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, Cambridge University Press,

 

 

Data description

 

Number of observations (rows): 5190

Number of variables (columns): 21

 

Variables:

sex= 1 if respondent is female, 0 if male

age = respondentís age in years divided by 100,

agesq = age squared

income =respondentís 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 = respondentís 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††† fixedfixed†††††† 152.72

††††††† 2††††††††† -5443.9813††††††† 1.0000††† fixedfixed†††††† 18.121

††††††† 3††††††††† -5443.3836††††††† 1.0000††† fixedfixed†††††† 102.08

††††††† 4††††††††† -5443.3440††††††† 1.0000††† fixedfixed†††††† 22.939

††††††† 5††††††††† -5443.3342††††††† 1.0000††† fixedfixed†††††† 28.176

††††††† 6††††††††† -5443.3319††††††† 1.0000††† fixedfixed†††††† 33.273

††††††† 7††††††††† -5443.3310††††††† 1.0000††† fixedfixed†††††† 41.235

††††††† 8††††††††† -5443.3310††††††† 1.0000††† fixedfixed

 

<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