mcBootMis {qape}

Monte Carlo simulation study of accuracy of estimators of accuracy measures

Description

The function computes in the Monte Carlo simulation study values of accuracy measures of estimators of accuracy measures of two predictors under the model defined by the first of them.

Usage

mcBootMis(Ypop, predictorLMM, predictorLMMmis, K, B1, B2, p, q)

Arguments

Ypop

population values of the variable of interest (already transformed if necessary) which are used as the dependent variable in the population model.

predictorLMM

plugInLMM object, the predictor used to define the model assumed in the simulation study.

predictorLMMmis

plugInLMM object, the second predictor, the properties of which are assessed under the misspecified model used in predictorLMM.

K

the number of Monte Carlo iterations.

B1

the number of first-level bootstrap iterations.

B2

the number of second-level bootstrap iterations.

p

orders of quantiles in the QAPE.

q

estimator bounds assumed for estMSE_db_1_EF and estMSE_db_telesc_EF (which are corrected versions of estMSE_db_1 and estMSE_db_telesc, respectively).

Details

In the model-based simulation study population values of the dependent variable are generated based on the (possibly transformed) Linear Mixed Model used in predictorLMM and the accuracy of predictors predictorLMM and predictorLMMmis is assessed. What is more, the the accuracy of parametric, residual and double bootstrap estimators of accuracy measures is studied under the model used in predictorLMM. Values of some MSE estimators can be negative, the number of negative values of MSE estimators obtained in the simulation study are presented in objects neg_estMSE_LMM and neg_estMSE_LMMmis. Hence, some RMSE estimators computed as square roots of MSE estimators can produce NaNs - see warnings.

Value

QAPElmm

value/s of the QAPE of predictorLMM assessed in the Monte Carlo study - the number of rows is equal to the number of orders of quantiles to be considered (declared in p), the number of columns is equal to the number of predicted characteristics (declared in thetaFun).

RMSElmm

value/s of the RMSE of predictorLMM assessed in the Monte Carlo study (more than one value is computed if in thetaFun more than one population characteristic is defined).

rRMSElmm

value/s of the rRMSE (in percentages) of predictorLMM assessed in the Monte Carlo study (more than one value is computed if in thetaFun more than one population characteristic is defined).

rBlmm

value/s of the relative bias (in percentages) of predictorLMM assessed in the Monte Carlo study (more than one value is computed if in thetaFun more than one population characteristic is defined).

QAPElmmMis

value/s of the QAPE of predictorLMM2 assessed in the Monte Carlo study - the number of rows is equal to the number of orders of quantiles to be considered (declared in p), the number of columns is equal to the number of predicted characteristics (declared in thetaFun).

RMSElmmMis

value/s of the RMSE of predictorLMM2 assessed in the Monte Carlo study (more than one value is computed if in thetaFun more than one population characteristic is defined).

rRMSElmmMis

value/s of the rRMSE (in percentages) of predictorLMM2 assessed in the Monte Carlo study (more than one value is computed if in thetaFun more than one population characteristic is defined).

rBlmmMis

value/s of the relative bias (in percentages) of predictorLMMmis assessed in the Monte Carlo study (more than one value is computed if in thetaFun more than one population characteristic is defined).

rB.estRMSE_rbF_LMM

relative bias (in percentages) of estimated value/s of RMSE of predictorLMM without correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rRMSE.estRMSE_rbF_LMM

relative RMSE (in percentages) of estimated value/s of RMSE of predictorLMM without correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rB.estRMSE_rbF_LMMmis

relative bias (in percentages) of estimated value/s of RMSE of predictorLMMmis without correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rRMSE.estRMSE_rbF_LMMmis

relative RMSE (in percentages) of estimated value/s of RMSE of predictorLMMmis without correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rB.estMSE_rbF_LMM

relative bias (in percentages) of estimated value/s of MSE of predictorLMM without correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rRMSE.estMSE_rbF_LMM

relative RMSE (in percentages) of estimated value/s of MSE of predictorLMM without correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rB.estMSE_rbF_LMMmis

relative bias (in percentages) of estimated value/s of MSE of predictorLMMmis without correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rRMSE.estMSE_rbF_LMMmis

relative RMSE (in percentages) of estimated value/s of MSE of predictorLMMmis without correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rB.estQAPE_rbF_LMM

relative bias (in percentages) of estimated value/s of QAPE of predictorLMM without correction to avoid the problem of underdispersion of residual bootstrap distributions, the number of rows is equal to the number of orders of quantiles to be considered (declared in p), the number of columns is equal to the number of predicted characteristics (declared in thetaFun).

