Demand for Medical Care in NMES 1988
Cross-section data originating from the US National Medical Expenditure Survey (NMES) conducted in 1987 and 1988. The NMES is based upon a representative, national probability sample of the civilian non-institutionalized population and individuals admitted to long-term care facilities during 1987. The data are a subsample of individuals ages 66 and over all of whom are covered by Medicare (a public insurance program providing substantial protection against health-care costs).
data("NMES1988")A data frame containing 4,406 observations on 19 variables.
Number of physician office visits.
Number of non-physician office visits.
Number of physician hospital outpatient visits.
Number of non-physician hospital outpatient visits.
Emergency room visits.
Number of hospital stays.
Factor indicating self-perceived health status, levels are
"poor", "average" (reference category), "excellent".
Number of chronic conditions.
Factor indicating whether the individual has a condition that
limits activities of daily living ("limited") or not ("normal").
Factor indicating region, levels are northeast,
midwest, west, other (reference category).
Age in years (divided by 10).
Factor. Is the individual African-American?
Factor indicating gender.
Factor. is the individual married?
Number of years of education.
Family income in USD 10,000.
Factor. Is the individual employed?
Factor. Is the individual covered by private insurance?
Factor. Is the individual covered by Medicaid?
Journal of Applied Econometrics Data Archive for Deb and Trivedi (1997).
Cameron, A.C. and Trivedi, P.K. (1998). Regression Analysis of Count Data. Cambridge: Cambridge University Press.
Deb, P., and Trivedi, P.K. (1997). Demand for Medical Care by the Elderly: A Finite Mixture Approach. Journal of Applied Econometrics, 12, 313–336.
Zeileis, A., Kleiber, C., and Jackman, S. (2008). Regression Models for Count Data in R. Journal of Statistical Software, 27(8). doi: 10.18637/jss.v027.i08.
## packages
library("MASS")
library("pscl")
## select variables for analysis
data("NMES1988")
nmes <- NMES1988[, c(1, 7:8, 13, 15, 18)]
## dependent variable
hist(nmes$visits, breaks = 0:(max(nmes$visits)+1) - 0.5)
plot(table(nmes$visits))
## convenience transformations for exploratory graphics
clog <- function(x) log(x + 0.5)
cfac <- function(x, breaks = NULL) {
if(is.null(breaks)) breaks <- unique(quantile(x, 0:10/10))
x <- cut(x, breaks, include.lowest = TRUE, right = FALSE)
levels(x) <- paste(breaks[-length(breaks)], ifelse(diff(breaks) > 1,
c(paste("-", breaks[-c(1, length(breaks))] - 1, sep = ""), "+"), ""), sep = "")
return(x)
}
## bivariate visualization
par(mfrow = c(3, 2))
plot(clog(visits) ~ health, data = nmes, varwidth = TRUE)
plot(clog(visits) ~ cfac(chronic), data = nmes)
plot(clog(visits) ~ insurance, data = nmes, varwidth = TRUE)
plot(clog(visits) ~ gender, data = nmes, varwidth = TRUE)
plot(cfac(visits, c(0:2, 4, 6, 10, 100)) ~ school, data = nmes, breaks = 9)
par(mfrow = c(1, 1))
## Poisson regression
nmes_pois <- glm(visits ~ ., data = nmes, family = poisson)
summary(nmes_pois)
## LM test for overdispersion
dispersiontest(nmes_pois)
dispersiontest(nmes_pois, trafo = 2)
## sandwich covariance matrix
coeftest(nmes_pois, vcov = sandwich)
## quasipoisson model
nmes_qpois <- glm(visits ~ ., data = nmes, family = quasipoisson)
## NegBin regression
nmes_nb <- glm.nb(visits ~ ., data = nmes)
## hurdle regression
nmes_hurdle <- hurdle(visits ~ . | chronic + insurance + school + gender,
data = nmes, dist = "negbin")
## zero-inflated regression model
nmes_zinb <- zeroinfl(visits ~ . | chronic + insurance + school + gender,
data = nmes, dist = "negbin")
## compare estimated coefficients
fm <- list("ML-Pois" = nmes_pois, "Quasi-Pois" = nmes_qpois, "NB" = nmes_nb,
"Hurdle-NB" = nmes_hurdle, "ZINB" = nmes_zinb)
round(sapply(fm, function(x) coef(x)[1:7]), digits = 3)
## associated standard errors
round(cbind("ML-Pois" = sqrt(diag(vcov(nmes_pois))),
"Adj-Pois" = sqrt(diag(sandwich(nmes_pois))),
sapply(fm[-1], function(x) sqrt(diag(vcov(x)))[1:7])),
digits = 3)
## log-likelihoods and number of estimated parameters
rbind(logLik = sapply(fm, function(x) round(logLik(x), digits = 0)),
Df = sapply(fm, function(x) attr(logLik(x), "df")))
## predicted number of zeros
round(c("Obs" = sum(nmes$visits < 1),
"ML-Pois" = sum(dpois(0, fitted(nmes_pois))),
"Adj-Pois" = NA,
"Quasi-Pois" = NA,
"NB" = sum(dnbinom(0, mu = fitted(nmes_nb), size = nmes_nb$theta)),
"NB-Hurdle" = sum(predict(nmes_hurdle, type = "prob")[,1]),
"ZINB" = sum(predict(nmes_zinb, type = "prob")[,1])))
## coefficients of zero-augmentation models
t(sapply(fm[4:5], function(x) round(x$coefficients$zero, digits = 3)))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.