Restrict coefficients in the model

Add restrictions, like a bonus-malus structure, on the risk factors used in the model. restrict_coef() must always be followed by update_glm().

Usage

restrict_coef(model, restrictions)

Arguments

model: object of class glm/restricted
restrictions: data.frame with two columns containing restricted data. The first column, with the name of the risk factor as column name, must contain the levels of the risk factor. The second column must contain the restricted coefficients.

Value

Object of class restricted.

Details

Although restrictions could be applied either to the frequency or the severity model, it is more appropriate to impose the restrictions on the premium model. This can be achieved by calculating the pure premium for each record (i.e. expected number of claims times the expected claim amount), then fitting an "unrestricted" Gamma GLM to the pure premium,and then imposing the restrictions in a final "restricted" Gamma GLM.

Author

Martin Haringa

Examples

if (FALSE) { # \dontrun{
# Add restrictions to risk factors for region (zip) -------------------------

# Fit frequency and severity model
library(dplyr)
freq <- glm(nclaims ~ bm + zip, offset = log(exposure), family = poisson(),
             data = MTPL)
sev <- glm(amount ~ bm + zip, weights = nclaims,
            family = Gamma(link = "log"),
            data = MTPL |> filter(amount > 0))

# Add predictions for freq and sev to data, and calculate premium
premium_df <- MTPL |>
   add_prediction(freq, sev) |>
   mutate(premium = pred_nclaims_freq * pred_amount_sev)

# Restrictions on risk factors for region (zip)
zip_df <- data.frame(zip = c(0,1,2,3), zip_rst = c(0.8, 0.9, 1, 1.2))

# Fit unrestricted model
burn <- glm(premium ~ bm + zip, weights = exposure,
            family = Gamma(link = "log"), data = premium_df)

# Fit restricted model
burn_rst <- burn |>
  restrict_coef(restrictions = zip_df) |>
  update_glm()

# Show rating factors
rating_factors(burn_rst)
} # }