A quick diagnostic for count models: the Pearson goodness-of-fit
statistic sum((y - mu)^2 / mu) divided by its residual degrees of
freedom should be close to 1 under a correctly-specified Poisson model;
values well above 1 indicate overdispersion (evidence for a negative
binomial specification instead). The diagnostic is available for pooled
and fixed-effects Poisson or negative binomial models. It is not applied
to random-effects models because their marginal variance includes the
fitted mixing distribution and is not equal to the observation-level
Poisson variance used by this statistic.
Value
a list of class "panglm_dispersiontest" with the Pearson
statistic, its degrees of freedom, the ratio (statistic/df), a
one-sided p-value against chisq(df), and n_excluded: the number of
observations dropped from the statistic because their fitted value was
exactly zero or unavailable (e.g. rows in a structurally-zero panel
individual screened out of a fixed-effects negbin fit)
Validation
No reference implementation exists for panel fits; the package tests check that it flags simulated overdispersed panels and not equidispersed ones.
See also
negbinfamily() for the negative binomial alternative.
Other tests:
jointtest(),
lineartest(),
panhausman()
Examples
data(copd)
fit <- panglm(exacerbations ~ treatment + age + smoker + crp, data = copd,
index = c("id", "visit"), model = "pooling", family = "poisson")
pandispersiontest(fit)
#>
#> Pearson chi-squared/df overdispersion test
#>
#> chisq = 378.5 , df = 295 , ratio = 1.283 , p-value = 0.0007215
#> alternative hypothesis: overdispersion (ratio > 1)
#>