rRMSE.estQAPE_rbF_LMM

relative RMSE (in percentages) of estimated value/s of QAPE of predictorLMM without correction to avoid the problem of underdispersion of residual bootstrap distributions, the number of rows is equal to the number of orders of quantiles to be considered (declared in p), the number of columns is equal to the number of predicted characteristics (declared in thetaFun).

rB.estQAPE_rbF_LMMmis

relative bias (in percentages) of estimated value/s of QAPE of predictorLMMmis without correction to avoid the problem of underdispersion of residual bootstrap distributions, the number of rows is equal to the number of orders of quantiles to be considered (declared in p), the number of columns is equal to the number of predicted characteristics (declared in thetaFun).

rRMSE.estQAPE_rbF_LMMmis

relative RMSE (in percentages) of estimated value/s of QAPE of predictorLMMmis without correction to avoid the problem of underdispersion of residual bootstrap distributions, the number of columns is equal to the number of predicted characteristics (declared in thetaFun) .

rB.estRMSE_rbT_LMM

relative bias (in percentages) of estimated value/s of RMSE of predictorLMM with correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rRMSE.estRMSE_rbT_LMM

relative RMSE (in percentages) of estimated value/s of RMSE of predictorLMM with correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rB.estRMSE_rbT_LMMmis

relative bias (in percentages) of estimated value/s of RMSE of predictorLMMmis with correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rRMSE.estRMSE_rbT_LMMmis

relative RMSE (in percentages) of estimated value/s of RMSE of predictorLMMmis with correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rB.estMSE_rbT_LMM

relative bias (in percentages) of estimated value/s of MSE of predictorLMM with correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rRMSE.estMSE_rbT_LMM

relative RMSE (in percentages) of estimated value/s of MSE of predictorLMM with correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rB.estMSE_rbT_LMMmis

relative bias (in percentages) of estimated value/s of MSE of predictorLMMmis with correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rRMSE.estMSE_rbT_LMMmis

relative RMSE (in percentages) of estimated value/s of MSE of predictorLMMmis with correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rB.estQAPE_rbT_LMM

relative bias (in percentages) of estimated value/s of QAPE of predictorLMM with correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rRMSE.estQAPE_rbT_LMM

relative RMSE (in percentages) of estimated value/s of QAPE of predictorLMM with correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rB.estQAPE_rbT_LMMmis

relative bias (in percentages) of estimated value/s of QAPE of predictorLMMmis with correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

rRMSE.estQAPE_rbT_LMMmis

relative RMSE (in percentages) of estimated value/s of QAPE of predictorLMMmis with correction to avoid the problem of underdispersion of residual bootstrap distributions (more than one value is computed if in thetaFun more than one population characteristic is defined).

neg_estMSE_LMM

the number of negative values of MSE estimators of predictorLMM obtained in the simulaton study out of K iterations, the number of rows is equal to 10 - the number of considered parametric and double bootstrap MSE estimators, the number of columns is equal to the number of predicted characteristics (declared in thetaFun).

neg_estMSE_LMMmis

the number of negative values of MSE estimators of predictorLMMmis obtained in the simulaton study out of K iterations, the number of rows is equal to 10 - the number of considered parametric and double bootstrap MSE estimators, the number of columns is equal to the number of predicted characteristics (declared in thetaFun).

