expectile.boost: Quantile and expectile regression using boosting

Description

Generalized additive models are fitted with gradient boosting for optimizing arbitrary loss functions to obtain the graphs of 11 different expectiles for continuous, spatial or random effects.

Usage

expectile.boost(formula, data = NULL, mstop = NA, expectiles = NA, parallel = FALSE, cv = TRUE)

quant.boost(formula, data = NULL, mstop = NA, expectiles = NA, parallel = FALSE, cv = TRUE)

Arguments

formula

An R formula object consisting of the response variable, '~' and the sum of all effects that should be taken into consideration (see gamboost). Each effect can be linear or represented through a no

data

data frame or matrix.

mstop

vector, number of bootstrap iterations for each of the 11 quantiles/expectiles that are fitted. Default is 4000.

expectiles

In default setting, the expectiles (0.01,0.02,0.05,0.1,0.2,0.5,0.8,0.9,0.95,0.98,0.99) are calculated. You may specify your own set of expectiles in a vector. Is overridden by density.

parallel

On Unix machines with the package multicore installed the different expectiles can be calculated simultaneously, if the computer has multiple CPUs.

A cross-validation can determine the optimal amount of boosting iterations between 1 and mstop. Uses cvrisk. If set to FALSE, the results from mstop iterations a

Value

An object of class 'expectreg', which is basically a list consisting of:
valuesThe fitted values for each observation and all expectiles, separately in a list for each effect in the model, sorted in order of ascending covariate values.
responseVector of the response variable.
formulaThe formula object that was given to the function.
expectilesVector of fitted expectile asymmetries as given by argument expectiles.
effectsList of characters giving the types of covariates.
helperList of additional parameters like neighbourhood structure for spatial effects or 'phi' for kriging.
fittedFitted values $\hat{y}$.
plot, predict, resid, fitted and effects methods are available for class 'expectreg'.

Details

A (generalized) additive model is fitted using a boosting algorithm based on component-wise univariate base learners. The base learner can be specified via the formula object. After fitting the model a cross-validation is done using cvrisk to determine the optimal stopping point for the boosting which results in the best fit.

References

Fenske N and Kneib T and Hothorn T (2009) Identifying Risk Factors for Severe Childhood Malnutrition by Boosting Additive Quantile Regression Technical Report 052, University of Munich Sobotka F and Kneib T (2010) Geoadditive Expectile Regression Computational Statistics and Data Analysis, doi: 10.1016/j.csda.2010.11.015.

Examples

Run this code

data(dutchboys)

dutch = dutchboys[sample(6848,500),] # reduce computing time for this example

expreg <- expectile.boost(hgt ~ bbs(age,df=5,degree=2),dutch,mstop=rep(550,11),expectiles=c(0.05,0.2,0.5,0.8,0.95))

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