IDEAS home Printed from https://ideas.repec.org/a/bla/presci/v101y2022i1p259-279.html
   My bibliography  Save this article

A Moran eigenvector spatial filtering specification of entropy measures

Author

Listed:
  • Daniel A. Griffith
  • Yongwan Chun
  • Jan Hauke

Abstract

Regional science investigations of geographical disparities in socio‐economic development sometimes utilize entropy, which measures a phenomenon's distributional uniformity across geographical space. Entropy also is widely utilized to measure random phenomenon dispersion, and often used to identify the most probable allocation of a phenomenon in space. Its common formulation is with empirical frequencies, following Shannon. Batty introduces spatial entropy assuming equal probability over space. His specification considers probabilities as fundamentally being spatially independent, which does not hold in most empirical geographical analyses. Hence, an entropy measure can be further modified by controlling extra variation caused by spatial autocorrelation. This paper proposes a Moran eigenvector spatial filtering (MESF) entropy specification that accounts for spatial autocorrelation when modelling georeferenced data. Using eigenvectors from a transformed spatial weights matrix, MESF identifies and isolates spatially autocorrelated components within a georeferenced variable. Coupling it with a non‐normal distribution, such as a binomial or beta probability model, which researchers often employ to describe empirical probabilities, expands its utility. The proposed method is examined with an application to regional income inequality in Poland during 2005–2012. This application demonstrates that accounting for spatial autocorrelation further enhances an entropy measure, showing that the MESF specification provides a flexible method for controlling spatial autocorrelation in an entropy formulation. Los estudios de las ciencias regionales sobre las disparidades geográficas en el desarrollo socioeconómico utilizan a veces la entropía, que mide la uniformidad distributiva de un fenómeno en un espacio geográfico. La entropía también se emplea a menudo para medir la dispersión de fenómenos aleatorios, y a menudo se utiliza para identificar la asignación más probable de un fenómeno en el espacio. Su formulación común implica frecuencias empíricas, de acuerdo con Shannon. Batty introduce la entropía espacial que asume una probabilidad igual en el espacio. Su especificación considera que las probabilidades son fundamentalmente independientes desde el punto de vista espacial, lo que no se cumple en la mayoría de los análisis geográficos empíricos. Por lo tanto, una medida de entropía puede modificarse aún más si se controla la variación adicional causada por la autocorrelación espacial. Este artículo propone una especificación de entropía de filtrado espacial mediante vectores propios de Moran (MESF, por sus siglas en inglés) que tiene en cuenta la autocorrelación espacial cuando se modelan datos georreferenciados. MESF usa los vectores propios de una matriz de pesos espaciales transformada para identificar y aislar los componentes autocorrelacionados espacialmente dentro de una variable georreferenciada. Si se acopla a una distribución no normal, como un modelo de probabilidad binomial o beta, empleada a menudo por investigadores para describir las probabilidades empíricas, se amplía su utilidad. El método propuesto se estudia mediante una aplicación sobre la desigualdad regional de ingresos en Polonia entre 2005 y 2012. Esta aplicación demuestra que tener en cuenta la autocorrelación espacial mejora la medición de la entropía, y muestra que la especificación MESF proporciona un método flexible para controlar la autocorrelación espacial en una formulación de entropía. 社会経済発展の地理的格差を地域科学的に調査する際には、エントロピーを利用することがあるが、これはある現象の地理的空間における分布の均一性を測定するものである。エントロピーはまた、ランダムな現象の分散を測定するのに広く利用されており、ある現象の空間的分布で最も可能性の高いと考えられるパターンを特定するのによく使用される。その一般的な定式は、Shannonの理論に従った、経験的頻度を用いるものである。Battyは、空間のどこにおいても確率は等しいと仮定して空間エントロピーを導入している。Battyは、確率は基本的に空間的に独立していると考えているが、これはほとんどの地理学的実証分析では当てはまらない。したがって、エントロピーによる測定は、空間的自己相関により生じる余分な変動を制御して、改善することができる。本稿では、地理参照データをモデル化する際の空間的自己相関を考慮する、Moran固有ベクトル空間フィルタリング (Moran eigenvector spatial filtering: MESF)エントロピーの仕様を提案する。改変空間重み行列から得た固有値を用いて、MESFにより地理参照変数内の空間的自己相関の成分を特定し分離する。これを、経験的確率を説明するのによく使用される二項分布またはベータ分布の確率モデルなどの非正規分布と結合させることで、その有用性を拡大する。この方法を2005~2012年のポーランドにおける地域所得不平等に適用して検証する。結果から、空間的自己相関を考慮することがエントロピー測定をさらに強化することが示され、MESFの仕様によりエントロピー定式化において空間的自己相関を制御するフレキシブルな方法が得られることが示される。