rB.estMSE_param_LMMmis

relative bias (in percentages) of estMSE_param estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estMSE_param_LMMmis

relative RMSE (in percentages) of estMSE_param estimator (see doubleBoot function) of predictorLMMmis.

rB.estMSE_db_B2_LMMmis

relative bias (in percentages) of estMSE_db_B2 estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estMSE_db_B2_LMMmis

relative RMSE (in percentages) of estMSE_db_B2 estimator (see doubleBoot function) of predictorLMMmis.

rB.estMSE_db_B2_WDZ_LMMmis

relative bias (in percentages) of estMSE_db_B2_WDZ estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estMSE_db_B2_WDZ_LMMmis

relative RMSE (in percentages) of estMSE_db_B2_WDZ estimator (see doubleBoot function) of predictorLMMmis.

rB.estMSE_db_B2_HM_LMMmis

relative bias (in percentages) of estMSE_db_B2_HM estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estMSE_db_B2_HM_LMMmis

relative RMSE (in percentages) of estMSE_db_B2_HM estimator (see doubleBoot function) of predictorLMMmis.

rB.estMSE_db_1_LMMmis

relative bias (in percentages) of estMSE_db_1 estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estMSE_db_1_LMMmis

relative RMSE (in percentages) of estMSE_db_1 estimator (see doubleBoot function) of predictorLMMmis.

rB.estMSE_db_1_WDZ_LMMmis

relative bias (in percentages) of estMSE_db_1_WDZ estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estMSE_db_1_WDZ_LMMmis

relative RMSE (in percentages) of estMSE_db_1_WDZ estimator (see doubleBoot function) of predictorLMMmis.

rB.estMSE_db_1_EF_LMMmis

relative bias (in percentages) of estMSE_db_1_EF estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estMSE_db_1_EF_LMMmis

relative RMSE (in percentages) of estMSE_db_1_EF estimator (see doubleBoot function) of predictorLMMmis.

rB.estMSE_db_telesc_LMMmis

relative bias (in percentages) of estMSE_db_telesc estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estMSE_db_telesc_LMMmis

relative RMSE (in percentages) of estMSE_db_telesc estimator (see doubleBoot function) of predictorLMMmis.

rB.estMSE_db_telesc_WDZ_LMMmis

relative bias (in percentages) of estMSE_db_telesc_WDZ estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estMSE_db_telesc_WDZ_LMMmis

relative RMSE (in percentages) of estMSE_db_telesc_WDZ estimator (see doubleBoot function) of predictorLMMmis.

rB.estMSE_db_telesc_EF_LMMmis

relative bias (in percentages) of estMSE_db_telesc_EF estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estMSE_db_telesc_EF_LMMmis

relative RMSE (in percentages) of estMSE_db_telesc_EF estimator (see doubleBoot function) of predictorLMMmis.

rB.estRMSE_param_LMMmis

relative bias (in percentages) of estRMSE_param estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estRMSE_param_LMMmis

relative RMSE (in percentages) of estRMSE_param estimator (see doubleBoot function) of predictorLMMmis.

rB.estRMSE_db_B2_LMMmis

relative bias (in percentages) of estRMSE_db_B2 estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estRMSE_db_B2_LMMmis

relative RMSE (in percentages) of estRMSE_db_B2 estimator (see doubleBoot function) of predictorLMMmis.

rB.estRMSE_db_B2_WDZ_LMMmis

relative bias (in percentages) of estRMSE_db_B2_WDZ estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estRMSE_db_B2_WDZ_LMMmis

relative RMSE (in percentages) of estRMSE_db_B2_WDZ estimator (see doubleBoot function) of predictorLMMmis.

rB.estRMSE_db_B2_HM_LMMmis

relative bias (in percentages) of estRMSE_db_B2_HM estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estRMSE_db_B2_HM_LMMmis

relative RMSE (in percentages) of estRMSE_db_B2_HM estimator (see doubleBoot function) of predictorLMMmis.

rB.estRMSE_db_1_LMMmis

relative bias (in percentages) of estRMSE_db_1 estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estRMSE_db_1_LMMmis

relative RMSE (in percentages) of estRMSE_db_1 estimator (see doubleBoot function) of predictorLMMmis.

