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.

See Also

hierCredibility hierCredGLM hierCredTweedie tweedieGLMM BalanceProperty

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)

Add random effects to the data frame

Description

Internal function

Usage

.addREs(obj, newdata)

Arguments

Balance property

Description

Function to assess whether the balance property holds

Usage

BalanceProperty(obj)

Arguments

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

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

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)

Number of unique elements in a vector

Description

Number of unique elements in a vector

Usage

NrUnique(x, na.rm = TRUE)

Arguments

Value

vector with the number of unique elements

Examples

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

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)

Arguments

Value

The object with the adjusted (fixed effects) coefficients.

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

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))

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)

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

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)

Arguments

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.

See Also

formula, model.frame, model.matrix.

Other utilities: mkRespMod, mkReTrms, nlformula, nobars, subbars

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)
  

Extract fixed-effects estimates

Description

Extract the fixed-effects estimates

Arguments

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)))
  

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, ...)

Arguments

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)

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

hachemeisterLong

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,
  ...
)

Arguments

Value

An object of type hierCredGLM with the following slots:

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)

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, ...)

Arguments

Value

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

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.

See Also

hierCredGLM

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,
  ...
)

Arguments

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:

References

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

See Also

hierCredTweedie-class, fitted.hierCredTweedie, predict.hierCredTweedie, ranef-actuaRE, weights-actuaRE, hierCredibility, hierCredGLM, cpglm, plotRE, adjustIntercept, BalanceProperty @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

Examples

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, ...)

Arguments

Value

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

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.

See Also

hierCredTweedie

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
)

Arguments

Value

An object of type hierCredibility with the following slots:

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

See Also

hierCredibility-class, fitted.hierCredibility, predict.hierCredibility, ranef-actuaRE, weights-actuaRE, hierCredTweedie, hierCredGLM, cpglm, plotRE

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)

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, ...)

Arguments

Value

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

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.

See Also

hierCredibility

Formula

Description

Checks if the object is of the type formula

Usage

is.formula(x)

Arguments

Value

logical indicating if the object is a formula or not.

Examples

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)

Arguments

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

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(), ...)

Arguments

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
  

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)

Arguments

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.

See Also

formula, model.frame, model.matrix.

Other utilities: findbars, mkRespMod, mkReTrms, nlformula, subbars

Examples

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

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
)

Arguments

Value

a list with ggplot objects.

Examples

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, ...)

Arguments

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.

See Also

hierCredGLM

Model predictions

Description

Obtain predictions based on the model fit with hierCredTweedie

Usage

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

Arguments

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.

See Also

hierCredTweedie

Model predictions

Description

Obtain predictions based on a model fit with hierCredibility

Usage

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

Arguments

Value

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

See Also

hierCredibility

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, ...)

Arguments

Value

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

See Also

BalanceProperty

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

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)
  

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, ...)

Arguments

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
)

Arguments

Value

an object of class cpglmm, containing the model fit.

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

See Also

cpglmm and hierCredTweedie

Examples

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"), ...)

Arguments

Value

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

See Also

weights, cpglm, glm, hierCredibility, hierCredGLM or hierCredTweedie