The Australian health survey was used by Bonat and Jorgensen (2016) as an example of multivariate count regression model. The data consists of five count response variables concerning health system access measures and nine covariates concerning social conditions in Australian for 1987-88.
sex - Factor with levels male and female.
age - Respondent's age in years divided by 100.
income - Respondent's annual income in Australian
dollars divided by 1000.
levyplus - Coded factor. If respondent is covered by
private health insurance fund for private patients in public
hospital with doctor of choice (1) or otherwise (0).
freepoor - Coded factor. If respondent is covered by
government because low income, recent immigrant, unemployed (1)
or otherwise (0).
freerepa - Coded factor. If respondent is covered free
by government because of old-age or disability pension, or
because invalid veteran or family of deceased veteran (1) or
otherwise (0).
illnes - Number of illnesses in past 2 weeks, with 5 or
illnesses coded as 5.
actdays - Number of days of reduced activity in the past
two weeks due to illness or injury.
hscore - Respondent's general health questionnaire score
using Goldberg's method. High score indicates poor health.
chcond - Factor with three levels. If respondent has
chronic condition(s) and is limited in activity (limited),
or if the respondent has chronic condition(s) but is not limited
in activity (nonlimited) or otherwise (otherwise,
reference level).
Ndoc - Number of consultations with a doctor or
specialist (response variable).
Nndoc - Number of consultations with health
professionals (response variable).
Nadm - Number of admissions to a hospital, psychiatric
hospital, nursing or convalescence home in the past 12 months
(response variable).
Nhosp - Number of nights in a hospital during the most
recent admission.
Nmed - Total number of prescribed and non prescribed
medications used in the past two days.
data(ahs)
a data.frame with 5190 records and 15 variables.
Deb, P. and Trivedi, P. K. (1997) Demand for medical care by the elderly: A finite mixture approach. Journal of Applied Econometrics 12(3):313--336.
Bonat, W. H. and Jorgensen, B. (2016) Multivariate covariance generalized linear models. Journal of Royal Statistical Society - Series C 65:649--675.
require(mcglm) data(ahs, package="mcglm") form1 <- Ndoc ~ income + age form2 <- Nndoc ~ income + age Z0 <- mc_id(ahs) fit.ahs <- mcglm(linear_pred = c(form1, form2), matrix_pred = list(Z0, Z0), link = c("log","log"), variance = c("poisson_tweedie","poisson_tweedie"), data = ahs)#> Automatic initial values selected.summary(fit.ahs)#> Call: Ndoc ~ income + age #> <environment: 0x556094746068> #> #> Link function: log #> Variance function: poisson_tweedie #> Covariance function: identity #> Regression: #> Estimates Std.error Z value Pr(>|z|) #> (Intercept) -1.6064259 0.1224424 -13.119845 2.534514e-39 #> income -0.3423238 0.1106829 -3.092833 1.982560e-03 #> age 1.3532370 0.1804182 7.500558 6.354669e-14 #> #> Dispersion: #> Estimates Std.error Z value Pr(>|z|) #> 1 1.029012 0.157786 6.521567 6.957648e-11 #> #> Call: Nndoc ~ income + age #> <environment: 0x556094746068> #> #> Link function: log #> Variance function: poisson_tweedie #> Covariance function: identity #> Regression: #> Estimates Std.error Z value Pr(>|z|) #> (Intercept) -2.3377656 0.2228618 -10.489756 9.627652e-26 #> income -0.4399401 0.1960479 -2.244044 2.482958e-02 #> age 2.2401837 0.3154228 7.102161 1.228210e-12 #> #> Dispersion: #> Estimates Std.error Z value Pr(>|z|) #> 1 3.085235 0.4403052 7.007037 2.434186e-12 #> #> Correlation matrix: #> Parameters Estimates Std.error Z value Pr(>|z|) #> 1 rho12 0.1232811 0.01584463 7.780623 7.216838e-15 #> #> Algorithm: chaser #> Correction: TRUE #> Number iterations: 5