rB.estRMSE_db_1_WDZ_LMMmis

relative bias (in percentages) of estRMSE_db_1_WDZ estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estRMSE_db_1_WDZ_LMMmis

relative RMSE (in percentages) of estRMSE_db_1_WDZ estimator (see doubleBoot function) of predictorLMMmis.

rB.estRMSE_db_1_EF_LMMmis

relative bias (in percentages) of estRMSE_db_1_EF estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estRMSE_db_1_EF_LMMmis

relative RMSE (in percentages) of estRMSE_db_1_EF estimator (see doubleBoot function) of predictorLMMmis.

rB.estRMSE_db_telesc_LMMmis

relative bias (in percentages) of estRMSE_db_telesc estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estRMSE_db_telesc_LMMmis

relative RMSE (in percentages) of estRMSE_db_telesc estimator (see doubleBoot function) of predictorLMMmis.

rB.estRMSE_db_telesc_WDZ_LMMmis

relative bias (in percentages) of estRMSE_db_telesc_WDZ estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estRMSE_db_telesc_WDZ_LMMmis

relative RMSE (in percentages) of estRMSE_db_telesc_WDZ estimator (see doubleBoot function) of predictorLMMmis.

rB.estRMSE_db_telesc_EF_LMMmis

relative bias (in percentages) of estRMSE_db_telesc_EF estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estRMSE_db_telesc_EF_LMMmis

relative RMSE (in percentages) of estRMSE_db_telesc_EF estimator (see doubleBoot function) of predictorLMMmis.

rB.estQAPE_param_LMMmis

relative bias (in percentages) of estQAPE_param estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estQAPE_param_LMMmis

relative RMSE (in percentages) of estQAPE_param estimator (see doubleBoot function) of predictorLMMmis.

rB.estQAPE_db_B2_LMMmis

relative bias (in percentages) of estQAPE_db_B2 estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estQAPE_db_B2_LMMmis

relative RMSE (in percentages) of estQAPE_db_B2 estimator (see doubleBoot function) of predictorLMMmis.

rB.estQAPE_db_1_LMMmis

relative bias (in percentages) of estQAPE_db_1 estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estQAPE_db_1_LMMmis

relative RMSE (in percentages) of estQAPE_db_1 estimator (see doubleBoot function) of predictorLMMmis.

rB.estQAPE_db_telesc_LMMmis

relative bias (in percentages) of estQAPE_db_telesc estimator (see doubleBoot function) of predictorLMMmis.

rRMSE.estQAPE_db_telesc_LMMmis

relative RMSE (in percentages) of estQAPE_db_telesc estimator (see doubleBoot function) of predictorLMMmis.

rB.estMSE_param_LMM

relative bias (in percentages) of estMSE_param estimator (see doubleBoot function) of predictorLMM.

rRMSE.estMSE_param_LMM

relative RMSE (in percentages) of estMSE_param estimator (see doubleBoot function) of predictorLMM.

rB.estMSE_db_B2_LMM

relative bias (in percentages) of estMSE_db_B2 estimator (see doubleBoot function) of predictorLMM.

rRMSE.estMSE_db_B2_LMM

relative RMSE (in percentages) of estMSE_db_B2 estimator (see doubleBoot function) of predictorLMM.

rB.estMSE_db_B2_WDZ_LMM

relative bias (in percentages) of estMSE_db_B2_WDZ estimator (see doubleBoot function) of predictorLMM.

rRMSE.estMSE_db_B2_WDZ_LMM

relative RMSE (in percentages) of estMSE_db_B2_WDZ estimator (see doubleBoot function) of predictorLMM.

rB.estMSE_db_B2_HM_LMM

relative bias (in percentages) of estMSE_db_B2_HM estimator (see doubleBoot function) of predictorLMM.

rRMSE.estMSE_db_B2_HM_LMM

relative RMSE (in percentages) of estMSE_db_B2_HM estimator (see doubleBoot function) of predictorLMM.

