Frontiers of Mathematics in China >

2023 , Vol. 18 >Issue 5: 327 - 339

DOI: https://doi.org/10.3868/s140-DDD-023-0023-x

The large sample property of the iterative generalized least squares estimation for hierarchical mixed effects model

  • Chunyu WANG 1 ,
  • Maozai TIAN , 1,2,3
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  • 1. Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100872, China
  • 2. School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730020, China
  • 3. Xinjiang Social & Economic Statistics Research Center, School of Statistics and Information, Xinjiang University of Finance and Economics, Urumqi 830012, China
mztian@ruc.edu.cn

Published date: 15 Oct 2023

Copyright

2023 Higher Education Press 2023
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Abstract

In many fields, we need to deal with hierarchically structured data. For this kind of data, hierarchical mixed effects model can show the correlation of variables in the same level by establishing a model for regression coefficients. Due to the complexity of the random part in this model, seeking an effective method to estimate the covariance matrix is an appealing issue. Iterative generalized least squares estimation method was proposed by Goldstein in 1986 and was applied in special case of hierarchical model. In this paper, we extend the method to the general hierarchical mixed effects model, derive its expressions in detail and apply it to economic examples.

Key words： Hierarchical model; iterative generalized least squares estimation; variance-covariance components; maximum likelihood estimation

Cite this article

Chunyu WANG , Maozai TIAN . The large sample property of the iterative generalized least squares estimation for hierarchical mixed effects model[J]. Frontiers of Mathematics in China, 2023 , 18(5) : 327 -339 . DOI: 10.3868/s140-DDD-023-0023-x

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