Package 'actuaRE' reference manual

Title:	Handling Hierarchically Structured Risk Factors using Random Effects Models
Description:	Using this package, you can fit a random effects model using either the hierarchical credibility model, a combination of the hierarchical credibility model with a generalized linear model or a Tweedie generalized linear mixed model. See Campo, B.D.C. and Antonio, K. (2023) <doi:10.1080/03461238.2022.2161413>.
Authors:	Campo Bavo D.C. [aut, cre]
Maintainer:	Campo Bavo D.C. <[email protected]>
License:	GPL (>= 3)
Version:	0.1.5
Built:	2025-03-08 04:01:34 UTC
Source:	https://github.com/cran/actuaRE

Handling Hierarchically Structured Risk Factors using Random Effects Models

Description

Using this package, you can fit a random effects model using either the hierarchical credibility model, a combination of the hierarchical credibility model with a generalized linear model or a Tweedie generalized linear mixed model. See Campo, B.D.C. and Antonio, K. (2023) <doi:10.1080/03461238.2022.2161413>.

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

Dannenburg, D. R., Kaas, R. and Goovaerts, M. J. (1996). Practical actuarial credibility models. Amsterdam: IAE (Institute of Actuarial Science and Econometrics of the University of Amsterdam).

Jewell, W. S. (1975). The use of collateral data in credibility theory: a hierarchical model. Laxenburg: IIASA.

Ohlsson, E. (2005). Simplified estimation of structure parameters in hierarchical credibility. Presented at the Zurich ASTIN Colloquium.http://www.actuaries.org/ASTIN/Colloquia/Zurich/Ohlsson.pdf

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

Examples


  library(actuaRE)
  # Vignette of the package
  vignette(package = "actuaRE")

  # Load data
  data(hachemeisterLong)
  data(dataCar)

  # Hierarchical credibility model of Jewell
  fit = hierCredibility(ratio, weight, cohort, state, hachemeisterLong)

  # Combination of the hierarchical credibility model with a GLM (Ohlsson, 2008)
  fit = hierCredGLM(Y ~ area + (1 | VehicleType / VehicleBody), dataCar, weights = w,
  p = 1.7)

library(actuaRE)
  # Vignette of the package
  vignette(package = "actuaRE")

  # Load data
  data(hachemeisterLong)
  data(dataCar)

  # Hierarchical credibility model of Jewell
  fit = hierCredibility(ratio, weight, cohort, state, hachemeisterLong)

  # Combination of the hierarchical credibility model with a GLM (Ohlsson, 2008)
  fit = hierCredGLM(Y ~ area + (1 | VehicleType / VehicleBody), dataCar, weights = w,
  p = 1.7)

Add random effects to the data frame

Description

Internal function

Usage

.addREs(obj, newdata)
.addREs(obj, newdata)

Arguments

`obj`	object with model fit
`newdata`	an object coercible to `data.table`.

Adjust the intercept to regain the balance property

Description

This function updates the intercept term of the model fit such that the balance property is satisfied.

Usage

adjustIntercept(obj, data)
adjustIntercept(obj, data)

Arguments

`obj`	an object of type `glm`, `cpglm` or `cpglmm` containing the model fit.
`data`	a `data.frame` or `data.table` object that was used to fit the model.

Value

The object with the adjusted (fixed effects) coefficients.

References

Wüthrich, M. V. (2020). Bias regularization in neural network models for general insurance pricing. European actuarial journal 10(1), 179–202.

Examples

library(statmod)
datas  = dataCar[1:1e3, ]
Fit    = glm(Y ~ area + gender, data = datas, weights = datas$w, family = tweedie(1.75, 0),
model = TRUE, control = glm.control(epsilon = 1e-4, maxit = 5e2))
w      = weights(Fit, "prior")
y      = Fit$y
sum(w * y) == sum(w * fitted(Fit))
adjFit = adjustIntercept(Fit, datas)
coef(adjFit)
sum(w * y) == sum(w * fitted(adjFit))
library(statmod)
datas  = dataCar[1:1e3, ]
Fit    = glm(Y ~ area + gender, data = datas, weights = datas$w, family = tweedie(1.75, 0),
model = TRUE, control = glm.control(epsilon = 1e-4, maxit = 5e2))
w      = weights(Fit, "prior")
y      = Fit$y
sum(w * y) == sum(w * fitted(Fit))
adjFit = adjustIntercept(Fit, datas)
coef(adjFit)
sum(w * y) == sum(w * fitted(adjFit))

Balance property

Description

Function to assess whether the balance property holds

Usage

BalanceProperty(obj)
BalanceProperty(obj)

Arguments

obj

an object containing the model fit

Value

a list with the slots call (the original call), BalanceProperty (logical indicating whether the balance property is satisfied) and Alpha (Ratio total observed damage to total predicted damage).

References

Wüthrich, M. V. (2020). Bias regularization in neural network models for general insurance pricing. European actuarial journal 10(1), 179–202.

Examples


fit = hierCredGLM(Y ~ area + (1 | VehicleType / VehicleBody), dataCar, weights = w,
 p = 1.75, epsilon = 1e-6)
BalanceProperty(fit)

fit = hierCredGLM(Y ~ area + (1 | VehicleType / VehicleBody), dataCar, weights = w,
 p = 1.75, epsilon = 1e-6)
BalanceProperty(fit)

data Car

Description

This data set is taken from the dataCar data set of the insuranceData package and slightly adjusted (see the code in examples for reproducing this data set). The original data set is based on one-year vehicle insurance policies taken out in 2004 or 2005. There are 67566 policies, of which 4589 (6.8%) had at least one claim.

