insurancerating (version 0.8.2)

add_rebasing: Rebase categorical tariff relativities to a reference level

Description

Rescale the current relativities of one categorical risk factor so that a selected level has relativity 1. add_rebasing() is an ordered refinement step: it uses the relativities available at that point in the workflow and retains all ratios between levels.

Usage

add_rebasing(model, model_variable, reference_level = NULL, weights = NULL)

Value

A rating_refinement object containing an ordered rebasing step. The step stores the original and rebased relativities, the selected reference level, its original relativity, the selection method and, when applicable, the aggregated level weights. The GLM is fitted only when refit() is called.

Arguments

model

A rating_refinement object created with prepare_refinement(). Rebasing uses the current relativities at this point in the ordered workflow.

model_variable

Character string naming the categorical risk factor to rebase. This may identify an original GLM factor or a tariff factor created by an earlier add_relativities(), add_restriction() or add_shrinkage() step.

reference_level

Optional single character value naming the level that should receive relativity 1. When NULL, the level with the largest aggregated weight is selected automatically.

weights

NULL or a character string naming a numeric, non-negative column in the refinement data. The weights are used only when reference_level = NULL. NULL derives the basis from explicit model weights or a simple exposure offset.

Author

Martin Haringa

Details

Rebasing changes the numerical reference of a tariff factor, but does not change its relative differentiation. If the current relativity of reference level \(j\) is \(r_j\), every level is transformed as

$$ r_i^{new} = \frac{r_i}{r_j}. $$

The selected reference level therefore becomes 1, while the ratio between any two levels remains unchanged. For example, relativities 0.8, 1.0 and 1.2 rebased to the first level become 1.0, 1.25 and 1.5. This is different from add_shrinkage(), which deliberately reduces the spread between levels.

Selecting the reference level

Supply reference_level when the tariff has an established reference class or when governance requires a particular level to remain at 1. If reference_level = NULL, the level with the largest aggregated weight is selected. Ties are resolved by the order of the current factor levels.

With weights = NULL, explicit GLM weights are used when available; otherwise a single offset of the form log(column) is used. This commonly selects claim count for a weighted severity GLM and exposure for a frequency or risk-premium GLM. An explicit numeric column can be supplied when another portfolio basis is required. weights is ignored when reference_level is supplied because no automatic selection is then needed.

Position in the refinement workflow

Rebasing is generally applied after the step that creates the final tariff levels. For example, add_relativities() may replace a broad level by several sublevels; add_rebasing() can then select one of those resulting sublevels as the new reference. It can also follow add_shrinkage() when the shrunken relativities should be reported relative to an established level.

set_reference_level() serves a different purpose. It changes the contrast reference of a factor before fitting a GLM. add_rebasing() rescales current tariff relativities inside an existing refinement specification. The refinement step and selected reference are retained for review by summary() and audit_refinement().

See Also

prepare_refinement(), set_reference_level(), add_relativities(), add_shrinkage(), add_restriction(), refit(), audit_refinement()

Examples

portfolio <- data.frame(
  claims = c(1, 2, 1, 3, 2, 4, 1, 5),
  exposure = c(1, 1, 1, 1, 2, 1, 1, 1),
  sector = factor(rep(c("Industry", "Office", "Retail", "Transport"), 2))
)

model <- glm(
  claims ~ sector + offset(log(exposure)),
  family = poisson(),
  data = portfolio
)

# Keep Office as the explicit tariff reference after shrinkage.
refinement <- prepare_refinement(model, data = portfolio) |>
  add_shrinkage(
    model_variable = "sector",
    credibility = 0.9,
    weights = "exposure"
  ) |>
  add_rebasing(
    model_variable = "sector",
    reference_level = "Office"
  )

summary(refinement)
refined_model <- refit(refinement)
rating_table(refined_model)

# Omitting reference_level selects the level with the largest exposure.
exposure_reference <- prepare_refinement(model, data = portfolio) |>
  add_rebasing(
    model_variable = "sector",
    weights = "exposure"
  )