rB.estMSE_db_1_LMM

relative bias (in percentages) of estMSE_db_1 estimator (see doubleBoot function) of predictorLMM.

rRMSE.estMSE_db_1_LMM

relative RMSE (in percentages) of estMSE_db_1 estimator (see doubleBoot function) of predictorLMM.

rB.estMSE_db_1_WDZ_LMM

relative bias (in percentages) of estMSE_db_1_WDZ estimator (see doubleBoot function) of predictorLMM.

rRMSE.estMSE_db_1_WDZ_LMM

relative RMSE (in percentages) of estMSE_db_1_WDZ estimator (see doubleBoot function) of predictorLMM.

rB.estMSE_db_1_EF_LMM

relative bias (in percentages) of estMSE_db_1_EF estimator (see doubleBoot function) of predictorLMM.

rRMSE.estMSE_db_1_EF_LMM

relative RMSE (in percentages) of estMSE_db_1_EF estimator (see doubleBoot function) of predictorLMM.

rB.estMSE_db_telesc_LMM

relative bias (in percentages) of estMSE_db_telesc estimator (see doubleBoot function) of predictorLMM.

rRMSE.estMSE_db_telesc_LMM

relative RMSE (in percentages) of estMSE_db_telesc estimator (see doubleBoot function) of predictorLMM.

rB.estMSE_db_telesc_WDZ_LMM

relative bias (in percentages) of estMSE_db_telesc_WDZ estimator (see doubleBoot function) of predictorLMM.

rRMSE.estMSE_db_telesc_WDZ_LMM

relative RMSE (in percentages) of estMSE_db_telesc_WDZ estimator (see doubleBoot function) of predictorLMM.

rB.estMSE_db_telesc_EF_LMM

relative bias (in percentages) of estMSE_db_telesc_EF estimator (see doubleBoot function) of predictorLMM.

rRMSE.estMSE_db_telesc_EF_LMM

relative RMSE (in percentages) of estMSE_db_telesc_EF estimator (see doubleBoot function) of predictorLMM.

rB.estRMSE_param_LMM

relative bias (in percentages) of estRMSE_param estimator (see doubleBoot function) of predictorLMM.

rRMSE.estRMSE_param_LMM

relative RMSE (in percentages) of estRMSE_param estimator (see doubleBoot function) of predictorLMM.

rB.estRMSE_db_B2_LMM

relative bias (in percentages) of estRMSE_db_B2 estimator (see doubleBoot function) of predictorLMM.

rRMSE.estRMSE_db_B2_LMM

relative RMSE (in percentages) of estRMSE_db_B2 estimator (see doubleBoot function) of predictorLMM.

rB.estRMSE_db_B2_WDZ_LMM

relative bias (in percentages) of estRMSE_db_B2_WDZ estimator (see doubleBoot function) of predictorLMM.

rRMSE.estRMSE_db_B2_WDZ_LMM

relative RMSE (in percentages) of estRMSE_db_B2_WDZ estimator (see doubleBoot function) of predictorLMM.

rB.estRMSE_db_B2_HM_LMM

relative bias (in percentages) of estRMSE_db_B2_HM estimator (see doubleBoot function) of predictorLMM.

rRMSE.estRMSE_db_B2_HM_LMM

relative RMSE (in percentages) of estRMSE_db_B2_HM estimator (see doubleBoot function) of predictorLMM.

rB.estRMSE_db_1_LMM

relative bias (in percentages) of estRMSE_db_1 estimator (see doubleBoot function) of predictorLMM.

rRMSE.estRMSE_db_1_LMM

relative RMSE (in percentages) of estRMSE_db_1 estimator (see doubleBoot function) of predictorLMM.

rB.estRMSE_db_1_WDZ_LMM

relative bias (in percentages) of estRMSE_db_1_WDZ estimator (see doubleBoot function) of predictorLMM.

rRMSE.estRMSE_db_1_WDZ_LMM

relative RMSE (in percentages) of estRMSE_db_1_WDZ estimator (see doubleBoot function) of predictorLMM.