Usage

data(dataCar)data(dataCar)

Format

A data frame with 67566 observations on the following 15 variables.

veh_value: vehicle value, in $10,000s
exposure: 0-1
clm: occurrence of claim (0 = no, 1 = yes)
numclaims: number of claims
claimcst0: claim amount (0 if no claim)
veh_body: vehicle body, coded as BUS CONVT COUPE HBACK HDTOP MCARA MIBUS PANVN RDSTR SEDAN STNWG TRUCK UTE
veh_age: 1 (youngest), 2, 3, 4
gender: a factor with levels F M
area: a factor with levels A B C D E F
agecat: 1 (youngest), 2, 3, 4, 5, 6
X_OBSTAT_: a factor with levels 01101 0 0 0
Y: the loss ratio, defined as the number of claims divided by the exposure
w: the exposure, identical to exposure
VehicleType: type of vehicle, common vehicle or uncommon vehicle
VehicleBody: vehicle body, identical to veh_body

Details

Adjusted data set dataCar, where we removed claims with a loss ratio larger than 1 000 000. In addition, we summed the exposure per vehicle body and removed those where the summed exposure was less than 100. Hereby, we ensure that there is sufficient exposure for each vehicle body category.

Source

http://www.acst.mq.edu.au/GLMsforInsuranceData

References

De Jong P., Heller G.Z. (2008), Generalized linear models for insurance data, Cambridge University Press

Examples

  # How to construct the data set using the original dataCar data set from the insuranceData package
  library(plyr)
  library(magrittr)
  data("dataCar", package = "insuranceData")
  dataCar$Y = with(dataCar, claimcst0 / exposure)
  dataCar$w = dataCar$exposure
  dataCar   = dataCar[which(dataCar$Y < 1e6), ]
  Yw = ddply(dataCar, .(veh_body), function(x) c(crossprod(x$Y, x$w) / sum(x$w), sum(x$w)))
  dataCar = dataCar[!dataCar$veh_body %in% Yw[Yw$V2 < 1e2, "veh_body"], ]
  dataCar$veh_body %<>% droplevels()
  dataCar$VehicleType = sapply(tolower(dataCar$veh_body), function(x) {
    if(x %in% c("sedan", "ute", "hback"))
      "Common vehicle"
    else
      "Uncommon vehicle"
  })
  dataCar$VehicleBody = dataCar$veh_body
# How to construct the data set using the original dataCar data set from the insuranceData package
  library(plyr)
  library(magrittr)
  data("dataCar", package = "insuranceData")
  dataCar$Y = with(dataCar, claimcst0 / exposure)
  dataCar$w = dataCar$exposure
  dataCar   = dataCar[which(dataCar$Y < 1e6), ]
  Yw = ddply(dataCar, .(veh_body), function(x) c(crossprod(x$Y, x$w) / sum(x$w), sum(x$w)))
  dataCar = dataCar[!dataCar$veh_body %in% Yw[Yw$V2 < 1e2, "veh_body"], ]
  dataCar$veh_body %<>% droplevels()
  dataCar$VehicleType = sapply(tolower(dataCar$veh_body), function(x) {
    if(x %in% c("sedan", "ute", "hback"))
      "Common vehicle"
    else
      "Uncommon vehicle"
  })
  dataCar$VehicleBody = dataCar$veh_body

Determine random-effects expressions from a formula

Description

From the right hand side of a formula for a mixed-effects model, determine the pairs of expressions that are separated by the vertical bar operator. Also expand the slash operator in grouping factor expressions and expand terms with the double vertical bar operator into separate, independent random effect terms.

Usage

  findbars(term)
findbars(term)

Arguments

term

a mixed-model formula

Value

pairs of expressions that were separated by vertical bars

Note

This function is called recursively on individual terms in the model, which is why the argument is called term and not a name like form, indicating a formula.

Examples

  findbars(f1 <- Reaction ~ Days + (Days | Subject))
  ## => list( Days | Subject )
  ## These two are equivalent:% tests in ../inst/tests/test-doubleVertNotation.R
  findbars(y ~ Days + (1 | Subject) + (0 + Days | Subject))
  findbars(y ~ Days + (Days || Subject))
  ## => list of length 2:  list ( 1 | Subject ,  0 + Days | Subject)
  findbars(~ 1 + (1 | batch / cask))
  ## => list of length 2:  list ( 1 | cask:batch ,  1 | batch)
  
findbars(f1 <- Reaction ~ Days + (Days | Subject))
  ## => list( Days | Subject )
  ## These two are equivalent:% tests in ../inst/tests/test-doubleVertNotation.R
  findbars(y ~ Days + (1 | Subject) + (0 + Days | Subject))
  findbars(y ~ Days + (Days || Subject))
  ## => list of length 2:  list ( 1 | Subject ,  0 + Days | Subject)
  findbars(~ 1 + (1 | batch / cask))
  ## => list of length 2:  list ( 1 | cask:batch ,  1 | batch)

Extract fixed-effects estimates

Description

Extract the fixed-effects estimates

Arguments

object

any fitted model object from which fixed effects estimates can be extracted.

Details

Extract the estimates of the fixed-effects parameters from a fitted model.

Value

a named, numeric vector of fixed-effects estimates.

