gof: Goodness of fit diagnostic

In SAEval: Small Area Estimation Evaluation

Goodness of fit diagnostic

Description

The goodness of fit diagnostic allows to evaluate how close the model-based estimates are to the direct estimates when they are good.

Usage

gof(data,dir,sae,v.dir,mse.sae,alfa=0.05)

Arguments

data	a data frame containing the direct and small area estimates among with their variance, e.g. SAEval_example.
dir	formula identifing the direct estimates.
sae	formula identifing the small area estimates.
v.dir	formula identifing the direct estimates variance.
mse.sae	formula identifing the small area estimates mean squared error.
alfa	double number. The significance level of the Chi-squared test (default=0.05).

Details

As in the bias diagnostic, even with this procedure we want to know if the model estimates are close to the direct estimates. To evaluate this we compute the squared difference between the model estimates and the direct estimate which are weighted inversely by their variance and summed over all the domains. As a check for the lack of bias of the model estimates this statistic is compared with the quantiles of Chi-squared distribution. Finally results are provided using a Wald goodness of fit statistic.

The small area with both direct estimate and variance of the direct estimates equal to NA value are automatically removed from the data.

Value

Object of class data.frame. The data frame contains information for the small area estimators (methods), Wald statistic (W), Chi-squared statistic (c2), p-value for Wald statistic (p_value) and the test result (results).

Author(s)

Developed by Andrea Fasulo

References

Brown, G., Chambers, R., Heady, P., Heasman, D. (2001), Evaluation of small area estimation methods - An application to unemployment estimates from the UK LFS, in Proceedings of Statistics Canada Symposium 2001: Achieving Data Quality in a Statistical Agency: A Methodological Perspective, Statistics Canada.

Mukhopadhyay, P. K., McDowell, A. (2011). Small area estimation for survey data analysis using SAS software, http://support.sas.com/rnd/app/papers/smallarea.pdf.

Srivastava, A. K., Sud, U. C., Chandra, H. (2007). Small area estimation - An application to National Sample Survey Data, Journal of the Indian Society of Agricultural Statistics, 61(2), 249-254.

Examples

# Load example data
data(SAEval_example)

SAEval.gof<-gof(data=SAEval_example,
       dir=~y_d,
       sae=~y_syna+y_eblupa+y_spaznr+y_eblupb+y_synb+y_logis,
       v.dir=~mse_d,
       mse.sae=~mse_sa+mse_eba2+mse_spaznr+mse_ebb+mse_sb+mse_log)

SAEval.gof

SAEval documentation built on March 31, 2023, 9 p.m.