msef function

Analytic MSE for Model 1

This function calculates the analytic MSE for the multinomial mixed model with one independent random effect per category of the response variable (Model 1). See Lopez-Vizcaino et al. (2013), section 4, for details. The formulas of Prasad and Rao (1990) are adapted to Model 1. This function uses the output of modelfit1.

msef(pp, X, Z, resul, MM, M)

Arguments

• resul: the output of the function modelfit1.
• 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.
• pp: vector with the number of the auxiliary variables per category.
• M: vector with the area sample sizes.
• MM: vector with the population sample sizes.

Returns

mse is a matrix with the MSE estimator calculated by adapting the explicit formulas of Prasad and Rao (1990).

Examples

require(Matrix)

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)  #data
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)

#Analytic MSE
mse=msef(pp,datar$X,datar$Z,result,datar$N,datar$n)

References

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

Prasad, NGN, Rao, JNK (1990).The estimation of the mean squared error of small area estimators. Journal of the American Statistical Association, 85, 163-171.

See Also

data.mme, initial.values, wmatrix, phi.mult, prmu, phi.direct, sPhikf, modelfit1, Fbetaf, ci, mseb.