Examples

  
  library(lme4)
  fixef(lmer(Reaction ~ Days + (1|Subject) + (0+Days|Subject), sleepstudy))
  fm2 <- lmer(Reaction ~ Days + Days2 + (1|Subject),
              data=transform(sleepstudy,Days2=Days))
  fixef(fm2,add.dropped=TRUE)
  ## first two parameters are the same ...
  stopifnot(all.equal(fixef(fm2,add.dropped=TRUE)[1:2],
                      fixef(fm2)))
  
library(lme4)
  fixef(lmer(Reaction ~ Days + (1|Subject) + (0+Days|Subject), sleepstudy))
  fm2 <- lmer(Reaction ~ Days + Days2 + (1|Subject),
              data=transform(sleepstudy,Days2=Days))
  fixef(fm2,add.dropped=TRUE)
  ## first two parameters are the same ...
  stopifnot(all.equal(fixef(fm2,add.dropped=TRUE)[1:2],
                      fixef(fm2)))

Extract the fixed-effects estimates from a fitted random effects model

Description

A generic function to extract the fixed effects (i.e. the company-specific effects) estimates from a fitted random effects model.

Usage

## S3 method for class 'hierCredGLM'
fixef(object, ...)

## S3 method for class 'hierCredTweedie'
fixef(object, ...)
## S3 method for class 'hierCredGLM'
fixef(object, ...)

## S3 method for class 'hierCredTweedie'
fixef(object, ...)

Arguments

`object`	an object of type `hierCredGLM` or `hierCredTweedie`
`...`	ignored.

Value

a named, numeric vector of fixed-effects estimates.

Examples


fit = hierCredGLM(Y ~ area + (1 | VehicleType / VehicleBody), dataCar,
weights = w, p = 1.75, epsilon = 1e-6)
fixef(fit)

fit = hierCredGLM(Y ~ area + (1 | VehicleType / VehicleBody), dataCar,
weights = w, p = 1.75, epsilon = 1e-6)
fixef(fit)

Hachemeister Data Set

Description

Long format of the Hachemeister (1975) data set giving average claim amounts in private passenger bodily injury insurance. We have data of five U.S. states over 12 quarters between July 1970 and June 1973 and we have the corresponding number of claims. To obtain a hierarchical structure, we created an artificial variable cohort. With this, we created a hierarchical multi-level factor, with cohort as the first hierarchical level and state as the second hierarchical level, nested within cohort.

Usage

hachemeisterLonghachemeisterLong

Format

A data.frame with 60 rows and the following 5 columns:

cohort: artificially created variable;
state: the state number;
time: time variable (quarter of the observation);
ratio: the average claim amount;
weight: the corresponding number of claims.

Source

Hachemeister, C. A. (1975), Credibility for regression models with application to trend, Proceedings of the Berkeley Actuarial Research Conference on Credibility, Academic Press.

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,
  ...
)
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 `formula` that specifies which model should be fitted. Syntax is the same as for `lmer` and `glmer`. For example, `Yijkt ~ x1 + x2 + (1 \| Industry / Branch)`.
`data`	an object that is coercible by `as.data.table`, containing the variables in the model.
`weights`	variable name of the exposure weight.
`p`	the value for the power parameter of the Tweedie distribution, which is passed to `tweedie`. Default is `1.5`.
`link.power`	index of power link function, which is passed to `tweedie`. `link.power = 0` produces a log-link. Defaults to the canonical link, which is `1 - p`.
`muHatGLM`	indicates which estimate has to be used in the algorithm for the intercept term. Default is `TRUE`, which used the intercept as estimated by the GLM. If `FALSE`, the estimate of the hierarchical credibility model is used.
`epsilon`	positive convergence tolerance $\epsilon$ ; the iterations converge when 7 $\|\|\theta[k] - \theta[k - 1]\|\|^2[[2]]/\|\|\theta[k - 1]\|\|^2[[2]] < \epsilon$ . Here, $\theta[k]$ is the parameter vector at the $k^{th}$ iteration.
`maxiter`	maximum number of iterations.
`maxiterGLM`	maximum number of iterations when fitting the GLM part. Passed to `glm`.
`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 `glm`

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 `TRUE`.

References

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

Examples


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

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

Class "hierCredGLM" of fitted random effects models estimated with Ohlsson's GLMC algorithm

Description

Class "hierCredGLM" of fitted random effects models estimated with Ohlsson's GLMC algorithm

Usage

## S3 method for class 'hierCredGLM'
print(x, ...)

## S3 method for class 'hierCredGLM'
summary(object, ...)

## S3 method for class 'hierCredGLM'
fitted(object, ...)
## S3 method for class 'hierCredGLM'
print(x, ...)

## S3 method for class 'hierCredGLM'
summary(object, ...)

## S3 method for class 'hierCredGLM'
fitted(object, ...)

Arguments

`x`	an object of class `hierCredGLM`
`...`	currently ignored.
`object`	an object of class `hierCredGLM`

Value

The function hierCredGLM returns an object of class hierCredGLM, which has 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 `TRUE`.

S3 methods

print:: Prints the call, the estimated variance parameters, the unique number of categories of the hierarchical MLF and the output of the GLM part. The ... argument is currently ignored. Returns an invisible copy of the original object.
summary:: In addition to the output of the print.hierCredGLM function, the summary function also prints the random effect estimates and a summary of the GLM (see summary.glm). Returns an invisible copy of the original object.
fitted:: Returns the fitted values.

Hierarchical credibility model of Jewell

Description

Fit a random effects model, without contract-specific risk factors, using the hierarchical credibility model of Jewell.

Usage

hierCredibility(
  Yijkt,
  wijkt,
  sector,
  group,
  data,
  muHat = NULL,
  type = c("additive", "multiplicative"),
  returnData = FALSE
)
hierCredibility(
  Yijkt,
  wijkt,
  sector,
  group,
  data,
  muHat = NULL,
  type = c("additive", "multiplicative"),
  returnData = FALSE
)

Arguments

`Yijkt`	variable name of the response variable (the loss cost within actuarial applications).
`wijkt`	variable name of the exposure weight.
`sector`	variable name of the first hierarchical level.
`group`	variable name of the second hierarchical level that is nested within the first hierarchical level.
`data`	an object that is coercible by `as.data.table`, containing the variables in the model.
`muHat`	estimate for the intercept term. Default is `NULL` and in this case, the estimator as given in Ohlsson (2005) is used.
`type`	specifies whether the additive (Dannenburg, 1996) or multiplicative (Ohlsson, 2005) formulation of the hierarchical credibility model is used. Default is additive.
`returnData`	Logical, indicates whether the data object has to be returned. Default is `FALSE`.

