The paper introduces an R Package of multivariate Fay-Herriot models for small area estimation named msae. This package implements four types of Fay-Herriot models, including univariate Fay-Herriot model (model 0), multivariate Fay-Herriot model (model 1), autoregressive multivariate Fay-Herriot model (model 2), and heteroskedastic autoregressive multivariate Fay-Herriot model (model 3). It also contains some datasets generated based on multivariate Fay-Herriot models. We describe and implement functions through various practical examples. Multivariate Fay-Herriot models produce a more efficient parameter estimation than direct estimation and univariate model.
In general, surveys are designed for large areas with sufficient sample size. If the survey is used for small areas in which the sample sizes are not sufficient, the results of estimates may not be reliable due to the large standard error. Therefore, a Small Area Estimation (SAE) method was developed, to increase the effectiveness of the sample size by borrowing the strength of the neighboring region and information from the auxiliary variables that have a strong relationship with the observational variable. This study aims to analyze the SAE using Multivariate Fay-Herriot (MFH) model and Univariate Fay-Herriot (UFH) model for a variety of sample sizes. Simulations were conducted by using household expenditure per capita of food group and non-food group data from Susenas on March 2017. The simulation results showed that the average Root Mean Square Errors (RMSEs) using the MFH models in various sample size are smaller than the UFH model and the direct estimation.
The linear mixed models (LMMs) are widely used for data analysis to account fixed effects and random effects in Gaussian response models. In LMMs, the random effects and the within-subject errors have been assumed to be normally distributed but in practice, such an assumption could easily be violated due to the presence of atypical data. Motivated by a concern of sensitivity to potential outliers or data with longer-than-normal tails, many researchers have developed robust LMMs using t distribution (abbreviated as tLMM). This paper discussed the comparison between the LMMs and the tLMMs especially 58 Azka Ubaidillah et al. from perspectives of the fitness and robustness of the models. The application of tLMM to household consumption per capita expenditure data was also demonstrated in this paper. The results of this study showed that the tLMMs provided better estimates than LMMs in term of performance and robustness. Furthermore, it was also showed that the best model to handle outliers was found to be the tLMM with the smallest degrees of freedom.
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