Abstract
Standard regression model parameters are assumed to apply globally over the entire territory where measured data have been taken, under the assumption of spatial stationarity in the relationship between the variables under study. In most cases this assumption is invalid. Instead, geographically weighted regression (GWR) explicitly deals with the spatial non-stationarity of empirical relationships. Considering a georeferenced dataset on provincial total fertility rate (TFR) in Italy, GWR technique shows a significant improvement in model performance over ordinary least squares (OLS). We also discuss about the test for spatial non-stationarity.
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Notes
- 1.
For GWR is defined as: \(AI{C}_{c} = 2n\;ln(\hat{\sigma } + n\;ln(2\pi ) + n\left \{ \frac{n+tr(S)} {n-2tr(S)}\right \}\), where n is the sample size, \(\hat{\sigma }\) is the estimated standard deviation of he error term and tr(S) is the trace of the hat matrix (Fotheringham et al., 2002).
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The authors would like to thank the anonymous reviewers who provided detailed feedback on the earlier version of this article.
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Mucciardi, M., Bertuccelli, P. (2013). Modelling Spatial Variations of Fertility Rate in Italy. In: Giusti, A., Ritter, G., Vichi, M. (eds) Classification and Data Mining. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28894-4_30
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DOI: https://doi.org/10.1007/978-3-642-28894-4_30
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