Value

An object of type hierCredibility with the following slots:

`call`	the matched call
`type`	Whether additive or multiplicative hierarchical credibility model is used.
`Variances`	The estimated variance components. `s2` is the estimated variance of the individual contracts, `tausq` the estimate of $Var(V[j])$ and `nusq` is the estimate of $Var(V[jk])$ .
`Means`	The estimated averages at the portfolio level (intercept term $\mu$ ), at the first hierarchical level ( $bar(Y)[\%.\% j \%.\% \%.\%]^z$ ) and at the second hierarchical level ( $bar(Y)[\%.\% jk \%.\%]$ ).
`Weights`	The weights at the first hierarchical level $z[j\%.\%]$ and at the second hierarchical level $w[\%.\%jk\%.\%]$ .
`Credibility`	The credibility weights at the first hierarchical level $q[j\%.\%]$ and at the second hierarchical level $z[jk]$ .
`Premiums`	The overall expectation $widehat(\mu)$ , sector expectation $widehat(V)[j]$ and group expectation $widehat(V)[jk]$ .
`Relativity`	The estimated random effects $widehat(U)[j]$ and $widehat(U)[jk]$ of the sector and group, respectively.
`RawResults`	Objects of type `data.table` with all intermediate results.
`fitted.values`	the fitted mean values, resulting from the model fit.

References

Dannenburg, D. R., Kaas, R. and Goovaerts, M. J. (1996). Practical actuarial credibility models. Amsterdam: IAE (Institute of Actuarial Science and Econometrics of the University of Amsterdam).

Jewell, W. S. (1975). The use of collateral data in credibility theory: a hierarchical model. Laxenburg: IIASA.

Ohlsson, E. (2005). Simplified estimation of structure parameters in hierarchical credibility. Presented at the Zurich ASTIN Colloquium.http://www.actuaries.org/ASTIN/Colloquia/Zurich/Ohlsson.pdf

Examples

library(actuar)
library(actuaRE)
data("hachemeister", package = "actuar")
Df = as.data.frame(hachemeister)
X  = as.data.frame(cbind(cohort = c(1, 2, 1, 2, 2), hachemeister))
Df = reshape(X, idvar = "state", varying = list(paste0("ratio.", 1:12),
 paste0("weight.", 1:12)), direction = "long")
fitActuar  = cm(~ cohort + cohort:state, data = X, ratios = ratio.1:ratio.12,
weights = weight.1:weight.12, method = "Ohlsson")
fitActuaRE = hierCredibility(ratio.1, weight.1, cohort, state, Df)
summary(fitActuar)
summary(fitActuaRE)
library(actuar)
library(actuaRE)
data("hachemeister", package = "actuar")
Df = as.data.frame(hachemeister)
X  = as.data.frame(cbind(cohort = c(1, 2, 1, 2, 2), hachemeister))
Df = reshape(X, idvar = "state", varying = list(paste0("ratio.", 1:12),
 paste0("weight.", 1:12)), direction = "long")
fitActuar  = cm(~ cohort + cohort:state, data = X, ratios = ratio.1:ratio.12,
weights = weight.1:weight.12, method = "Ohlsson")
fitActuaRE = hierCredibility(ratio.1, weight.1, cohort, state, Df)
summary(fitActuar)
summary(fitActuaRE)

Class "hierCredibility" of fitted hierarchical credibility models

Description

Class "hierCredibility" of fitted hierarchical credibility models

Usage

## S3 method for class 'hierCredibility'
print(x, ...)

## S3 method for class 'hierCredibility'
summary(object, ...)

## S3 method for class 'hierCredibility'
fitted(object, ...)
## S3 method for class 'hierCredibility'
print(x, ...)

## S3 method for class 'hierCredibility'
summary(object, ...)

## S3 method for class 'hierCredibility'
fitted(object, ...)

Arguments

`x`	an object of class `hierCredibility`
`...`	currently ignored.
`object`	an object of class `hierCredibility`

Value

The function hierCredibility returns an object of class hierCredibility, which has the following slots:

`call`	the matched call
`type`	Whether additive or multiplicative hierarchical credibility model is used.
`Variances`	The estimated variance components. `s2` is the estimated variance of the individual contracts, `tausq` the estimate of $Var(V[j])$ and `nusq` is the estimate of $Var(V[jk])$ .
`Means`	The estimated averages at the portfolio level (intercept term $\mu$ ), at the first hierarchical level ( $bar(Y)[\%.\% j \%.\% \%.\%]^z$ ) and at the second hierarchical level ( $bar(Y)[\%.\% jk \%.\%]$ ).
`Weights`	The weights at the first hierarchical level $z[j\%.\%]$ and at the second hierarchical level $w[\%.\%jk\%.\%]$ .
`Credibility`	The credibility weights at the first hierarchical level $q[j\%.\%]$ and at the second hierarchical level $z[jk]$ .
`Premiums`	The overall expectation $widehat(\mu)$ , sector expectation $widehat(V)[j]$ and group expectation $widehat(V)[jk]$ .
`Relativity`	The estimated random effects $widehat(U)[j]$ and $widehat(U)[jk]$ of the sector and group, respectively.
`RawResults`	Objects of type `data.table` with all intermediate results.
`fitted.values`	the fitted mean values, resulting from the model fit.

