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Add model predictions to a pricing data set

Source: R/model_add_prediction.R
add_prediction.Rd

add_prediction() adds predictions from one or more fitted glm models to a data frame.

In pricing workflows, this is often used to bring count and severity model output together on the same portfolio. For example, an expected claim count can be normalised by exposure and multiplied by an expected average claim amount to calculate a risk premium per exposure unit.

The function is deliberately small: it does not refit models or decide how predictions should be combined. It only adds model predictions, and optionally confidence intervals, using clear output column names.

Usage

add_prediction(
  data,
  ...,
  predictions = NULL,
  prefix = "pred",
  confidence = FALSE,
  interval_names = c("lower", "upper"),
  alpha = 0.1,
  var = NULL,
  conf_int = NULL
)

Arguments

data

A data.frame containing the new data for which predictions should be generated.

...

One or more fitted model objects of class "glm".

predictions

Optional character vector giving names for the new prediction columns. Must have the same length as the number of models supplied. If NULL (default), names are generated automatically using prefix, the model response, and the model object name.

prefix

Character. Prefix used for automatically generated prediction column names. Default is "pred".

confidence

Logical. If TRUE, add confidence intervals for predictions. Default is FALSE.

interval_names

Character vector of length two. Names appended to the prediction column name for lower and upper confidence interval bounds. Default is c("lower", "upper").

alpha

Numeric between 0 and 1. Controls the miscoverage level for interval estimates. Default is 0.10, corresponding to a 90% confidence interval.

var

Deprecated. Use predictions instead.

conf_int

Deprecated. Use confidence instead.

Value

A data.frame containing the original data and additional columns for model predictions. If confidence = TRUE, confidence interval columns are added as well.

Details

Predictions are calculated on the response scale using stats::predict(..., type = "response"). For GLMs with a log link, such as Poisson count models or Gamma severity models, the added columns are already on the original response scale. For a Poisson claim-count model containing an exposure offset, this is the expected claim count for the supplied exposure, not frequency per exposure unit. Divide by exposure when a rate is required.

If confidence = TRUE, lower and upper confidence interval columns are added next to each prediction column. The default interval suffixes are "lower" and "upper".

Predictions containing missing values are retained. If one or more NA predictions are produced, the function issues a warning with the affected prediction columns and number of missing predictions. This is typically caused by missing predictor values in data or by predictor values outside the domain supported by the fitted model.

Author

Martin Haringa

Examples

mod1 <- glm(nclaims ~ age_policyholder,
            data = MTPL,
            offset = log(exposure),
            family = poisson())

# Add the expected claim count for each record's exposure
mtpl_pred <- add_prediction(
  MTPL,
  mod1,
  predictions = "expected_claim_count"
)

# Add predicted values with confidence bounds
mtpl_pred_ci <- add_prediction(
  MTPL,
  mod1,
  predictions = "expected_claim_count",
  confidence = TRUE
)

# Combine frequency and severity predictions into a risk premium
freq <- glm(nclaims ~ bm + zip,
            data = MTPL,
            offset = log(exposure),
            family = poisson())

severity_data <- MTPL[MTPL$nclaims > 0 & MTPL$amount > 0, ]
severity_data$average_claim_amount <-
  severity_data$amount / severity_data$nclaims

sev <- glm(average_claim_amount ~ bm + zip,
           data = severity_data,
           weights = nclaims,
           family = Gamma(link = "log"))

pricing <- add_prediction(
  MTPL,
  freq,
  sev,
  predictions = c("expected_claim_count", "expected_average_severity")
)

pricing$claim_frequency <-
  pricing$expected_claim_count / pricing$exposure
pricing$expected_loss <-
  pricing$expected_claim_count * pricing$expected_average_severity
pricing$risk_premium <-
  pricing$claim_frequency * pricing$expected_average_severity