Suggested Citation

  • Daniel A. Griffith & Yongwan Chun & Jan Hauke, 2022. "A Moran eigenvector spatial filtering specification of entropy measures," Papers in Regional Science, Wiley Blackwell, vol. 101(1), pages 259-279, February.
  • Handle: RePEc:bla:presci:v:101:y:2022:i:1:p:259-279
    DOI: 10.1111/pirs.12646
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/pirs.12646
    Download Restriction: no

    File URL: https://libkey.io/10.1111/pirs.12646?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Daniel Griffith, 2006. "Hidden negative spatial autocorrelation," Journal of Geographical Systems, Springer, vol. 8(4), pages 335-355, October.
    2. Yongwan Chun & Daniel A. Griffith & Monghyeon Lee & Parmanand Sinha, 2016. "Eigenvector selection with stepwise regression techniques to construct eigenvector spatial filters," Journal of Geographical Systems, Springer, vol. 18(1), pages 67-85, January.
    3. Florent Bonneu & Christine Thomas-Agnan, 2015. "Measuring and Testing Spatial Mass Concentration with Micro-geographic Data," Spatial Economic Analysis, Taylor & Francis Journals, vol. 10(3), pages 289-316, September.
    4. HOROWITZ, Ira, 1970. "Employment concentration in the Common Market: An entropy approach," LIDAM Reprints CORE 66, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Daniel A. Griffith, 2003. "Spatial Autocorrelation and Spatial Filtering," Advances in Spatial Science, Springer, number 978-3-540-24806-4.
    6. Czyż Teresa & Hauke Jan, 2015. "Entropy In Regional Analysis," Quaestiones Geographicae, Sciendo, vol. 34(4), pages 69-78, December.
    7. Yu. V. Medvedkov, 1967. "The Concept Of Entropy In Settlement Pattern Analysis," Papers in Regional Science, Wiley Blackwell, vol. 18(1), pages 165-168, January.
    8. Yongwan Chun & Daniel Griffith & Monghyeon Lee & Parmanand Sinha, 2016. "Eigenvector selection with stepwise regression techniques to construct eigenvector spatial filters," Journal of Geographical Systems, Springer, vol. 18(1), pages 67-85, January.
    9. Eric Marcon & Florence Puech, 2010. "Measures of the geographic concentration of industries: improving distance-based methods," Journal of Economic Geography, Oxford University Press, vol. 10(5), pages 745-762, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lan Hu & Yongwan Chun & Daniel A. Griffith, 2020. "Uncovering a positive and negative spatial autocorrelation mixture pattern: a spatial analysis of breast cancer incidences in Broward County, Florida, 2000–2010," Journal of Geographical Systems, Springer, vol. 22(3), pages 291-308, July.
    2. Lan Hu & Daniel A. Griffith & Yongwan Chun, 2018. "Space-Time Statistical Insights about Geographic Variation in Lung Cancer Incidence Rates: Florida, USA, 2000–2011," IJERPH, MDPI, vol. 15(11), pages 1-18, October.
    3. Daniel A. Griffith, 2019. "Negative Spatial Autocorrelation: One of the Most Neglected Concepts in Spatial Statistics," Stats, MDPI, vol. 2(3), pages 1-28, August.
    4. Rodolfo Metulini & Roberto Patuelli & Daniel A. Griffith, 2018. "A Spatial-Filtering Zero-Inflated Approach to the Estimation of the Gravity Model of Trade," Econometrics, MDPI, vol. 6(1), pages 1-15, February.
    5. Franz-Josef Bade & Eckhardt Bode & Eleonora Cutrini, 2015. "Spatial fragmentation of industries by functions," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 54(1), pages 215-250, January.
