Add expert-based relativities to a refinement workflow

Splits an existing model variable into more detailed tariff segments using supplied relativities. This is useful when the GLM is fitted on a coarser rating factor for credibility or stability, but the final tariff needs a more detailed split that is based on portfolio exposure, expert judgement or externally agreed relativities.

Usage

add_relativities(
  model,
  model_variable,
  split_variable,
  relativities,
  exposure,
  normalize = TRUE
)

Arguments

model

Object of class rating_refinement, usually created with prepare_refinement().

model_variable

Character string. Existing variable in the GLM. Levels of this variable can be split into more detailed tariff segments.

split_variable

Character string. More granular portfolio variable that defines the detailed groups inside model_variable.

relativities

Named list of data frames, usually created with relativities() and split_level().

exposure

Character string. Exposure column used for weighting and, when requested, normalisation.

normalize

Logical. If TRUE, normalise the supplied relativities by exposure within each split model level.

Value

Object of class rating_refinement.

Details

model_variable is the variable already used in the GLM. split_variable is the more detailed variable in the portfolio data that will be used to split one or more levels of model_variable. The relativities argument should be a named list describing those splits, usually built with relativities() and split_level().

The step is stored on the rating_refinement object and is applied when refit() is called. When normalize = TRUE, the supplied relativities are normalised using exposure so that the refined split keeps the original level effect on average. This helps prevent an expert split from unintentionally changing the total premium level for the original model group.

When to use

add_relativities() is intended for refinement within an already reasonably homogeneous GLM segment. It redistributes an existing coefficient across sublevels using exposure-weighted relativities, while preserving the overall level of the original coefficient. This is useful for mild heterogeneity, commercial refinement, monotonic tariff differentiation, or expert-based segmentation within a stable risk group where the original GLM coefficient is broadly representative.

Limitations

The method is not a substitute for creating a separate risk segment when the original GLM coefficient is itself distorted. For example, suppose a broad industry segment contains many relatively stable businesses, but a few chemical companies drive most of the losses while representing little exposure. The fitted industry coefficient may then be dominated by the chemical companies' experience. Applying exposure-weighted relativities inside that segment may barely reduce the coefficient for the large exposure group, because the original coefficient is already pulled upward by the outlier subgroup.

In that situation it is often better to create a separate GLM factor level, derive a separate tariff segment, or apply explicit segmentation or acceptation rules, instead of relying only on add_relativities().

Author

Martin Haringa

Examples

portfolio <- data.frame(
  claims = c(1, 2, 1, 3, 2, 4),
  exposure = rep(1, 6),
  construction = factor(c("residential", "commercial", "residential",
                          "commercial", "residential", "commercial")),
  construction_detail = factor(c("flat", "shop", "house",
                                 "office", "flat", "shop"))
)

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

relativities <- relativities(
  split_level(
    "residential",
    new_levels = c("flat", "house"),
    relativities = c(0.95, 1.05)
  )
)

refined <- prepare_refinement(model, data = portfolio) |>
  add_relativities(
    model_variable = "construction",
    split_variable = "construction_detail",
    relativities = relativities,
    exposure = "exposure"
  )