S3 methods

print:: Prints the call, the estimated variance parameters and the unique number of categories of the hierarchical MLF. The ... argument is currently ignored. Returns an invisible copy of the original object.
summary:: In addition to the output of the print.hierCredibility function, the summary function prints the random effect estimates as well. Returns an invisible copy of the original object.
fitted:: Returns the fitted values.

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

Description

Fit a random effects model using Ohlsson's methodology. In this function you estimate the power parameter p. See hierCredGLM when you want fix p.

Usage

hierCredTweedie(
  formula,
  data,
  weights,
  muHatGLM = TRUE,
  epsilon = 1e-04,
  maxiter = 500,
  verbose = FALSE,
  returnData = TRUE,
  cpglmControl = list(bound.p = c(1.01, 1.99)),
  balanceProperty = TRUE,
  optimizer = "bobyqa",
  y = TRUE,
  ...
)
hierCredTweedie(
  formula,
  data,
  weights,
  muHatGLM = TRUE,
  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 is the same as for `lmer` and `glmer`. For example, `Yijkt ~ x1 + x2 + (1 \| Industry / Branch)`.
`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 `TRUE`, which used the intercept as estimated by the GLM. If `FALSE`, the estimate of the hierarchical 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 hierCredTweedie 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 `TRUE`.

References

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

Examples


data("dataCar")
fit = hierCredTweedie(Y ~ area + (1 | VehicleType / VehicleBody), dataCar,
weights = w, epsilon = 1e-6)
fit
summary(fit)
ranef(fit)
fixef(fit)

data("dataCar")
fit = hierCredTweedie(Y ~ area + (1 | VehicleType / VehicleBody), dataCar,
weights = w, epsilon = 1e-6)
fit
summary(fit)
ranef(fit)
fixef(fit)

Class "hierCredTweedie" of fitted random effects models estimated with Ohlsson's GLMC algorithm

Description

Class "hierCredTweedie" of fitted random effects models estimated with Ohlsson's GLMC algorithm

Usage

## S3 method for class 'hierCredTweedie'
print(x, ...)

## S3 method for class 'hierCredTweedie'
summary(object, ...)

## S3 method for class 'hierCredTweedie'
fitted(object, ...)
## S3 method for class 'hierCredTweedie'
print(x, ...)

## S3 method for class 'hierCredTweedie'
summary(object, ...)

## S3 method for class 'hierCredTweedie'
fitted(object, ...)

Arguments

`x`	an object of class `hierCredTweedie`
`...`	currently ignored.
`object`	an object of class `hierCredTweedie`

Value

The function hierCredGLM returns an object of class hierCredGLM, which has 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 `TRUE`.

S3 methods

print:: Prints the call, the estimated variance parameters, the unique number of categories of the hierarchical MLF and the output of the GLM part. The ... argument is currently ignored. Returns an invisible copy of the original object.
summary:: In addition to the output of the print.hierCredTweedie function, the summary function also prints the random effect estimates and a summary of the GLM (see summary.glm). Returns an invisible copy of the original object.
fitted:: Returns the fitted values.

Formula

Description

Checks if the object is of the type formula

Usage

is.formula(x)
is.formula(x)

Arguments

`x`	the object.

Value

logical indicating if the object is a formula or not.

Examples

f = formula(y ~ x)
is.formula(f)
f = formula(y ~ x)
is.formula(f)

Is f1 nested within f2?

Description

Does every level of f1 occur in conjunction with exactly one level of f2? The function is based on converting a triplet sparse matrix to a compressed column-oriented form in which the nesting can be quickly evaluated.

Usage

  isNested(f1, f2)
isNested(f1, f2)

Arguments

`f1`	factor 1
`f2`	factor 2

Value

TRUE if factor 1 is nested within factor 2

Examples

  library(lme4)
  with(Pastes, isNested(cask, batch))   ## => FALSE
  with(Pastes, isNested(sample, batch))  ## => TRUE
library(lme4)
  with(Pastes, isNested(cask, batch))   ## => FALSE
  with(Pastes, isNested(sample, batch))  ## => TRUE

Modular Functions for Mixed Model Fits

Description

Modular functions for mixed model fits

Usage

  glFormula(formula, data = NULL, family = gaussian,
            subset, weights, na.action, offset, contrasts = NULL,
            start, mustart, etastart, control = glmerControl(), ...)
glFormula(formula, data = NULL, family = gaussian,
            subset, weights, na.action, offset, contrasts = NULL,
            start, mustart, etastart, control = glmerControl(), ...)

