dispersiontest {AER}  R Documentation 
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 quasiPoisson 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). Regressionbased 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)