    6. Wenwen Sun & Daisuke Murakami & Xin Hu & Zhuoran Li & Akari Nakai Kidd & Chunlu Liu, 2023. "Supply–Demand Imbalance in School Land: An Eigenvector Spatial Filtering Approach," Sustainability, MDPI, vol. 15(17), pages 1-14, August.
    7. Marcon, Eric & Puech, Florence, 2017. "A typology of distance-based measures of spatial concentration," Regional Science and Urban Economics, Elsevier, vol. 62(C), pages 56-67.
    8. Jingyi Zhang & Bin Li & Yumin Chen & Meijie Chen & Tao Fang & Yongfeng Liu, 2018. "Eigenvector Spatial Filtering Regression Modeling of Ground PM 2.5 Concentrations Using Remotely Sensed Data," IJERPH, MDPI, vol. 15(6), pages 1-24, June.
    9. Oshan, Taylor M., 2020. "The spatial structure debate in spatial interaction modeling: 50 years on," OSF Preprints 42vxn, Center for Open Science.
    10. Yongwan Chun, 2008. "Modeling network autocorrelation within migration flows by eigenvector spatial filtering," Journal of Geographical Systems, Springer, vol. 10(4), pages 317-344, December.
    11. Daisuke Murakami & Daniel Griffith, 2015. "Random effects specifications in eigenvector spatial filtering: a simulation study," Journal of Geographical Systems, Springer, vol. 17(4), pages 311-331, October.
    12. Donegan, Connor & Chun, Yongwan & Hughes, Amy E., 2020. "Bayesian estimation of spatial filters with Moran's eigenvectors and hierarchical shrinkage priors," OSF Preprints fah3z, Center for Open Science.
    13. Gabriel Lang & Eric Marcon & Florence Puech, 2020. "Distance-based measures of spatial concentration: introducing a relative density function," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 64(2), pages 243-265, April.
    14. Gabriel Lang & Eric Marcon & Florence Puech, 2020. "Distance-based measures of spatial concentration: Introducing a relative density function," Post-Print hal-01082178, HAL.
    15. Eric Marcon & Florence Puech, 2016. "A typology of distance-based measures of spatial concentration," Post-Print halshs-00679993, HAL.
    16. A. Tidu & S. Usai & Frederick Guy, 2021. "Agglomeration in manufacturing and services: an experimental application of a distance-based measure to Sardinia," Working Paper CRENoS 202110, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    17. S. Usai & Frederick Guy & A. Tidu, 2022. "Measuring spatial dispersion: an experimental test on the M-index," Working Paper CRENoS 202206, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    18. Isabelle M. Nilsson & Oleg A. Smirnov, 2017. "Clustering vs. relative location: Measuring spatial interaction between retail outlets," Papers in Regional Science, Wiley Blackwell, vol. 96(4), pages 721-741, November.
    19. Giuseppe Espa & Giuseppe Arbia & Diego Giuliani, 2013. "Conditional versus unconditional industrial agglomeration: disentangling spatial dependence and spatial heterogeneity in the analysis of ICT firms’ distribution in Milan," Journal of Geographical Systems, Springer, vol. 15(1), pages 31-50, January.
    20. Tse-Chuan Yang & Stephen A Matthews, 2015. "Death by Segregation: Does the Dimension of Racial Segregation Matter?," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-26, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:presci:v:101:y:2022:i:1:p:259-279. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=1056-8190 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.