Arguments

`formula`	a two-sided linear formula object describing both the fixed-effects and random-effects parts of the model, with the response on the left of a `~` operator and the terms, separated by `+` operators, on the right. Random-effects terms are distinguished by vertical bars (`"\|"`) separating expressions for design matrices from grouping factors.
`data`	an optional data frame containing the variables named in `formula`. By default the variables are taken from the environment from which `lmer` is called. While `data` is optional, the package authors strongly recommend its use, especially when later applying methods such as `update` and `drop1` to the fitted model (such methods are not guaranteed to work properly if `data` is omitted). If `data` is omitted, variables will be taken from the environment of `formula` (if specified as a formula) or from the parent frame (if specified as a character vector).
`subset`	an optional expression indicating the subset of the rows of `data` that should be used in the fit. This can be a logical vector, or a numeric vector indicating which observation numbers are to be included, or a character vector of the row names to be included. All observations are included by default.
`weights`	an optional vector of ‘prior weights’ to be used in the fitting process. Should be `NULL` or a numeric vector.
`na.action`	a function that indicates what should happen when the data contain `NA`s. The default action (`na.omit`, inherited from the 'factory fresh' value of `getOption("na.action")`) strips any observations with any missing values in any variables.
`offset`	this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be `NULL` or a numeric vector of length equal to the number of cases. One or more `offset` terms can be included in the formula instead or as well, and if more than one is specified their sum is used. See `model.offset`.
`contrasts`	an optional `list`. See the `contrasts.arg` of `model.matrix.default`.
`control`	a list giving for `[g]lFormula`: all options for running the model, see `lmerControl`; for `mkLmerDevfun,mkGlmerDevfun`: options for the inner optimization step; for `optimizeLmer` and `optimizeGlmer`: control parameters for nonlinear optimizer (typically inherited from the ... argument to `lmerControl`).
`start`	starting values (see `lmer`; for `glFormula`, should be just a numeric vector of fixed-effect coefficients)
`family`	a GLM family; see `glm` and `family`.
`mustart`	optional starting values on the scale of the conditional mean; see `glm` for details.
`etastart`	optional starting values on the scale of the unbounded predictor; see `glm` for details.
`...`	other potential arguments; for `optimizeLmer` and `optimizeGlmer`, these are passed to internal function `optwrap`, which has relevant parameters `calc.derivs` and `use.last.params` (see `lmerControl`).

Details

These functions make up the internal components of an [gn]lmer fit.

[g]lFormula takes the arguments that would normally be passed to [g]lmer, checking for errors and processing the formula and data input to create a list of objects required to fit a mixed model.
mk(Gl|L)merDevfun takes the output of the previous step (minus the formula component) and creates a deviance function
optimize(Gl|L)mer takes a deviance function and optimizes over theta (or over theta and beta, if stage is set to 2 for optimizeGlmer
updateGlmerDevfun takes the first stage of a GLMM optimization (with nAGQ=0, optimizing over theta only) and produces a second-stage deviance function
mkMerMod takes the environment of a deviance function, the results of an optimization, a list of random-effect terms, a model frame, and a model all and produces a [g]lmerMod object.

Value

lFormula and glFormula return a list containing components:

fr: model frame
X: fixed-effect design matrix
reTrms: list containing information on random effects structure: result of mkReTrms

mkLmerDevfun and mkGlmerDevfun return a function to calculate deviance (or restricted deviance) as a function of the theta (random-effect) parameters. updateGlmerDevfun returns a function to calculate the deviance as a function of a concatenation of theta and beta (fixed-effect) parameters. These deviance functions have an environment containing objects required for their evaluation. CAUTION: The environment of functions returned by mk(Gl|L)merDevfun contains reference class objects (see ReferenceClasses, merPredD-class, lmResp-class), which behave in ways that may surprise many users. For example, if the output of mk(Gl|L)merDevfun is naively copied, then modifications to the original will also appear in the copy (and vice versa). To avoid this behavior one must make a deep copy (see ReferenceClasses for details).

optimizeLmer and optimizeGlmer return the results of an optimization.

Examples

  
  library(lme4)
  ### Fitting a linear mixed model in 4 modularized steps

  ## 1.  Parse the data and formula:
  lmod <- lFormula(Reaction ~ Days + (Days|Subject), sleepstudy)
  names(lmod)
  ## 2.  Create the deviance function to be optimized:
  (devfun <- do.call(mkLmerDevfun, lmod))
  ls(environment(devfun)) # the environment of 'devfun' contains objects
  # required for its evaluation
  ## 3.  Optimize the deviance function:
  opt <- optimizeLmer(devfun)
  opt[1:3]
  ## 4.  Package up the results:
  mkMerMod(environment(devfun), opt, lmod$reTrms, fr = lmod$fr)


  ### Same model in one line
  lmer(Reaction ~ Days + (Days|Subject), sleepstudy)


  ### Fitting a generalized linear mixed model in six modularized steps

  ## 1.  Parse the data and formula:
  glmod <- glFormula(cbind(incidence, size - incidence) ~ period + (1 | herd),
                     data = cbpp, family = binomial)
  #.... see what've got :
  str(glmod, max=1, give.attr=FALSE)
  ## 2.  Create the deviance function for optimizing over theta:
  (devfun <- do.call(mkGlmerDevfun, glmod))
  ls(environment(devfun)) # the environment of devfun contains lots of info
  ## 3.  Optimize over theta using a rough approximation (i.e. nAGQ = 0):
  (opt <- optimizeGlmer(devfun))
  ## 4.  Update the deviance function for optimizing over theta and beta:
  (devfun <- updateGlmerDevfun(devfun, glmod$reTrms))
  ## 5.  Optimize over theta and beta:
  opt <- optimizeGlmer(devfun, stage=2)
  str(opt, max=1) # seeing what we'got
  ## 6.  Package up the results:
  (fMod <- mkMerMod(environment(devfun), opt, glmod$reTrms, fr = glmod$fr))

  ### Same model in one line
  fM <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd),
              data = cbpp, family = binomial)
  all.equal(fMod, fM, check.attributes=FALSE, tolerance = 1e-12)
  # ----  --  even tolerance = 0  may work
  
library(lme4)
  ### Fitting a linear mixed model in 4 modularized steps

  ## 1.  Parse the data and formula:
  lmod <- lFormula(Reaction ~ Days + (Days|Subject), sleepstudy)
  names(lmod)
  ## 2.  Create the deviance function to be optimized:
  (devfun <- do.call(mkLmerDevfun, lmod))
  ls(environment(devfun)) # the environment of 'devfun' contains objects
  # required for its evaluation
  ## 3.  Optimize the deviance function:
  opt <- optimizeLmer(devfun)
  opt[1:3]
  ## 4.  Package up the results:
  mkMerMod(environment(devfun), opt, lmod$reTrms, fr = lmod$fr)


