Dispersion Test
Tests the null hypothesis of equidispersion in Poisson GLMs against the alternative of overdispersion and/or underdispersion.
dispersiontest(object, trafo = NULL, alternative = c("greater", "two.sided", "less"))object |
a fitted Poisson GLM of class |
trafo |
a specification of the alternative (see also details),
can be numeric or a (positive) function or |
alternative |
a character string specifying the alternative hypothesis:
|
The standard Poisson GLM models the (conditional) mean
E[y] = mu which is assumed to be equal to the
variance VAR[y] = mu. dispersiontest
assesses the hypothesis that this assumption holds (equidispersion) against
the alternative that the variance is of the form:
VAR[y] = mu + alpha * trafo(mu).
Overdispersion corresponds to alpha > 0 and underdispersion to alpha < 0. The coefficient alpha can be estimated by an auxiliary OLS regression and tested with the corresponding t (or z) statistic which is asymptotically standard normal under the null hypothesis.
Common specifications of the transformation function trafo are trafo(mu) = mu^2 or trafo(mu) = mu. The former corresponds to a negative binomial (NB) model with quadratic variance function (called NB2 by Cameron and Trivedi, 2005), the latter to a NB model with linear variance function (called NB1 by Cameron and Trivedi, 2005) or quasi-Poisson model with dispersion parameter, i.e.,
VAR[y] = (1 + alpha) * mu = dispersion * mu.
By default, for trafo = NULL, the latter dispersion formulation is used in
dispersiontest. Otherwise, if trafo is specified, the test is formulated
in terms of the parameter alpha. The transformation trafo can either
be specified as a function or an integer corresponding to the function function(x) x^trafo,
such that trafo = 1 and trafo = 2 yield the linear and quadratic formulations
respectively.
An object of class "htest".
Cameron, A.C. and Trivedi, P.K. (1990). Regression-based Tests for Overdispersion in the Poisson Model. Journal of Econometrics, 46, 347–364.
Cameron, A.C. and Trivedi, P.K. (1998). Regression Analysis of Count Data. Cambridge: Cambridge University Press.
Cameron, A.C. and Trivedi, P.K. (2005). Microeconometrics: Methods and Applications. Cambridge: Cambridge University Press.
data("RecreationDemand")
rd <- glm(trips ~ ., data = RecreationDemand, family = poisson)
## linear specification (in terms of dispersion)
dispersiontest(rd)
## linear specification (in terms of alpha)
dispersiontest(rd, trafo = 1)
## quadratic specification (in terms of alpha)
dispersiontest(rd, trafo = 2)
dispersiontest(rd, trafo = function(x) x^2)
## further examples
data("DoctorVisits")
dv <- glm(visits ~ . + I(age^2), data = DoctorVisits, family = poisson)
dispersiontest(dv)
data("NMES1988")
nmes <- glm(visits ~ health + age + gender + married + income + insurance,
data = NMES1988, family = poisson)
dispersiontest(nmes)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.