

Description

poi.obs.pred is used to produce a table of a Poisson model count response with mean observed vs mean predicted proportions, and their difference.

Usage

poi.obs.pred(len, model)

Arguments

len	highest count for the table
model	name of the Poisson model created

Details

poi.obs.pred is used to determine where disparities exist in the mean observed and predicted proportions in the range of model counts. poi.obs.pred is used in Table 6.15 and other places in Hilbe (2011). poi.obs.pred follows glm(), where both y=TRUE and model=TRUE options must be used.

Value

Count	count value
obsPropFreq	Observed proportion of counts
avgp	Predicted proportion of counts
Diff	Difference in observed vs predicted

Author(s)

Joseph M. Hilbe, Arizona State University, and Jet Propulsion Laboratory, California Institute of Technology Andrew Robinson, University of Melbourne, Australia

References

Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press.

See Also

myTable

Examples

data(medpar)
mdpar <- glm(los ~ hmo+white+type2+type3, family=poisson, data=medpar, y=TRUE, model=TRUE)
poi.obs.pred(len=25, model=mdpar)

---

Poisson : generic synthetic Poisson data and model

Description

poisson_syn is a generic function for developing synthetic Poisson data and a model given user defined specifications.

Usage

poisson_syn(nobs = 50000, off = 0, xv = c(1, -.5,  1))

Arguments

nobs	number of observations in model, Default is 50000
off	optional: log of offset variable
xv	predictor coefficient values. First argument is intercept. Use as xv = c(intercept , x1_coef, x2_coef, ...)

Details

Create a synthetic Poisson regression model using the appropriate arguments. Offset optional. Model data with predictors indicated as a group with a period (.). See examples.

Value

py	Poisson response; number of counts
sim.data	synthetic data set

Author(s)

Joseph M. Hilbe, Arizona State University, and Jet Propulsion Laboratory, California Institute of Technology Andrew Robinson, Universty of Melbourne, Australia.

References

Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press.

See Also

nb2_syn

Examples

# standard Poisson model with two predictors and intercept
sim.data <- poisson_syn(nobs = 500, xv = c(2, .75, -1.25))
mypo <- glm(py ~ . , family=poisson, data = sim.data)
summary(mypo)
confint(mypo)

# Poisson with offset and three predictors
oset <- rep(1:5, each=100, times=1)*100 
loff <- log(oset)   
sim.data <- poisson_syn(nobs = 500, off = loff, xv = c(1.2, -.75, .25, -1.3))
mypof <- glm(py ~ . + loff, family=poisson, data = sim.data)
summary(mypof)
confint(mypof)

# Poisson without offset, exponentiated coefficients, CI's
sim.data <- poisson_syn(nobs = 500, xv = c(2, .75, -1.25))
mypo <- glm(py ~ . , family=poisson, data = sim.data)
exp(coef(mypo))
exp(confint(mypo))

## Not run: 
# default (without offset)
sim.data <- poisson_syn()
dmypo <- glm( py ~ . , family=poisson, data = sim.data)
summary(dmypo)

## End(Not run)

---

Probit regression : generic synthetic binary/binomial probit data and model

Description

probit_syn is a generic function for developing synthetic probit regression data and a model given user defined specifications.

Usage

probit_syn(nobs=50000, d=1,  xv = c(1, 0.5, -1.5))

Arguments

nobs	number of observations in model, Default is 50000
d	binomial denominator, Default is 1, a binary probit model. May use a variable containing different denominator values.
xv	predictor coefficient values. First argument is intercept. Use as xv = c(intercept , x1_coef, x2_coef, ...)

Details

Create a synthetic probit regression model using the appropriate arguments. Binomial denominator must be declared. For a binary probit model, d=1. A variable may be used as the denominator when values differ. See examples.

Value

py	binomial probit numerator; number of successes
sim.data	synthetic data set

Author(s)

Joseph M. Hilbe, Arizona State University, and Jet Propulsion Laboratory, California Institute of Technology Andrew Robinson, Universty of Melbourne, Australia.

References

Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press. Hilbe, J.M. (2009), Logistic Regression Models, Chapman & Hall/CRCD

See Also

logit_syn

Examples

# Binary probit regression (denominator=1)
sim.data <-probit_syn(nobs = 5000, d = 1, xv = c(1, .5, -1.5))
myprobit <- glm(cbind(py,dpy) ~ ., family=binomial(link="probit"), data = sim.data)
summary(myprobit)
confint(myprobit)

# Binary probit regression with 3 predictors (denominator=1)
sim.data <-probit_syn(nobs = 5000, d = 1, xv = c(1, .75, -1.5, 1.15))
myprobit <- glm(cbind(py,dpy) ~ ., family=binomial(link="probit"), data = sim.data)
summary(myprobit)
confint(myprobit)

# Binomial or grouped probit regression with defined denominator, den
den <- rep(1:5, each=1000, times=1)*100
sim.data <- probit_syn(nobs = 5000, d = den, xv = c(1, .5, -1.5))
gpy <- glm(cbind(py,dpy) ~ ., family=binomial(link="probit"), data = sim.data)
summary(gpy)

## Not run: 
# default
sim.data <- probit_syn()
dprobit <- glm(cbind(py,dpy) ~ . , family=binomial(link="probit"), data = sim.data)
summary(dprobit)

## End(Not run)

---

rwm

Description

German health registry for the years 1984-1988. Health information for years prior to health reform.

