Parametric bootstrap mean squared error estimators of EB estimators.
Description
This function obtains estimators of the mean squared errors of the EB estimators of domain parameters by a parametric bootstrap method. Population values of auxiliary variables are required.
Usage
1 2  pbmseebBHF(formula, dom, selectdom, Xnonsample, B = 100, MC = 100, data,
transform = "BoxCox", lambda = 0, constant = 0, indicator)

Arguments
formula 
an object of class 
dom 

selectdom 

Xnonsample 
matrix or data frame containing in the first column the domain codes and in the rest of columns the values of each of

B 
number of bootstrap replicates. Default value is 
MC 
number of Monte Carlo replicates for the empirical approximation of the EB estimator. Default value is 
data 
optional data frame containing the variables named in 
transform 
type of transformation for the dependent variable to be chosen between the 
lambda 
value for the parameter of the family of transformations specified in 
constant 
constant added to the dependent variable before doing the transformation, to achieve a distribution close to Normal. Default value is 
indicator 
function of the (untransformed) variable on the left hand side of 
Details
This function uses random number generation. To fix the seed, use set.seed
.
A typical model has the form response ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response. A terms specification of the form first + second indicates all the terms in first together with all the terms in second with duplicates removed. A terms specification of the form first + second indicates all the terms in first together with all the terms in second with any duplicates removed.
A formula has an implied intercept term. To remove this use either y ~ x  1 or y ~ 0 + x. See formula
for more details of allowed formulae.
Value
The function returns a list with the following objects:
est 
a list with the results of the estimation process: 
mse 
data frame with number of rows equal to number of selected domains, containing in its columns the domain codes ( 
Cases with NA values in formula
or dom
are ignored.
References
 Small Area Methods for Poverty and Living Conditions Estimates (SAMPLE), funded by European Commission, Collaborative Project 217565, Call identifier FP7SSH20071.
 Molina, I. and Rao, J.N.K. (2010). Small Area Estimation of Poverty Indicators. The Canadian Journal of Statistics 38, 369385.
See Also
ebBHF
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  data(incomedata) # Load data set
attach(incomedata)
# Construct design matrix for sample elements
Xs<cbind(age2,age3,age4,age5,nat1,educ1,educ3,labor1,labor2)
# Select the domains to compute EB estimators
data(Xoutsamp)
domains < c(5)
# Poverty incidence indicator
povertyline < 0.6*median(incomedata$income)
povertyline # 6477.484
povinc < function(y)
{
z < 6477.484
result < mean(y<z)
return (result)
}
# Compute parametric bootstrap MSE estimators of the EB
# predictors of poverty incidence. Take constant=3600 to achieve
# approximately symmetric residuals.
set.seed(123)
result < pbmseebBHF(income~Xs, dom=prov, selectdom=domains,
Xnonsample=Xoutsamp, B=2, MC=2, constant=3600,
indicator=povinc)
result$est$eb
result$mse
result$est$fit$refvar
detach(incomedata)
