eblupfh_ns: Synthetic Estimator.

In saens: Small Area Estimation with Cluster Information for Estimation of Non-Sampled Areas

Synthetic Estimator.

Description

Synthetic estimator is one of the simple methods to obtain predicted values of mean specific area parameters, which the direct estimates are unknown. Based on estimated of parameter coefficient models using Empirical Best Unbiased Prediction (EBLUP), the synthetic estimator is obtained by calibrating the estimated parameter coefficient to the auxiliary variables.

Usage

eblupfh_ns(
  formula,
  data,
  vardir,
  method = "REML",
  maxiter = 100,
  precision = 1e-04,
  scale = FALSE,
  print_result = TRUE
)

Arguments

formula	an object of class formula that contains a description of the model to be fitted. The variables included in the formula must be contained in the data.
data	a data frame or a data frame extension (e.g. a tibble).
vardir	vector or column names from data that contain variance sampling from the direct estimator for each area.
method	Fitting method can be chosen between 'ML' and 'REML'
maxiter	maximum number of iterations allowed in the Fisher-scoring algorithm. Default is 100 iterations.
precision	convergence tolerance limit for the Fisher-scoring algorithm. Default value is 0.0001.
scale	scaling auxiliary variable or not, default value is FALSE.
print_result	print coefficient or not, default value is TRUE.

Details

The model is defined as response ~ auxiliary variables, where the response variable, of numeric type, may contain NA values. When the response variable contains NA, it will be estimated using a synthetic estimator.

Value

The function returns a list with the following objects df_res and fit: df_res a data frame that contains the following columns:

• y variable response
  

• eblup estimated results for each area
  

• random_effect random effect for each area
  

• vardir variance sampling from the direct estimator for each area
  

• mse Mean Square Error
  

• cluster cluster information for each area
  

• rse Relative Standart Error (%)
  

fit a list containing the following objects:

• estcoef a data frame with the estimated model coefficients in the first column (beta), their asymptotic standard errors in the second column (std.error), the t-statistics in the third column (tvalue) and the p-values of the significance of each coefficient in last column (pvalue)
  

• model_formula model formula applied
  

• method type of fitting method applied (ML or REML)
  

• random_effect_var estimated random effect variance
  

• convergence logical value that indicates the Fisher-scoring algorithm has converged or not
  

• n_iter number of iterations performed by the Fisher-scoring algorithm.
  

• goodness vector containing several goodness-of-fit measures: loglikehood, AIC, and BIC
  

References

1. Rao, J. N., & Molina, I. (2015). Small area estimation. John Wiley & Sons.

Examples

library(saens)

m1 <- eblupfh_ns(y ~ x1 + x2 + x3, data = mys, vardir = "var")
m1 <- eblupfh_ns(y ~ x1 + x2 + x3, data = mys, vardir = ~var)

saens documentation built on April 4, 2025, 4:43 a.m.