bootResMis: Residual bootstrap estimators of prediction accuracy under...

In qape: Quantile of Absolute Prediction Errors

Residual bootstrap estimators of prediction accuracy under the misspecified model

Description

The function computes values of residual bootstrap estimators of RMSE and QAPE prediction accuracy measures of two predictors under the model assumed for one of them.

Usage

bootResMis(predictorLMM, predictorLMMmis, B, p, correction)

Arguments

predictorLMM	plugInLMM object, the first predictor used to define the bootstrap model.
predictorLMMmis	plugInLMM object, the second predictor.
B	number of iterations in the bootstrap procedure.
p	orders of quantiles in the QAPE.
correction	logical. If TRUE, both bootstrapped random effects and random components are tranformed to avoid the problem of underdispersion of residual bootstrap distributions (see Details).

Details

Residual bootstrap considered by Carpener, Goldstein and Rasbash (2003), Chambers and Chandra (2013) and Thai et al. (2013) is used. We use model specification used in predictorLMM. To generate one bootstrap realization of the population vector of the variable of interest: (i) from the sample vector of predicted random components the simple random sample with replacement of population size is drawn at random, (ii) from the vector of predicted random effects the simple random sample with replacement of size equal the number of random effects in the whole population is drawn at random. If correction is TRUE, then predicted random effects are transformed as described in Carpener, Goldstein and Rasbash (2003) in Section 3.2 and predicted random components as presented in Chambers and Chandra (2013) in Section 2.2. We use the MSE estimator defined as the mean of squared bootstrap errors considered by Rao and Molina (2015) p. 141 given by equation (6.2.22). The QAPE is a quantile of absolute prediction error which means that at least p100% of realizations of absolute prediction errors are smaller or equal to QAPE. It is estimated as a quantile of absolute bootstrap errors as proposed by Zadlo (2017) in Section 2. The prediction accuracy of two predictors predictorLMM and predictorLMMmis is estimated under the model specified in predictorLMM.

Value

estQAPElmm	estimated value/s of QAPE of predictorLMM - number of rows is equal the number of orders of quantiles to be considered (declared in p), number of columns is equal the number of predicted characteristics (declared in thetaFun).
estRMSElmm	estimated value/s of RMSE of predictorLMM (more than one value is computed if in thetaFun more than one population characteristic is defined).
estQAPElmmMis	estimated value/s of QAPE of predictorLMMmis - number of rows is equal the number of orders of quantiles to be considered (declared in p), number of columns is equal the number of predicted characteristics (declared in thetaFun).
estRMSElmmMis	estimated value/s of RMSE of predictorLMMmis (more than one value is computed if in thetaFun more than one population characteristic is defined).
predictorLMMSim	bootstrapped values of predictorLMM.
predictorLMMmisSim	bootstrapped values of predictorLMMmis.
thetaSim	bootstrapped values of the predicted population or subpopulation characteristic/s.
Ysim	simulated values of the (possibly tranformed) variable of interest.
errorLMM	differences between bootstrapped values of predictorLMM and bootstrapped values of the predicted characteristic/s.
errorLMMmis	differences between bootstrapped values of predictorLMMmis and bootstrapped values of the predicted characteristic/s.

Author(s)

Alicja Wolny-Dominiak, Tomasz Zadlo

References

1. Carpenter, J.R., Goldstein, H. and Rasbash, J. (2003), A novel bootstrap procedure for assessing the relationship between class size and achievement. Journal of the Royal Statistical Society: Series C (Applied Statistics), 52, 431-443.

2. Chambers, R. and Chandra, H. (2013) A Random Effect Block Bootstrap for Clustered Data, Journal of Computational and Graphical Statistics, 22(2), 452-470.

3. Thai, H.-T., Mentre, F., Holford, N.H., Veyrat-Follet, C. and Comets, E. (2013), A comparison of bootstrap approaches for estimating uncertainty of parameters in linear mixed-effects models. Pharmaceutical Statistics, 12, 129-140.

Examples

library(lme4)
library(Matrix)
library(mvtnorm)


data(invData) 
# data from one period are considered: 
invData2018 <- invData[invData$year == 2018,] 
attach(invData2018)

N <- nrow(invData2018) # population size

con <- rep(1,N) 
con[c(379:380)] <- 0 # last two population elements are not observed 

YS <- log(investments[con == 1]) # log-transformed values
backTrans <- function(x) exp(x) # back-transformation of the variable of interest
fixed.part <- 'log(newly_registered)'
random.part <- '(1|NUTS2)' 
random.part.mis <- '(1|NUTS4type)'

reg <- invData2018[, -which(names(invData2018) == 'investments')]
weights <- rep(1,N) # homoscedastic random components

# Characteristics to be predicted:
# values of the variable for last two population elements  
thetaFun <- function(x) {x[c(379:380)]}

predictorLMM <- plugInLMM(YS, fixed.part, random.part, reg, con, weights, backTrans, thetaFun)
predictorLMM$thetaP

predictorLMMmis <- plugInLMM(YS, fixed.part, random.part.mis, reg,con,weights,backTrans,thetaFun)
predictorLMMmis$thetaP

set.seed(123456)
### Estimation of prediction accuracy
est_accuracy <- bootResMis(predictorLMM, predictorLMMmis, 10, c(0.5,0.8), correction = TRUE)

# Estimation of prediction RMSE of predictorLMM 
est_accuracy$estRMSElmm

# Estimation of prediction RMSE of predictorLMMmis
est_accuracy$estRMSElmmMis

# Estimation of prediction QAPE of predictorLMM 
est_accuracy$estQAPElmm

# Estimation of prediction QAPE of predictorLMMmis
est_accuracy$estQAPElmmMis

detach(invData2018)

qape documentation built on Aug. 21, 2023, 5:07 p.m.