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Ecological inference and spatial heterogeneity: an entropy‐based distributionally weighted regression approach

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  • Ludo Peeters
  • Coro Chasco

Abstract

. In this article we compare two competing approaches to ecological modelling using test data. The first approach is based on the “traditional” method of Ordinary Least Squares (OLS), assuming constancy of parameters across disaggregated spatial units (spatial homogeneity). The second (new) approach is based on the method of Generalised Cross‐Entropy (GCE), assuming varying parameters (spatial heterogeneity). The latter approach is designated as entropy‐based “distributionally weighted regression” (DWR). The two approaches are tested in a real‐world application, using data on per‐capita GDP for the 17 regions and some covariates for the 50 provinces of Spain. Specifically, the performances of the two approaches are assessed by examining their capability in tracking the actual per‐capita GDP data for the provinces (while treating them as if they were not observed by the econometrician), and in showing evidence of spatial heterogeneity. Our findings indicate that the GCE varying‐parameter approach outperforms the OLS approach in terms of predictive power. Specifically, we find that the GCE predictions make efficient use of the lower‐level information that is available. In addition, it is shown that entropy‐based DWR has some potential as a useful technique for investigating spatially heterogeneous relationships at the lower level of analysis that might otherwise be overlooked.

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  • Ludo Peeters & Coro Chasco, 2006. "Ecological inference and spatial heterogeneity: an entropy‐based distributionally weighted regression approach," Papers in Regional Science, Wiley Blackwell, vol. 85(2), pages 257-276, June.
  • Handle: RePEc:bla:presci:v:85:y:2006:i:2:p:257-276
    DOI: 10.1111/j.1435-5957.2006.00082.x
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    References listed on IDEAS

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    1. William Greene, 2003. "A Interpreting Estimated Parameters and Measuring Individual Heterogeneity in Random Coefficient Models," Working Papers 03-19, New York University, Leonard N. Stern School of Business, Department of Economics.
    2. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
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    1. Breandán Ó'hUallacháin, 2008. "Regional growth transition clubs in the United States," Papers in Regional Science, Wiley Blackwell, vol. 87(1), pages 33-53, March.
    2. Rosa Bernardini Papalia, 2011. "An information theoretic approach to ecological inference in presence of spatial heterogeneity and dependence," ERSA conference papers ersa11p317, European Regional Science Association.
    3. Yuee Cao & Yunlu Jiang & Lin Feng & Ge Shi & Haotian He & Jianjun Yang, 2022. "Identification of Territorial Spatial Pattern Conflicts in Aksu River Basin, China, from 1990 to 2020," Sustainability, MDPI, vol. 14(22), pages 1-18, November.
    4. Diana Mitsova & Ann-Margaret Esnard & Alka Sapat & Betty S. Lai, 2018. "Socioeconomic vulnerability and electric power restoration timelines in Florida: the case of Hurricane Irma," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 94(2), pages 689-709, November.
    5. Maomao Zhang & Weigang Chen & Kui Cai & Xin Gao & Xuesong Zhang & Jinxiang Liu & Zhiyuan Wang & Deshou Li, 2019. "Analysis of the Spatial Distribution Characteristics of Urban Resilience and Its Influencing Factors: A Case Study of 56 Cities in China," IJERPH, MDPI, vol. 16(22), pages 1-22, November.
    6. Esteban Fernandez-Vazquez & Andre Lemelin & Fernando Rubiera-Morollón, 2014. "Applying entropy econometrics to estimate data at a disaggregated spatial scale," Letters in Spatial and Resource Sciences, Springer, vol. 7(3), pages 159-169, October.

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