Comparing Linear and non-linear Mixed Effects Models with Autoregressive Error under Small Area Estimation

Document Type : Original Article

Authors
Abdolreza Sayyareh 1
Sedigheh Zamani-Mehreyan 2
Omolbanin Bashiri Goudarzi 1
Mahmoud Torabi 3
1 Department of Computer Sciences and Statistics, Faculty of Mathematics, K.N. Toosi, University of Technology, Tehran, Iran.
2 Department of Statistics‎, ‎Imam Khomeini International University‎, ‎Qazvin‎, ‎Iran
3 Department of Biostatistics‎, ‎Manitoba University‎, ‎Winnipeg‎, ‎Canada
10.22034/jirss.2025.2046692.1086
Abstract
The problem of small area estimation is how to produce reliable estimates of characteristics of interest such as means, counts and quantiles. It is usually assumed that the observed values and the auxiliary values follow the linear regression model and the sampling errors are dependent and follow the autoregressive model. However, in practice, there are many situations in the observed values and the auxiliary values follow the non-linear regression model. We assume that the true model is unknown and consider some non-nested, non-linear or linear regression models as rival models and select an optimal model based on extensions of the model selection tests such as Vuong's test. This paper considers non-linear regression models to improve estimation and model selection based on latent variables and proposes a global model selection test for small-area estimation. A numerical example and real data analysis were carried out to illustrate the procedures obtained theoretically.
Keywords
EM Algorithm
Information Criterion
Model Selection
Mixed Effect Model
Small Area Estimation
Autoregressive Model
Subjects
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Journal of the Iranian Statistical Society
Volume 24, Issue 1
June 2025
Pages 67-96

  • Receive Date 24 November 2024
  • Revise Date 10 July 2025
  • Accept Date 31 August 2025