Example C5 Count
response model
Cameron and Trivedi (1988) use various forms of overdispersed Poisson model to study the relationship between type of health insurance and various responses which measure the demand for health care, e.g. total number of prescribed medications used in past 2 days. The data set they use in this analysis is from the Australian Health survey for 1977-1978. A copy of the original data set (racd.dat) and further details about the variables in racd.dat can be obtained from http://cameron.econ.ucdavis.edu/racd/racddata.html.
References
Cameron, A.C., Trivedi, P.K., Milne, F., Piggott, J., (1988) A microeconometric model of the demand for Health Care and Health Insurance in Australia, Review of Economic Studies, 55, 85-106.
Cameron, A.C., Trivedi, P.K (1998), Regression Analysis
of Count Data, Econometric Society Monograph No.30,
Data description
Number of observations (rows): 5190
Number of variables (columns): 21
Variables:
sex= 1 if respondent is female, 0 if male
age = respondent’s age in years divided by 100,
agesq = age squared
income = respondent’s annual income in Australian dollars divided by 1000
levyplus =1 if respondent is covered by private health insurance fund for private patient in public hospital (with doctor of choice), 0 otherwise
freepoor =1 if respondent is covered by government because low income, recent immigrant, unemployed, 0 otherwise
freerepa=1 if respondent is covered free by government because of old-age or disability pension, or because invalid veteran or family of deceased veteran, 0 otherwise
illness = number of illnesses in past 2 weeks with 5 or more coded as 5
actdays = number of days of reduced activity in past two weeks due to illness or injury
hscore = respondent’s general health questionnaire score using Goldberg's method, high score indicates bad health.
chcond1 = 1 if respondent has chronic condition(s) but not limited in activity, 0 otherwise
chcond2 = 1 if respondent has chronic condition(s) and limited in activity, 0 otherwise
dvisits = number of consultations with a doctor or specialist in the past 2 weeks
nondocco = number of consultations with non-doctor health professionals, (chemist, optician, physiotherapist, social worker, district community nurse, chiropodist or chiropractor in the past 2 weeks
hospadmi = number of admissions to a hospital, psychiatric hospital, nursing or convalescent home in the past 12 months (up to 5 or more admissions which is coded as 5)
hospdays = number of nights in a hospital, etc. during most recent admission, in past 12 months
medicine = total number of prescribed and nonprescribed medications used in past 2 days
prescribe = total number of prescribed medications used in past 2 days
nonprescribe = total number of nonprescribed medications used in past 2 days
constant = 1 for all observations
id= ij
The first few lines of racd.dat look like
Sabre commands
out prescribe.log
trace prescribe.trace
data sex age agesq income levyplus freepoor freerepa
illness actdays &
hscore chcond1
chcond2 dvisits nondocco hospadmi hospdays medicine &
prescrib
nonpresc constant id
read racd.dat
case id
yvar prescrib
family p
constant cons
lfit sex age agesq income levyplus freepoor freerepa
illness actdays &
hscore chcond1
chcond2 cons
dis m
dis e
fit sex age agesq income levyplus freepoor freerepa
illness actdays &
hscore chcond1
chcond2 cons
dis m
dis e
stop
Sabre log file
<S> trace prescribe.trace
<S> data sex age agesq income levyplus freepoor
freerepa illness actdays &
<S>
hscore chcond1 chcond2 dvisits nondocco hospadmi hospdays medicine &
<S>
prescrib nonpresc constant id
<S> read racd.dat
5190 observations
in dataset
<S> case id
<S> yvar prescrib
<S> family p
<S> constant cons
<S> lfit sex age agesq income levyplus freepoor
freerepa illness actdays &
<S>
hscore chcond1 chcond2 cons
Iteration Log. lik. Difference
__________________________________________
1 -8060.4643
2 -5938.7990 2122.
3 -5562.1399 376.7
4 -5531.1633 30.98
5 -5530.7670 0.3963
6 -5530.7669 0.9208E-04
<S> dis m
X-vars Y-var
______________________________
cons prescrib
sex
age
agesq
income
levyplus
freepoor
freerepa
illness
actdays
hscore
chcond1
chcond2
Univariate
model
Standard
Poisson
Number of
observations = 5190
X-var df =
13
Log likelihood
= -5530.7669 on
5177 residual degrees of freedom
<S> dis e
Parameter Estimate Std. Err.
___________________________________________________
cons -2.7412 0.12921
sex 0.48377 0.36639E-01
age 2.6497 0.61491
agesq -0.88778 0.64292
income -0.44661E-02 0.55766E-01
levyplus 0.28274 0.52278E-01
freepoor -0.45680E-01 0.12414
freerepa 0.29584 0.59667E-01
illness 0.20112 0.10530E-01
actdays 0.29261E-01 0.36746E-02
hscore 0.20103E-01 0.63664E-02
chcond1 0.77565 0.46130E-01
chcond2 1.0107 0.53895E-01
<S> fit sex age agesq income levyplus freepoor
freerepa illness actdays &
<S>
hscore chcond1 chcond2 cons
Initial
Homogeneous Fit:
Iteration Log. lik. Difference
__________________________________________
1 -8060.4643
2 -5938.7990 2122.
3 -5562.1399 376.7
4 -5531.1633 30.98
5 -5530.7670 0.3963
6 -5530.7669 0.9208E-04
Iteration Log. lik. Step End-points Orthogonality
length 0 1
criterion
________________________________________________________________________
1 -5469.1111 1.0000 fixed
fixed 152.72
2 -5443.9813 1.0000 fixed
fixed 18.121
3 -5443.3836 1.0000 fixed
fixed 102.08
4 -5443.3440 1.0000 fixed
fixed 22.939
5 -5443.3342 1.0000 fixed
fixed 28.176
6 -5443.3319 1.0000 fixed
fixed 33.273
7 -5443.3310 1.0000 fixed
fixed 41.235
8 -5443.3310 1.0000 fixed
fixed
<S> dis m
X-vars Y-var Case-var
________________________________________________
cons prescrib id
sex
age
agesq
income
levyplus
freepoor
freerepa
illness
actdays
hscore
chcond1
chcond2
Univariate
model
Standard
Poisson
Gaussian random
effects
Number of
observations = 5190
Number of
cases = 5190
X-var df =
13
Scale df =
1
Log likelihood
= -5443.3310 on
5176 residual degrees of freedom
<S> dis e
Parameter Estimate Std. Err.
___________________________________________________
cons -2.8668 0.14908
sex 0.56080 0.43164E-01
age 2.0861 0.73513
agesq -0.26325 0.78264
income 0.30450E-01 0.65221E-01
levyplus 0.27060 0.58009E-01
freepoor -0.61759E-01 0.13676
freerepa 0.29172 0.69172E-01
illness 0.20914 0.13260E-01
actdays 0.34688E-01 0.49475E-02
hscore 0.21604E-01 0.81424E-02
chcond1 0.77394 0.50771E-01
chcond2 1.0245 0.62314E-01
scale 0.52753 0.27207E-01
<S> stop