A Marginal Maximum Likelihood Approach for Hierarchical Simultaneous Autoregressive Models with Missing Data
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...
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2024-12-01
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| author | Anjana Wijayawardhana David Gunawan Thomas Suesse |
| author_facet | Anjana Wijayawardhana David Gunawan Thomas Suesse |
| author_sort | Anjana Wijayawardhana |
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| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><msup><mi>n</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow></semantics></math></inline-formula>, where <i>n</i> 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. |
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| language | English |
| publishDate | 2024-12-01 |
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| spelling | doaj-art-cdfcbca586214abda93ea96fbb36da4e2025-08-20T02:50:38ZengMDPI AGMathematics2227-73902024-12-011223387010.3390/math12233870A Marginal Maximum Likelihood Approach for Hierarchical Simultaneous Autoregressive Models with Missing DataAnjana Wijayawardhana0David Gunawan1Thomas Suesse2School of Mathematics and Applied Statistics, University of Wollongong, Wollongong 2522, AustraliaSchool of Mathematics and Applied Statistics, University of Wollongong, Wollongong 2522, AustraliaSchool of Mathematics and Applied Statistics, University of Wollongong, Wollongong 2522, AustraliaEfficient 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><msup><mi>n</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow></semantics></math></inline-formula>, where <i>n</i> 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.https://www.mdpi.com/2227-7390/12/23/3870spatial error modelspatial autoregressive modelmeasurement errorsmarginal likelihoodcomputational complexity |
| spellingShingle | Anjana Wijayawardhana David Gunawan Thomas Suesse A Marginal Maximum Likelihood Approach for Hierarchical Simultaneous Autoregressive Models with Missing Data Mathematics spatial error model spatial autoregressive model measurement errors marginal likelihood computational complexity |
| title | A Marginal Maximum Likelihood Approach for Hierarchical Simultaneous Autoregressive Models with Missing Data |
| title_full | A Marginal Maximum Likelihood Approach for Hierarchical Simultaneous Autoregressive Models with Missing Data |
| title_fullStr | A Marginal Maximum Likelihood Approach for Hierarchical Simultaneous Autoregressive Models with Missing Data |
| title_full_unstemmed | A Marginal Maximum Likelihood Approach for Hierarchical Simultaneous Autoregressive Models with Missing Data |
| title_short | A Marginal Maximum Likelihood Approach for Hierarchical Simultaneous Autoregressive Models with Missing Data |
| title_sort | marginal maximum likelihood approach for hierarchical simultaneous autoregressive models with missing data |
| topic | spatial error model spatial autoregressive model measurement errors marginal likelihood computational complexity |
| url | https://www.mdpi.com/2227-7390/12/23/3870 |
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