Usage

data(rwm)

Format

A data frame with 27,326 observations on the following 4 variables.

docvis

number of visits to doctor during year (0-121)

age

age: 25-64

educ

years of formal education (7-18)

hhninc

household yearly income in DM/1000)

Details

rwm is saved as a data frame. Count models typically use docvis as response variable. 0 counts are included

Source

German Health Reform Registry, years pre-reform 1984-1988, From Hilbe and Greene (2008)

References

Hilbe, Joseph M (2011), Negative Binomial Regression, Cambridge University Press Hilbe, J.M. and W.H. Greene (2008), "Count Response Regression Models", in Rao, CR, JP Miller and DC Rao (eds), Handbook of Statistics 27: Epidemiology and Medical Statistics, Amsterdam: Elsevier. pp. 210-252.

Examples

data(rwm)
glmrwp <- glm(docvis ~ age + educ + hhninc, family=poisson, data=rwm)
summary(glmrwp)
exp(coef(glmrwp))
library(MASS)
glmrwnb <- glm.nb(docvis ~ age + educ + hhninc, data=rwm)
summary(glmrwnb)
exp(coef(glmrwnb))

---

rwm1984

Description

German health registry for the year 1984.

Usage

data(rwm1984)

Format

A data frame with 3,874 observations on the following 17 variables.

docvis

number of visits to doctor during year (0-121)

hospvis

number of days in hospital during year (0-51)

edlevel

educational level (categorical: 1-4)

age

age: 25-64

outwork

out of work=1; 0=working

female

female=1; 0=male

married

married=1; 0=not married

kids

have children=1; no children=0

hhninc

household yearly income in marks (in Marks)

educ

years of formal education (7-18)

self

self-employed=1; not self employed=0

edlevel1

(1/0) not high school graduate

edlevel2

(1/0) high school graduate

edlevel3

(1/0) university/college

edlevel4

(1/0) graduate school

Details

rwm1984 is saved as a data frame. Count models typically use docvis as response variable. 0 counts are included

Source

German Health Reform Registry, year=1984, in Hilbe and Greene (2007)

References

Hilbe, Joseph, M (2014), Modeling Count Data, Cambridge University Press Hilbe, Joseph M (2011), Negative Binomial Regression, Cambridge University Press Hilbe, J. and W. Greene (2008). Count Response Regression Models, in ed. C.R. Rao, J.P Miller, and D.C. Rao, Epidemiology and Medical Statistics, Elsevier Handbook of Statistics Series. London, UK: Elsevier.

Examples

library(MASS)
library(msme)
data(rwm1984)

glmrp <- glm(docvis ~ outwork + female + age + factor(edlevel), family=poisson, data=rwm1984)
summary(glmrp)
exp(coef(glmrp))

summary(nb2 <- nbinomial(docvis ~ outwork + female + age + factor(edlevel), data=rwm1984))
exp(coef(nb2))

summary(glmrnb <- glm.nb(docvis ~ outwork + female + age + factor(edlevel), data=rwm1984))
exp(coef(glmrnb))

---

rwm5yr

Description

German health registry for the years 1984-1988. Health information for years immediately prior to health reform.

Usage

data(rwm5yr)

Format

A data frame with 19,609 observations on the following 17 variables.

id

patient ID (1=7028)

docvis

number of visits to doctor during year (0-121)

hospvis

number of days in hospital during year (0-51)

year

year; (categorical: 1984, 1985, 1986, 1987, 1988)

edlevel

educational level (categorical: 1-4)

age

age: 25-64

outwork

out of work=1; 0=working

female

female=1; 0=male

married

married=1; 0=not married

kids

have children=1; no children=0

hhninc

household yearly income in marks (in Marks)

educ

years of formal education (7-18)

self

self-employed=1; not self employed=0

edlevel1

(1/0) not high school graduate

edlevel2

(1/0) high school graduate

edlevel3

(1/0) university/college

edlevel4

(1/0) graduate school

Details

rwm5yr is saved as a data frame. Count models typically use docvis as response variable. 0 counts are included

Source

German Health Reform Registry, years pre-reform 1984-1988, in Hilbe and Greene (2007)

References

Hilbe, Joseph M (2014), Modeling Count Data, Cambridge University Press Hilbe, Joseph M (2011), Negative Binomial Regression, Cambridge University Press Hilbe, J. and W. Greene (2008). Count Response Regression Models, in ed. C.R. Rao, J.P Miller, and D.C. Rao, Epidemiology and Medical Statistics, Elsevier Handbook of Statistics Series. London, UK: Elsevier.

