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© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.

Abstract

Efficient estimation methods for simultaneous autoregressive (SAR) models with missing data in the response variable have been well explored in the literature. A common practice is introducing measurement error into SAR models to separate the noise component from the spatial process. However, prior studies have not considered incorporating measurement error into SAR models with missing data. Maximum likelihood estimation for such models, especially with large datasets, poses significant computational challenges. This paper proposes an efficient likelihood-based estimation method, the marginal maximum likelihood (ML), for estimating SAR models on large datasets with measurement errors and a high percentage of missing data in the response variable. The spatial autoregressive model (SAM) and the spatial error model (SEM), two popular SAR model types, are considered. The missing data mechanism is assumed to follow a missing-at-random (MAR) pattern. We propose a fast method for marginal ML estimation with a computational complexity of O(n3/2), where n is the total number of observations. This complexity applies when the spatial weight matrix is constructed based on a local neighbourhood structure. The effectiveness of the proposed methods is demonstrated through simulations and real-world data applications.

Details

Title
A Marginal Maximum Likelihood Approach for Hierarchical Simultaneous Autoregressive Models with Missing Data
Author
Wijayawardhana, Anjana; Gunawan, David; Suesse, Thomas
First page
3870
Publication year
2024
Publication date
2024
Publisher
MDPI AG
e-ISSN
22277390
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
3144154445
Copyright
© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.