insurancerating (version 0.8.2)

check_overdispersion: Check overdispersion of a Poisson claim frequency model

Description

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

Usage

check_overdispersion(object)

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.

Arguments

object

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

Author

Martin Haringa

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().

Examples

x <- glm(nclaims ~ area, offset = log(exposure),
         family = poisson(), data = MTPL2)
check_overdispersion(x)