risk_factor_gam: Fit a GAM for a continuous risk factor

In insurancerating: Actuarial Tools for Insurance Pricing Models

Fit a GAM for a continuous risk factor

Description

Fits a generalized additive model (GAM) to a continuous risk factor in one of three insurance pricing contexts: claim frequency, claim severity, or pure premium. The fitted curve helps assess non-linear rating effects before a continuous variable is grouped into tariff segments or used in a GLM workflow.

Usage

risk_factor_gam(
  data,
  risk_factor = NULL,
  claim_count = NULL,
  exposure = NULL,
  claim_amount = NULL,
  pure_premium = NULL,
  model = "frequency",
  round_risk_factor = NULL,
  x = NULL,
  nclaims = NULL,
  amount = NULL,
  round_x = NULL
)

Arguments

data	A data.frame containing the insurance portfolio.
risk_factor	Character, name of column in data with the continuous risk factor.
claim_count	Character, name of column in data with the number of claims.
exposure	Character, name of column in data with the exposure.
claim_amount	(Optional) Character, column name in data with the claim amount. Required for model = "severity".
pure_premium	(Optional) Character, column name in data with the pure premium. Required for model = "pure_premium".
model	Character string specifying the model type. One of "frequency", "severity", or "pure_premium". Default is "frequency". The old value "burning" is deprecated and maps to "pure_premium".
round_risk_factor	(Optional) Numeric value to round the risk factor to a multiple of round_risk_factor. Can speed up fitting for factors with many distinct values.
x, nclaims, amount, round_x	Deprecated argument names. Use risk_factor, claim_count, claim_amount, and round_risk_factor instead.

Details

• Frequency model: Fits a Poisson GAM to the number of claims. The log of the exposure is used as an offset so the expected number of claims is proportional to exposure.

• Severity model: Fits a Gamma GAM with log link to the average claim size (total amount divided by number of claims). The number of claims is included as a weight.

• Pure premium model: Fits a Gamma GAM with log link to the pure premium (risk premium). Implemented by aggregating exposure-weighted pure premiums. The deprecated model value "burning" is still accepted for backward compatibility.

Migration from fit_gam()

The function fit_gam() is deprecated as of version 0.8.0 and replaced by risk_factor_gam(). In addition to the name change, the interface has also changed:

• fit_gam() used non-standard evaluation (NSE), so column names could be passed unquoted (e.g. x = age_policyholder).

• risk_factor_gam() uses standard evaluation (SE), so column names must be passed as character strings (e.g. risk_factor = "age_policyholder").

This makes the function easier to use in programmatic workflows.

riskfactor_gam() and fit_gam() are still available for backward compatibility but will emit deprecation warnings.

Value

A list of class "riskfactor_gam" with the following elements:

prediction	A data frame with predicted values and confidence intervals.
x	Name of the continuous risk factor.
model	The model type: "frequency", "severity", or "pure_premium".
data	Merged data frame with predictions and observed values.
x_obs	Observed values of the continuous risk factor.

Author(s)

Martin Haringa

References

Antonio, K. and Valdez, E. A. (2012). Statistical concepts of a priori and a posteriori risk classification in insurance. Advances in Statistical Analysis, 96(2):187–224.

Henckaerts, R., Antonio, K., Clijsters, M. and Verbelen, R. (2018). A data driven binning strategy for the construction of insurance tariff classes. Scandinavian Actuarial Journal, 2018:8, 681–705.

Wood, S.N. (2011). Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. Journal of the Royal Statistical Society (B) 73(1):3–36.

Examples

## --- Recommended new usage (SE) ---
# Column names must be passed as strings
risk_factor_gam(MTPL,
                risk_factor = "age_policyholder",
                claim_count = "nclaims",
                exposure = "exposure")

## --- Deprecated usage (NSE) ---
# This still works but will show a warning
fit_gam(MTPL,
        nclaims = nclaims,
        x = age_policyholder,
        exposure = exposure)

insurancerating documentation built on July 30, 2026, 5:09 p.m.