  ### Same model in one line
  lmer(Reaction ~ Days + (Days|Subject), sleepstudy)


  ### Fitting a generalized linear mixed model in six modularized steps

  ## 1.  Parse the data and formula:
  glmod <- glFormula(cbind(incidence, size - incidence) ~ period + (1 | herd),
                     data = cbpp, family = binomial)
  #.... see what've got :
  str(glmod, max=1, give.attr=FALSE)
  ## 2.  Create the deviance function for optimizing over theta:
  (devfun <- do.call(mkGlmerDevfun, glmod))
  ls(environment(devfun)) # the environment of devfun contains lots of info
  ## 3.  Optimize over theta using a rough approximation (i.e. nAGQ = 0):
  (opt <- optimizeGlmer(devfun))
  ## 4.  Update the deviance function for optimizing over theta and beta:
  (devfun <- updateGlmerDevfun(devfun, glmod$reTrms))
  ## 5.  Optimize over theta and beta:
  opt <- optimizeGlmer(devfun, stage=2)
  str(opt, max=1) # seeing what we'got
  ## 6.  Package up the results:
  (fMod <- mkMerMod(environment(devfun), opt, glmod$reTrms, fr = glmod$fr))

  ### Same model in one line
  fM <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd),
              data = cbpp, family = binomial)
  all.equal(fMod, fM, check.attributes=FALSE, tolerance = 1e-12)
  # ----  --  even tolerance = 0  may work

Omit terms separated by vertical bars in a formula

Description

Remove the random-effects terms from a mixed-effects formula, thereby producing the fixed-effects formula.

Usage

  nobars(term)
nobars(term)

Arguments

term

the right-hand side of a mixed-model formula

Value

the fixed-effects part of the formula

Note

This function is called recursively on individual terms in the model, which is why the argument is called term and not a name like form, indicating a formula.

Examples

  nobars(Reaction ~ Days + (Days|Subject)) ## => Reaction ~ Days
nobars(Reaction ~ Days + (Days|Subject)) ## => Reaction ~ Days

Number of unique elements in a vector

Description

Number of unique elements in a vector

Usage

NrUnique(x, na.rm = TRUE)
NrUnique(x, na.rm = TRUE)

Arguments

`x`	object of type `vector`.
`na.rm`	logical indicating if missing values have to be removed. Default to `TRUE`.

Value

vector with the number of unique elements

Examples

set.seed(1)
x = sample(letters, 50, TRUE)
NrUnique(x)
set.seed(1)
x = sample(letters, 50, TRUE)
NrUnique(x)

Visualizing the random effect estimates using ggplot2

Description

Using this function, you can create plots of the random effect estimates from fitted random effects models. To make the plots, we rely on the ggplot2 package.

Usage

plotRE(
  obj,
  levelRE = c("all", "first", "second"),
  colour = "black",
  plot = TRUE
)
plotRE(
  obj,
  levelRE = c("all", "first", "second"),
  colour = "black",
  plot = TRUE
)

Arguments

`obj`	an object of type `hierCredibility`, `hierCredGLM` or `hierCredTweedie`
`levelRE`	indicates which hierarchical level has to be used. `"all"` plots both levels in the hierarchy, `"first"` the first level in the hierarchy and `"second"` the second level.
`colour`	colour for `geom_point`
`plot`	logical indicating if the `ggplot` objects have to be plotted.

Value

a list with ggplot objects.

Examples


fitHGLM <- hierCredGLM(Y ~ area + gender + (1 | VehicleType / VehicleBody), dataCar, weights = w)
plotRE(fitHGLM)

fitHGLM <- hierCredGLM(Y ~ area + gender + (1 | VehicleType / VehicleBody), dataCar, weights = w)
plotRE(fitHGLM)

Model predictions

Description

Obtain predictions based on the model fit with hierCredGLM

Usage

## S3 method for class 'hierCredGLM'
predict(object, newdata = NULL, ...)
## S3 method for class 'hierCredGLM'
predict(object, newdata = NULL, ...)

Arguments

`object`	a model object for which prediction is desired.
`newdata`	optionally, a data frame in which to look for variables with which to predict. If omitted, the fitted values are used.
`...`	arguments passed to `glm`

Details

The random effects are taken into account by specifying these as an offset in the predict.glm function.

Value

If newdata is omitted the predictions are based on the data used for the fit.

Model predictions

Description

Obtain predictions based on a model fit with hierCredibility

Usage

## S3 method for class 'hierCredibility'
predict(object, newdata = NULL, ...)
## S3 method for class 'hierCredibility'
predict(object, newdata = NULL, ...)

Arguments

`object`	a model object for which prediction is desired.
`newdata`	optionally, a data frame in which to look for variables with which to predict. If omitted, the fitted values are used.
`...`	ignored.

Value

If newdata is omitted the predictions are based on the data used for the fit.

Model predictions

Description

Obtain predictions based on the model fit with hierCredTweedie

Usage

## S3 method for class 'hierCredTweedie'
predict(object, newdata = NULL, ...)
## S3 method for class 'hierCredTweedie'
predict(object, newdata = NULL, ...)

Arguments

`object`	a model object for which prediction is desired.
`newdata`	optionally, a data frame in which to look for variables with which to predict. If omitted, the fitted values are used.
`...`	arguments passed to `cpglm`

Details

The random effects are taken into account by specifying these as an offset in the predict.cpglm function.

Value

If newdata is omitted the predictions are based on the data used for the fit.

