mspeNERlin: Compute MSPE through linearization method for Nested error...

In saeMSPE: Computing MSPE Estimates in Small Area Estimation

Compute MSPE through linearization method for Nested error regression model

Description

This function returns MSPE estimator with linearization method for Nested error regression model. These include the seminal Prasad-Rao method and its generalizations by Datta-Lahiri. All these methods are developed for general linear mixed effects models

Usage

mspeNERlin(ni, formula, data, X.mean,
			 method = "PR", var.method = "default", na_rm, na_omit)

mspeNERPR(ni, formula, data, X.mean,
			 var.method = "default", na_rm, na_omit)

mspeNERDL(ni, formula, data, X.mean,
			 var.method = "default", na_rm, na_omit)

Arguments

ni	(vector). It represents the sample number for every small area.
formula	(formula). Stands for the model formula that specifies the auxiliary variables to be used in the regression model. This should follow the R model formula syntax.
data	(data frame). It represents the data containing the response values and auxiliary variables for the Nested Error Regression Model.
X.mean	(matrix). Stands for the population mean of auxiliary values.
method	The MSPE estimation method to be used. See "Details".
var.method	The variance component estimation method to be used. See "Details".
na_rm	A logical value indicating whether to remove missing values (NaN) from the input matrices and vectors. If TRUE, missing values in the input data (X, Y, ni, and X.mean) are automatically cleaned using internal functions. If FALSE, missing values are not removed. Defaults to FALSE.
na_omit	A logical value indicating whether to stop the execution if missing values (NaN) are present in the input data. If TRUE, the function will check for missing values in X, Y, ni, and X.mean. If any missing values are found, an error message will be raised, prompting the user to handle the missing data before proceeding. Defaults to FALSE.

Details

Default method for mspeNERlin is "PR", proposed by N. G. N. Prasad and J. N. K. Rao, Prasad-Rao (PR) method uses Taylor series expansion to obtain a second-order approximation to the MSPE. Function mspeNERlin also provide the following method:

Method "DL" advanced PR method to cover the cases when the variance components are estimated by ML and REML estimator. Set method = "DL".

For method = "PR", var.method = "MOM" is the only available variance component estimation method,

For method = "DL", var.method = "ML" or var.method = "REML" are available.

Value

This function returns a list with components:

MSPE	(vector) MSPE estimates for NER model.
bhat	(vector) Estimates of the unknown regression coefficients.
sigvhat2	(numeric) Estimates of the area-specific variance component.
sigehat2	(numeric) Estimates of the random error variance component.

Author(s)

Peiwen Xiao, Xiaohui Liu, Yu Zhang, Yuzi Liu, Jiming Jiang

References

N. G. N. Prasad and J. N. K. Rao. The estimation of the mean squared error of small-area estimators. Journal of the American Statistical Association, 85(409):163-171, 1990.

G. S. Datta and P. Lahiri. A unified measure of uncertainty of estimated best linear unbiased predictors in small area estimation problems. Statistica Sinica, 10(2):613-627, 2000.

Examples

### parameter setting 
Ni <- 1000
sigmaX <- 1.5
m <- 10
beta <- c(0.5, 1)
sigma_v2 <- 0.8
sigma_e2 <- 1
ni <- sample(seq(1, 10), m, replace = TRUE)
n <- sum(ni)
p <- length(beta)

pop.model <- function(Ni, sigmaX, beta, sigma_v2, sigma_e2, m) {
  x <- rnorm(m * Ni, 1, sqrt(sigmaX))
  v <- rnorm(m, 0, sqrt(sigma_v2))
  y <- numeric(m * Ni)
  theta <- numeric(m)
  kk <- 1
  for (i in 1:m) {
    sumx <- 0
    for (j in 1:Ni) {
      sumx <- sumx + x[kk]
      y[kk] <- beta[1] + beta[2] * x[kk] + v[i] + rnorm(1, 0, sqrt(sigma_e2))
      kk <- kk + 1
    }
    meanx <- sumx / Ni
    theta[i] <- beta[1] + beta[2] * meanx + v[i]
  }
  group <- rep(seq(m), each = Ni)
  data <- data.frame(y = y, group = group, x1 = x)
  return(list(data = data, theta = theta))
} 

sampleXY <- function(Ni, ni, m, Population) {
  Indx <- c()
  for (i in 1:m) {
    Indx <- c(Indx, sample(c(((i - 1) * Ni + 1):(i * Ni)), ni[i]))
  }
  Sample <- Population[Indx, ]
  return(Sample)
} 

Population <- pop.model(Ni, sigmaX, beta, sigma_v2, sigma_e2, m)$data
XY <- sampleXY(Ni, ni, m, Population)

formula <- y ~ x1
data <- XY

Xmean <- matrix(NA, m, p)
for (tt in 1:m) {
  Xmean[tt, ] <- colMeans(Population[which(Population$group == tt), "x1", drop = FALSE])
}

result <- mspeNERlin(ni, formula, data, Xmean, method = "PR", var.method = "default")

saeMSPE documentation built on April 4, 2025, 5:18 a.m.