hierCredGLM {actuaRE} | R Documentation |

## Combining the hierarchical credibility model with a GLM (Ohlsson, 2008)

### Description

Fit a random effects model using Ohlsson's methodology. In this function you explicitly specify the power parameter p.
See `hierCredTweedie`

when you also want to estimate the p.

### Usage

```
hierCredGLM(
formula,
data,
weights,
p = 1.5,
link.power = 0,
muHatGLM = TRUE,
epsilon = 1e-04,
maxiter = 500,
maxiterGLM = 500,
verbose = FALSE,
returnData = TRUE,
balanceProperty = TRUE,
y = TRUE,
...
)
```

### Arguments

`formula` |
object of type |

`data` |
an object that is coercible by |

`weights` |
variable name of the exposure weight. |

`p` |
the value for the power parameter of the Tweedie distribution, which is passed to |

`link.power` |
index of power link function, which is passed to |

`muHatGLM` |
indicates which estimate has to be used in the algorithm for the intercept term. Default is |

`epsilon` |
positive convergence tolerance |

`maxiter` |
maximum number of iterations. |

`maxiterGLM` |
maximum number of iterations when fitting the GLM part. Passed to |

`verbose` |
logical indicating if output should be produced during the algorithm. |

`returnData` |
logical indicating if input data has to be returned. |

`balanceProperty` |
logical indicating if the balance property should be satisfied. |

`y` |
logical indicating whether the response vector should be returned as a component of the returned value. |

`...` |
arguments passed to |

### Value

An object of type `hierCredGLM`

with the following slots:

`call` |
the matched call |

`HierarchicalResults` |
results of the hierarchical 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 |

### 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

`hierCredGLM-class`

, `fitted.hierCredGLM`

, `predict.hierCredGLM`

, `ranef-actuaRE`

,
`weights-actuaRE`

, `hierCredibility`

, `hierCredTweedie`

, `plotRE`

,
`adjustIntercept`

, `BalanceProperty`

### Examples

```
data("dataCar")
fit = hierCredGLM(Y ~ area + (1 | VehicleType / VehicleBody), dataCar, weights = w,
p = 1.7)
fit
summary(fit)
ranef(fit)
fixef(fit)
```

*actuaRE*version 0.1.5 Index]