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


  • Ludo Peeters
  • Coro Chasco


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. Copyright (c) 2006 the author(s). Journal compilation (c) 2006 RSAI.

Suggested Citation

  • 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

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    References listed on IDEAS

    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.
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    Cited by:

    1. Breandán Ã'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. 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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