Examples

library(MASS)
data(rwm5yr)

glmrp <- glm(docvis ~ outwork + female + age + factor(edlevel), family=poisson, data=rwm5yr)
summary(glmrp)
exp(coef(glmrp))

## Not run: 
library(msme)
nb2 <- nbinomial(docvis ~ outwork + female + age + factor(edlevel), data=rwm5yr)
summary(nb2)
exp(coef(nb2)) 

glmrnb <- glm.nb(docvis ~ outwork + female + age + factor(edlevel), data=rwm5yr)
summary(glmrnb)
exp(coef(glmrnb))

## End(Not run)

---

ships

Description

Data set used in McCullagh & Nelder (1989), Hardin & Hilbe (2003), and other sources. The data contains values on the number of reported accidents for ships belonging to a company over a given time period. When a ship was constructed is also recorded.

Usage

data(ships)

Format

A data frame with 40 observations on the following 7 variables.

accident

number of shipping accidents

op

1=ship operated 1975-1979;0=1965-74

co.65.69

ship was in construction 1965-1969 (1/0)

co.70.74

ship was in construction 1970-1974 (1/0)

co.75.79

ship was in construction 1975-1979 (1/0)

service

months in service

ship

ship identification : 1-5

Details

ships is saved as a data frame. Count models use accident as the response variable, with log(service) as the offset. ship can be used as a panel identifier.

Source

McCullagh and Nelder, 1989.

References

Hilbe, Joseph M (2007, 2011), Negative Binomial Regression, Cambridge University Press Hilbe, Joseph M (2009), Logistic Regression Models, Chapman & Hall/CRC Hardin, JW and JM Hilbe (2001, 2007), Generalized Linear Models and Extensions, Stata Press McCullagh, P.A, and J. Nelder (1989), Generalized Linear Models, Chapman & Hall

Examples

data(ships)
glmshp <- glm(accident ~ op + co.70.74 + co.75.79 + offset(log(service)),
              family=poisson, data=ships)
summary(glmshp)
exp(coef(glmshp))
library(MASS)
glmshnb <- glm.nb(accident ~ op + co.70.74 + co.75.79 + offset(log(service)),
                   data=ships)
summary(glmshnb)
exp(coef(glmshnb))
## Not run: 
library(gee)
shipgee <- gee(accident ~ op + co.70.74 + co.75.79 + offset(log(service)),
              data=ships, family=poisson, corstr="exchangeable", id=ship)
summary(shipgee)

## End(Not run)

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smoking

Description

A simple data set with only 6 observations.

Usage

data(smoking)

Format

A data frame with 6 observations on the following 4 variables.

sbp

systolic blood pressure of subject

male

1=male; 0=female

smoker

1=hist of smoking; 0= no hist of smoking

age

age of subject

Details

smoking is saved as a data frame.

Source

none

References

Hilbe, Joseph M (2014), Modeling Count Data, Cambridge University Press

Examples

sbp    <- c(131,132,122,119,123,115)
male   <- c(1,1,1,0,0,0)
smoker <- c(1,1,0,0,1,0)
age    <- c(34,36,30,32,26,23)
summary(reg1 <- lm(sbp~ male+smoker+age))

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titanic

Description

The data is an observation-based version of the 1912 Titanic passenger survival log,

Usage

data(titanic)

Format

A data frame with 1316 observations on the following 4 variables.

class

a factor with levels 1st class 2nd class 3rd class crew

age

a factor with levels child adults

sex

a factor with levels women man

survived

a factor with levels no yes

Details

titanic is saved as a data frame. Used to assess risk ratios

Source

Found in many other texts

References

Hilbe, Joseph M (2014), Modeling Count Data, Cambridge University Press Hilbe, Joseph M (2007, 2011), Negative Binomial Regression, Cambridge University Press Hilbe, Joseph M (2009), Logistic Regression Models, Chapman & Hall/CRC

Examples

data(titanic)
titanic$survival <- titanic$survived == "yes"
glmlr <- glm(survival ~ age + sex + factor(class), family=binomial, data=titanic)
summary(glmlr)

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titanicgrp

Description

The data is an grouped version of the 1912 Titanic passenger survival log,

Usage

data(titanicgrp)

Format

A data frame with 12 observations on the following 5 variables.

survive

number of passengers who survived

cases

number of passengers with same pattern of covariates

age

1=adult; 0=child

sex

1=Male; 0=female

class

ticket class 1= 1st class; 2= second class; 3= third class

Details

titanicgrp is saved as a data frame. Used to assess risk ratios

Source

Found in many other texts

References

Hilbe, Joseph M (2014), Modeling Count Data, Cambridge University Press Hilbe, Joseph M (2007, 2011), Negative Binomial Regression, Cambridge University Press Hilbe, Joseph M (2009), Logistic Regression Models, Chapman & Hall/CRC

Examples

library(MASS)
library(msme)
data(titanicgrp)
glmlr <- glm(survive ~ age + sex + factor(class) + offset(log(cases)),
             family=poisson, data=titanicgrp)
summary(glmlr)
exp(coef(glmlr))

lcases <- titanicgrp$cases
nb2o <- nbinomial(survive ~ age + sex + factor(class), 
                                        formula2 =~ age + sex,
                                        offset = lcases,
                                        mean.link="log",
                                        scale.link="log_s",
                                        data=titanicgrp)
summary(nb2o)
exp(coef(nb2o))

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