rB.estRMSE_db_1_EF_LMM

relative bias (in percentages) of estRMSE_db_1_EF estimator (see doubleBoot function) of predictorLMM.

rRMSE.estRMSE_db_1_EF_LMM

relative RMSE (in percentages) of estRMSE_db_1_EF estimator (see doubleBoot function) of predictorLMM.

rB.estRMSE_db_telesc_LMM

relative bias (in percentages) of estRMSE_db_telesc estimator (see doubleBoot function) of predictorLMM.

rRMSE.estRMSE_db_telesc_LMM

relative RMSE (in percentages) of estRMSE_db_telesc estimator (see doubleBoot function) of predictorLMM.

rB.estRMSE_db_telesc_WDZ_LMM

relative bias (in percentages) of estRMSE_db_telesc_WDZ estimator (see doubleBoot function) of predictorLMM.

rRMSE.estRMSE_db_telesc_WDZ_LMM

relative RMSE (in percentages) of estRMSE_db_telesc_WDZ estimator (see doubleBoot function) of predictorLMM.

rB.estRMSE_db_telesc_EF_LMM

relative bias (in percentages) of estRMSE_db_telesc_EF estimator (see doubleBoot function) of predictorLMM.

rRMSE.estRMSE_db_telesc_EF_LMM

relative RMSE (in percentages) of estRMSE_db_telesc_EF estimator (see doubleBoot function) of predictorLMM.

rB.estQAPE_param_LMM

relative bias (in percentages) of estQAPE_param estimator (see doubleBoot function) of predictorLMM.

rRMSE.estQAPE_param_LMM

relative RMSE (in percentages) of estQAPE_param estimator (see doubleBoot function) of predictorLMM.

rB.estQAPE_db_B2_LMM

relative bias (in percentages) of estQAPE_db_B2 estimator (see doubleBoot function) of predictorLMM.

rRMSE.estQAPE_db_B2_LMM

relative RMSE (in percentages) of estQAPE_db_B2 estimator (see doubleBoot function) of predictorLMM.

rB.estQAPE_db_1_LMM

relative bias (in percentages) of estQAPE_db_1 estimator (see doubleBoot function) of predictorLMM.

rRMSE.estQAPE_db_1_LMM

relative RMSE (in percentages) of estQAPE_db_1 estimator (see doubleBoot function) of predictorLMM.

rB.estQAPE_db_telesc_LMM

relative bias (in percentages) of estQAPE_db_telesc estimator (see doubleBoot function) of predictorLMM.

rRMSE.estQAPE_db_telesc_LMM

relative RMSE (in percentages) of estQAPE_db_telesc estimator (see doubleBoot function) of predictorLMM.

MCpositiveDefiniteEstGlev1

number of cases ouf of K with postive definite estimated covariance matrix of random effects used to generate bootstrap realizations of the dependent variable at the first level of the double bootstrap.

MCpositiveDefiniteEstGlev2

number of cases ouf of K*B1 with positive definite estimated covariance matrix of random effects used to generate bootstrap realizations of the dependent variable at the second level of the double bootstrap.

Author(s)

Tomasz Zadlo

References

1. Chatterjee, S., Lahiri, P. Li, H. (2008) Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models, Annals of Statistics, Vol. 36 (3), pp. 1221?1245.

2. Rao, J.N.K. and Molina, I. (2015) Small Area Estimation. Second edition, John Wiley & Sons, New Jersey.

3. Zadlo T. (2017), On asymmetry of prediction errors in small area estimation, Statistics in Transition, 18 (3), 413-432.

Examples

library(lme4)
library(Matrix)
library(mvtnorm)
library(matrixcalc) 
library(qape)

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

Ypop <- log(invData2018$investments)

# Monte Carlo simulation study under the model defined in predictorLMM
# correctly specified for predictorLMM and misspecified for predictorLMMmis
set.seed(211)
mcBootMis(Ypop, predictorLMM, predictorLMMmis, 2, 2, 2, c(0.5, 0.9), 0.77) 

detach(invData2018)