eblupfh_cluster {saens}

EBLUPs based on a Fay-Herriot Model with Cluster Information.

Description

This function gives the Empirical Best Linear Unbiased Prediction (EBLUP) or Empirical Best (EB) predictor based on a Fay-Herriot model with cluster information for non-sampled areas.

Usage

eblupfh_cluster(
  formula,
  data,
  vardir,
  cluster,
  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.

cluster

vector or column name from data that contain cluster information.

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 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 cluster information.

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.

2. Anisa, R., Kurnia, A., & Indahwati, I. (2013). Cluster information of non-sampled area in small area estimation. E-Prosiding Internasional| Departemen Statistika FMIPA Universitas Padjadjaran, 1(1), 69-76.

Examples

library(saens)

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