Check overdispersion of a Poisson claim frequency model — check

Tests whether a fitted Poisson GLM shows overdispersion using Pearson's chi-squared statistic.

Usage

check_overdispersion(object)

Arguments

object: A fitted model of class "glm" with family Poisson.

Value

An object of class "overdispersion_check" and "overdispersion", which is a list with elements:

pearson_chisq: Pearson's chi-squared statistic.
dispersion_ratio: Dispersion ratio, calculated as Pearson's chi-squared statistic divided by residual degrees of freedom.
residual_df: Residual degrees of freedom.
p_value: P-value from the chi-squared test.

For backwards compatibility the object also contains the aliases chisq, ratio, rdf, and p.

Details

In Poisson claim frequency models, the variance is assumed to be equal to the mean. A dispersion ratio above 1 indicates that the observed variation is larger than expected under that assumption. In pricing work this can be a useful diagnostic signal for omitted heterogeneity, clustering, outliers, or model misspecification. It does not automatically mean that the model is unusable.

A dispersion ratio close to 1 is broadly consistent with the Poisson variance assumption.
A dispersion ratio above 1 suggests overdispersion.
A p-value below 0.05 indicates statistically significant overdispersion.

References

Bolker B. et al. (2017). GLMM FAQ See also: performance::check_overdispersion().

Author

Martin Haringa

Examples

x <- glm(nclaims ~ area, offset = log(exposure),
         family = poisson(), data = MTPL2)
check_overdispersion(x)
#> Dispersion ratio =    1.229
#> Pearson's Chi-squared = 3684.679
#> p-value =  < 0.001
#> 
#> Overdispersion detected.