tweedieGLMM: Fitting a Tweedie GLMM, using initial estimates from credibility models

Description

This function first estimates the random effects model using Ohlsson's GLMC algorithm (Ohlsson, 2008) and then uses these estimates as initial estimates when fitting a Tweedie GLMM. Supports both single random effects and nested random effects.

Usage

tweedieGLMM(
  formula,
  data,
  weights,
  muHatGLM = FALSE,
  epsilon = 1e-04,
  maxiter = 500,
  verbose = FALSE,
  balanceProperty = TRUE
)

Value

an object of class cpglmm, containing the model fit.

Arguments

formula: object of type formula that specifies which model should be fitted. Syntax is the same as for lmer and glmer. For single random effect: Y ~ x1 + x2 + (1 | Cluster). For nested random effects: Y ~ x1 + x2 + (1 | cluster / subcluster).
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. Default is FALSE, which uses the intercept as estimated by the credibility model. If TRUE, the estimate of the GLM 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.
balanceProperty: logical indicating if the balance property should be satisfied.

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.

Examples

Run this code

# \donttest{
# Nested random effects example
data("tweedietraindata")
fit = tweedieGLMM(y ~ x1 + (1 | cluster / subcluster), tweedietraindata, weights = wt)
fit
# }