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

.  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) approac...

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Bibliographic Details
Published in:Papers in regional science 2006-06, Vol.85 (2), p.257-276
Main Authors: Peeters, Ludo, Chasco, Coro
Format: Article
Language:English
Subjects:
C21
C51
C53
Comparative analysis
Ecological inference
Ecology
generalised cross-entropy
Model testing
O18
R12
R15
Regional economics
Regional variation
Regression analysis
Spain
Spatial analysis
Spatial distribution
spatial heterogeneity
spatial non-stationarity
spatial prediction
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Summary:.  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.
ISSN:1056-8190
1435-5957
DOI:10.1111/j.1435-5957.2006.00082.x