Print method for an object of class `BalanceProperty`

Description

Print method for an object of class BalanceProperty

Usage

## S3 method for class 'BalanceProperty'
print(x, ...)
## S3 method for class 'BalanceProperty'
print(x, ...)

Arguments

`x`	an object of type `BalanceProperty`
`...`	Currently ignored.

Value

Prints the call and whether the balance property is satisfied or not. Returns an invisible copy of the original object.

Extract the modes of the random effects

Description

A generic function to extract the conditional modes of the random effects from a fitted model object. For linear mixed models the conditional modes of the random effects are also the conditional means.

Arguments

object

an object of a class of fitted models with random effects.

Details

If grouping factor i has k levels and j random effects per level the ith component of the list returned by ranef is a data frame with k rows and j columns.

Value

From ranef: An object composed of a list of data frames, one for each grouping factor for the random effects. The number of rows in the data frame is the number of levels of the grouping factor. The number of columns is the dimension of the random effect associated with each level of the factor.

Examples

  
  library(lattice) ## for dotplot, qqmath
  library(lme4)
  fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)
  fm2 <- lmer(Reaction ~ Days + (1|Subject) + (0+Days|Subject), sleepstudy)
  fm3 <- lmer(diameter ~ (1|plate) + (1|sample), Penicillin)
  ranef(fm1)
  
library(lattice) ## for dotplot, qqmath
  library(lme4)
  fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)
  fm2 <- lmer(Reaction ~ Days + (1|Subject) + (0+Days|Subject), sleepstudy)
  fm3 <- lmer(diameter ~ (1|plate) + (1|sample), Penicillin)
  ranef(fm1)

Extract the random effect estimates from a fitted random effects model

Description

A generic function to extract the estimates/predictions of the random effects from a fitted random effects model.

Usage

## S3 method for class 'hierCredibility'
ranef(object, ...)

## S3 method for class 'hierCredGLM'
ranef(object, ...)

## S3 method for class 'hierCredTweedie'
ranef(object, ...)
## S3 method for class 'hierCredibility'
ranef(object, ...)

## S3 method for class 'hierCredGLM'
ranef(object, ...)

## S3 method for class 'hierCredTweedie'
ranef(object, ...)

Arguments

`object`	an object of type `hierCredibility`, `hierCredGLM` or `hierCredTweedie`
`...`	Currently ignored.

Value

A list of data frames, one for each grouping factor for the random effects. The number of rows in the data frame is the number of levels of the grouping factor. The first (two) columns correspond(s) to the grouping factor. The last column corresponds to the estimated random effect.

Fitting a Tweedie GLMM, using the initial estimates of hierCredTweedie

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.

Usage

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

Arguments

`formula`	object of type `formula` that specifies which model should be fitted. Syntax is the same as for `lmer` and `glmer`. For example, `Yijkt ~ x1 + x2 + (1 \| Industry / Branch)`.
`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 `TRUE`, which used the intercept as estimated by the GLM. If `FALSE`, the estimate of the hierarchical 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.
`balanceProperty`	logical indicating if the balance property should be satisfied.

Value

an object of class cpglmm, containing the model fit.

References

Examples


data("dataCar")
fitTweedieGLMM = tweedieGLMM(Y ~ area + gender + (1 | VehicleType / VehicleBody), dataCar,
 weights = w, verbose = TRUE, epsilon = 1e-4)

data("dataCar")
fitTweedieGLMM = tweedieGLMM(Y ~ area + gender + (1 | VehicleType / VehicleBody), dataCar,
 weights = w, verbose = TRUE, epsilon = 1e-4)

Extract the model weights

Description

weights is a generic function which extracts fitting weights from objects returned by modeling functions. Methods can make use of napredict methods to compensate for the omission of missing values. The default methods does so.

Usage

## S3 method for class 'cpglm'
weights(object, type = c("prior", "working"), ...)

## S3 method for class 'hierCredGLM'
weights(object, type = c("prior", "working"), ...)

## S3 method for class 'hierCredTweedie'
weights(object, type = c("prior", "working"), ...)
## S3 method for class 'cpglm'
weights(object, type = c("prior", "working"), ...)

## S3 method for class 'hierCredGLM'
weights(object, type = c("prior", "working"), ...)

## S3 method for class 'hierCredTweedie'
weights(object, type = c("prior", "working"), ...)

Arguments

`object`	an object for which the extraction of model weights is meaningful. Can be either `cpglm`, `glm`, `hierCredibility`, `hierCredGLM` or `hierCredTweedie`
`type`	indicates if prior or working weights need to be extracted.
`...`	ignored

Value

Weights extracted from the object object: the default method looks for component "weights" and if not NULL calls napredict on it.

Package 'actuaRE'

Help Index

Handling Hierarchically Structured Risk Factors using Random Effects Models

Description

References

See Also

Examples

Add random effects to the data frame

Description

Usage

Arguments

Adjust the intercept to regain the balance property

Description

Usage

Arguments

Value

References

Examples

Balance property

Description

Usage

Arguments

Value

References

Examples

data Car

Description

Usage

Format

Details

Source

References

Examples

Determine random-effects expressions from a formula

Description

Usage

Arguments

Value

Note

See Also

Examples

Extract fixed-effects estimates

Description

Arguments

Details

Value

Examples

Extract the fixed-effects estimates from a fitted random effects model

Description

Usage

Arguments

Value

Examples

Hachemeister Data Set

Description

Usage

Format

Source

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

Description

Usage

Arguments

Value

References

See Also

Examples

Class "hierCredGLM" of fitted random effects models estimated with Ohlsson's GLMC algorithm

Description

Usage

Arguments

Value

S3 methods

See Also

Hierarchical credibility model of Jewell

Description

Usage

Arguments

Value

References

See Also