mseb {mme}

Bias and MSE using parametric bootstrap

Description

This function calculates the bias and the mse for the multinomial mixed effects models using parametric bootstrap. Three types of multinomial mixed models are considered, with one independent domain random effect in each category of the response variable (Model 1), with two random effects: the first, with a domain random effect and with independent time and domain random effect (Model 2) and the second, with a domain random effect and with correlated time and domain random effect (Model 3). See details of the parametric bootstrap procedure in Gonzalez-Manteiga et al. (2008) and in Lopez-Vizcaino et al. (2013) for the adaptation to these three models. This function uses the output of modelfit1, modelfit2 or modelfit3, depending of the current multinomial mixed model.

Usage

mseb(pp, Xk, X, Z, M, MM, resul, B, mod)

Arguments

pp

vector with the number of the auxiliary variables per category.

Xk

list of matrices with the auxiliary variables per category obtained from data.mme. The dimension of the list is the number of domains.

X

list of matrices with the auxiliary variables obtained from data.mme. The dimension of the list is the number of categories of the response variable minus one.

Z

design matrix of random effects obtained from data.mme.

M

vector with the area sample sizes.

MM

vector with the population sample sizes.

resul

output of the function modelfit1, modelfit2 or modelfit3.

B

number of bootstrap replications.

mod

a number specifying the type of models: 1=multinomial mixed model with one independent random effect in each category of the response variable (Model 1), 2=multinomial mixed model with two independent random effects in each category of the response variable: one domain random effect and another independent time and domain random effect (Model 2) and 3= multinomial model with two independent random effects in each category of the response variable: one domain random effect and another correlated time and domain random effect (Model 3).

Value

a list containing the following components.

bias.pboot

BIAS of the parametric bootstrap estimator of the mean of the response variable

mse.pboot

MSE of the parametric bootstrap estimator of the mean of the response variable

rmse.pboot

RMSE of the parametric bootstrap estimator of the mean of the response variable

References

Lopez-Vizcaino, ME, Lombardia, MJ and Morales, D (2013). Multinomial-based small area estimation of labour force indicators. Statistical Modelling, 13 ,153-178.

Lopez-Vizcaino, ME, Lombardia, MJ and Morales, D (2013). Small area estimation of labour force indicator under a multinomial mixed model with correlated time and area effects. Submitted for review.

Gonzalez-Manteiga, W, Lombardia, MJ, Molina, I, Morales, D, Santamaria, L (2008). Estimation of the mean squared error of predictors of small area linear parameters under a logistic mixed model, Computational Statistics and Data Analysis, 51, 2720-2733.

See Also

data.mme, initial.values, wmatrix, phi.mult, phi.mult.it, phi.mult.ct, prmu, prmu.time, phi.direct, phi.direct.it, phi.direct.ct, sPhikf, sPhikf.it, sPhikf.ct, modelfit1, modelfit2, modelfit3, omega, Fbetaf, Fbetaf.it, Fbetaf.ct, ci.

Examples

k=3 #number of categories of the response variable
pp=c(1,1) #vector with the number of auxiliary variables in each category
data(simdata)
mod=1  # Type of model
datar=data.mme(simdata,k,pp,mod)
##Model fit
result=modelfit1(pp,datar$Xk,datar$X,datar$Z,datar$initial,datar$y[,1:(k-1)],datar$n,datar$N)

B=1    #Bootstrap iterations
ss=12345 #SEED
set.seed(ss)

##Bootstrap parametric BIAS and MSE
mse.pboot=mseb(pp,datar$Xk,datar$X,datar$Z,datar$n,datar$N,result,B,mod)