The SAR Model for Very Large Datasets: A Reduced Rank Approach
The SAR model is widely used in spatial econometrics to model Gaussian processes on a discrete spatial lattice, but for large datasets, fitting it becomes computationally prohibitive, and hence, its usefulness can be limited. A computationally-efficient spatial model is the spatial random effects (S...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2015-05-01
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| Series: | Econometrics |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2225-1146/3/2/317 |
| _version_ | 1811307730935218176 |
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| author | Sandy Burden Noel Cressie David G. Steel |
| author_facet | Sandy Burden Noel Cressie David G. Steel |
| author_sort | Sandy Burden |
| collection | DOAJ |
| description | The SAR model is widely used in spatial econometrics to model Gaussian processes on a discrete spatial lattice, but for large datasets, fitting it becomes computationally prohibitive, and hence, its usefulness can be limited. A computationally-efficient spatial model is the spatial random effects (SRE) model, and in this article, we calibrate it to the SAR model of interest using a generalisation of the Moran operator that allows for heteroskedasticity and an asymmetric SAR spatial dependence matrix. In general, spatial data have a measurement-error component, which we model, and we use restricted maximum likelihood to estimate the SRE model covariance parameters; its required computational time is only the order of the size of the dataset. Our implementation is demonstrated using mean usual weekly income data from the 2011 Australian Census. |
| first_indexed | 2024-04-13T09:10:38Z |
| format | Article |
| id | doaj.art-f840527cdf784538b62163eb6a021641 |
| institution | Directory Open Access Journal |
| issn | 2225-1146 |
| language | English |
| last_indexed | 2024-04-13T09:10:38Z |
| publishDate | 2015-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Econometrics |
| spelling | doaj.art-f840527cdf784538b62163eb6a0216412022-12-22T02:52:54ZengMDPI AGEconometrics2225-11462015-05-013231733810.3390/econometrics3020317econometrics3020317The SAR Model for Very Large Datasets: A Reduced Rank ApproachSandy Burden0Noel Cressie1David G. Steel2National Institute for Applied Statistics Research Australia, University of Wollongong, Wollongong, NSW 2522, AustraliaNational Institute for Applied Statistics Research Australia, University of Wollongong, Wollongong, NSW 2522, AustraliaNational Institute for Applied Statistics Research Australia, University of Wollongong, Wollongong, NSW 2522, AustraliaThe SAR model is widely used in spatial econometrics to model Gaussian processes on a discrete spatial lattice, but for large datasets, fitting it becomes computationally prohibitive, and hence, its usefulness can be limited. A computationally-efficient spatial model is the spatial random effects (SRE) model, and in this article, we calibrate it to the SAR model of interest using a generalisation of the Moran operator that allows for heteroskedasticity and an asymmetric SAR spatial dependence matrix. In general, spatial data have a measurement-error component, which we model, and we use restricted maximum likelihood to estimate the SRE model covariance parameters; its required computational time is only the order of the size of the dataset. Our implementation is demonstrated using mean usual weekly income data from the 2011 Australian Census.http://www.mdpi.com/2225-1146/3/2/317asymmetric spatial dependence matrixAustralian censusheteroskedasticityMoran operatorspatial autoregressive modelspatial basis functionsspatial random effects model |
| spellingShingle | Sandy Burden Noel Cressie David G. Steel The SAR Model for Very Large Datasets: A Reduced Rank Approach Econometrics asymmetric spatial dependence matrix Australian census heteroskedasticity Moran operator spatial autoregressive model spatial basis functions spatial random effects model |
| title | The SAR Model for Very Large Datasets: A Reduced Rank Approach |
| title_full | The SAR Model for Very Large Datasets: A Reduced Rank Approach |
| title_fullStr | The SAR Model for Very Large Datasets: A Reduced Rank Approach |
| title_full_unstemmed | The SAR Model for Very Large Datasets: A Reduced Rank Approach |
| title_short | The SAR Model for Very Large Datasets: A Reduced Rank Approach |
| title_sort | sar model for very large datasets a reduced rank approach |
| topic | asymmetric spatial dependence matrix Australian census heteroskedasticity Moran operator spatial autoregressive model spatial basis functions spatial random effects model |
| url | http://www.mdpi.com/2225-1146/3/2/317 |
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