pbmseebBHF: Parametric bootstrap mean squared error estimators of EB...
In sae: Small Area Estimation

Description Usage Arguments Details Value References See Also Examples

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.

1 2	pbmseebBHF(formula, dom, selectdom, Xnonsample, B = 100, MC = 100, data, transform = "BoxCox", lambda = 0, constant = 0, indicator)

`formula`	an object of class `formula` (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under Details.
`dom`	`n*1` vector or factor (same size as `y` in `formula`) with domain codes.
`selectdom`	`I*1` optional vector or factor with the domain codes for which we want to estimate the indicators. It must be a subset of the domain codes in `dom`. If this parameter is not included, the unique domain codes included in `dom` are considered.
`Xnonsample`	matrix or data frame containing in the first column the domain codes and in the rest of columns the values of each of `p` auxiliary variables for the out-of-sample units in each selected domain.
`B`	number of bootstrap replicates. Default value is `100`.
`MC`	number of Monte Carlo replicates for the empirical approximation of the EB estimator. Default value is `100`.
`data`	optional data frame containing the variables named in `formula` and `dom`. By default the variables are taken from the environment from which `pbmseebBHF` is called.
`transform`	type of transformation for the dependent variable to be chosen between the `"BoxCox"` and `"power"` families so that the dependent variable in `formula` follows approximately a Normal distribution. Default value is `"BoxCox"`.
`lambda`	value for the parameter of the family of transformations specified in `transform`. Default value is `0`, which gives the log transformation for the two possible families.
`constant`	constant added to the dependent variable before doing the transformation, to achieve a distribution close to Normal. Default value is `0`.
`indicator`	function of the (untransformed) variable on the left hand side of `formula` that we want to estimate in each domain.

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.

The function returns a list with the following objects:

`est`	a list with the results of the estimation process: `eb` and `fit`. For the description of these objects, see Value of `ebBHF` function.
`mse`	data frame with number of rows equal to number of selected domains, containing in its columns the domain codes (`domain`) and the parametric bootstrap mean squared error estimates of `indicator` (`mse`).

Cases with NA values in formula or dom are ignored.

- Small Area Methods for Poverty and Living Conditions Estimates (SAMPLE), funded by European Commission, Collaborative Project 217565, Call identifier FP7-SSH-2007-1.

- Molina, I. and Rao, J.N.K. (2010). Small Area Estimation of Poverty Indicators. The Canadian Journal of Statistics 38, 369-385.

ebBHF

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)