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Empirical Best Linear Unbiased Prediction based on a Fay-Herriot Model.

Source: R/eblup_fh.R
eblup_fh.Rd

This function gives the Empirical Best Linear Unbiased Prediction (EBLUP) or Empirical Best (EB) predictor under normality based on a Fay-Herriot model.

Usage

eblup_fh(
  formula,
  vardir,
  domain = NULL,
  data,
  method = c("REML", "ML"),
  maxiter = 100,
  precision = 1e-04,
  print_result = TRUE
)

Arguments

formula

an object of class formula that contains a description of the model to be fitted.

vardir

vector or column names from data that contain variance sampling from the direct estimator.

domain

vector, column name or one-sided formula referencing a domain names column in data. If NULL, the domains are numbered consecutively.

data

a data frame or a data frame extension (e.g. a tibble).

method

Fitting method can be chosen between 'ML' and 'REML'.

maxiter

maximum number of iterations allowed in the Fisher-scoring algorithm.

precision

convergence tolerance limit for the Fisher-scoring algorithm.

print_result

print coefficient or not, default value is TRUE.

Value

The function returns a list with the following objects: estcoef a data frame with the estimated model coefficients, random_effect_var estimated random effect variance, goodness vector containing several goodness-of-fit measures, df_eblup a data frame that contains y, eblup, random_effect, vardir, mse, and rse.

  • 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

  • rse Relative Standart Error (%)

Details

The model has a form that is response ~ auxiliary variables. where numeric type response variables can contain NA. When the response variable contains NA it will be estimated with synthetic estimator.

References

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

Examples

library(fastsae)

# Standard Fay-Herriot model
m1 <- eblup_fh(
  y ~ x1 + x2 + x3,
  data = mys,
  vardir = "vardir"
)
#> 
#> ── Fast Small Area Estimation (fastsae) ────────────────────────────────────────
#> Call:
#> eblup_fh(formula = y ~ x1 + x2 + x3, vardir = "vardir", data = mys)
#> 
#> ✔ Convergence: Yes (in 6 iterations)
#> Model: Fay-Herriot (Area-level)
#> Method: eblup
#> Random effect variance (sigma2_u): 2.608103 
#> 
#> Fixed Effects Coefficients:
#>                   beta  std.error     zvalue pvalue
#> (Intercept)  3.1077510  0.7697687  4.0372527 0.0001
#> x1          -0.0019323  0.0098886 -0.1954019 0.8451
#> x2           0.0555184  0.0614129  0.9040187 0.3660
#> x3           0.0335344  0.0580013  0.5781663 0.5632
#> 
#> EBLUP Estimates (First 6 domains):
#>   domain        y    eblup    vardir random_effect       mse       rse
#> 1      1 8.359527 7.612738 0.6618838    2.94266461 0.5616180  9.844182
#> 2      2 7.599650 6.782316 0.8374691    2.54539588 0.6784873 12.144869
#> 3      3 5.514137 5.187060 0.8822257    0.96692722 0.7190378 16.347620
#> 4      4 3.869326 4.201545 0.6581716   -1.31646412 0.5619314 17.841554
#> 5      5 6.305063 6.323679 1.2788021   -0.03796677 0.9370273 15.307573
#> 6      6 3.926807 4.048590 0.3878004   -0.81904048 0.3548310 14.713194
#> ... and 36 more rows.
#>