buhlmannStraubTweedie: Combining the Buhlmann-Straub credibility model with a...

In actuaRE: Handling Single-Level and Hierarchically Structured Risk Factors using Credibility and Random Effects Models

Combining the Buhlmann-Straub credibility model with a Tweedie GLM (Ohlsson, 2008)

Description

Fit a single-level random effects model using Ohlsson's methodology combined with Buhlmann-Straub credibility. This function estimates the power parameter p. For fixed p, see buhlmannStraubGLM.

Usage

buhlmannStraubTweedie(
  formula,
  data,
  weights,
  muHatGLM = FALSE,
  epsilon = 1e-04,
  maxiter = 500,
  verbose = FALSE,
  returnData = TRUE,
  cpglmControl = list(bound.p = c(1.01, 1.99)),
  balanceProperty = TRUE,
  optimizer = "bobyqa",
  y = TRUE,
  ...
)

Arguments

formula	object of type formula that specifies which model should be fitted. Syntax follows lmer: e.g., Y ~ x1 + x2 + (1 | Cluster). Only one random effect is allowed.
data	an object that is coercible by as.data.table, containing the variables in the model.
weights	variable name of the exposure weight.
muHatGLM	indicates which estimate has to be used in the algorithm for the intercept term. Set to TRUE to use the intercept as estimated by the GLM. If FALSE, the estimate of the Buhlmann-Straub credibility model is used.
epsilon	positive convergence tolerance \epsilon; the iterations converge when ||\theta[k] - \theta[k - 1]||^2_2/||\theta[k - 1]||^2_2 < \epsilon. Here, \theta[k] is the parameter vector at the k^{th} iteration.
maxiter	maximum number of iterations.
verbose	logical indicating if output should be produced during the algorithm.
returnData	logical indicating if input data has to be returned.
cpglmControl	a list of parameters to control the fitting process in the GLM part. By default, cpglmControl = list(bound.p = c(1.01, 1.99)) which restricts the range of the power parameter p to [1.01, 1.99] in the fitting process. This list is passed to cpglm.
balanceProperty	logical indicating if the balance property should be satisfied.
optimizer	a character string that determines which optimization routine is to be used in estimating the index and the dispersion parameters. Possible choices are "nlminb" (the default, see nlminb), "bobyqa" (bobyqa) and "L-BFGS-B" (optim).
y	logical indicating whether the response vector should be returned as a component of the returned value.
...	arguments passed to cpglm.

Details

When estimating the GLM part, this function uses the cpglm function from the cplm package.

Value

An object of type buhlmannStraubTweedie with the following slots:

call	the matched call
CredibilityResults	results of the Buhlmann-Straub credibility model.
fitGLM	the results from fitting the GLM part.
iter	total number of iterations.
Converged	logical indicating whether the algorithm converged.
LevelsCov	object that summarizes the unique levels of each of the contract-specific covariates.
fitted.values	the fitted mean values, resulting from the model fit.
prior.weights	the weights (exposure) initially supplied.
y	if requested, the response vector. Default is TRUE.

References

Campo, B.D.C. and Antonio, Katrien (2023). Insurance pricing with hierarchically structured data an illustration with a workers' compensation insurance portfolio. Scandinavian Actuarial Journal, doi: 10.1080/03461238.2022.2161413

Ohlsson, E. (2008). Combining generalized linear models and credibility models in practice. Scandinavian Actuarial Journal 2008(4), 301–314.

See Also

buhlmannStraubTweedie-class, buhlmannStraub, buhlmannStraubGLM, hierCredTweedie, cpglm, plotRE, adjustIntercept, BalanceProperty

Examples

data("hachemeister", package = "actuar")
X = as.data.frame(hachemeister)
Df = reshape(X, idvar = "state",
             varying = list(paste0("ratio.", 1:12), paste0("weight.", 1:12)),
             direction = "long")
Df$time_factor = factor(Df$time)
fit = buhlmannStraubTweedie(ratio.1 ~ time_factor + (1 | state), Df,
                            weights = weight.1, epsilon = 1e-6)
summary(fit)
ranef(fit)
fixef(fit)

actuaRE documentation built on July 3, 2026, 5:07 p.m.