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Testing local versions of correlation coefficients

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  • Stamatis Kalogirou

Abstract

The aim of this paper is to define and test local versions of standard correlation coefficients in statistical analysis. This research is motivated by the increasing number of applications using local versions of explanatory spatial data analysis methods such as local regression. Local statistical methods should be applied together with local measures of statistical inference in order to check their performance and to provide an indication of the quality of their results. One example of local explanatory data analysis method is the Geographically Weighted Regression, the application of which allows the researcher to check for the existence of spatial nonstationarity in the relationships between a geographic phenomenon and its determinants. In this paper, a local version of Pearson correlation coefficient is defined and applied to internal migration data in Sweden. The results suggest that globally independent variables are not necessarily independent locally, thus the independence criterion may be violated when local regression analysis is performed. Thus, the results of local regression analysis should be presented in light of the local statistical inference and their interpretation should be made with care. Copyright Springer-Verlag 2012

Suggested Citation

  • Stamatis Kalogirou, 2012. "Testing local versions of correlation coefficients," Review of Regional Research: Jahrbuch für Regionalwissenschaft, Springer;Gesellschaft für Regionalforschung (GfR), vol. 32(1), pages 45-61, March.
    • Handle: RePEc:spr:jahrfr:v:32:y:2012:i:1:p:45-61
    DOI: 10.1007/s10037-011-0061-y
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    1. P J Boyle & R Flowerdew, 1993. "Modelling Sparse Interaction Matrices: Interward Migration in Hereford and Worcester, and the Underdispersion Problem," Environment and Planning A, , vol. 25(8), pages 1201-1209, August.
    2. Thomas Niedomysl, 2004. "Evaluating the Effects of Place-Marketing Campaigns on Interregional Migration in Sweden," Environment and Planning A, , vol. 36(11), pages 1991-2009, November.
    3. Manfred M. Fischer & Arthur Getis (ed.), 2010. "Handbook of Applied Spatial Analysis," Springer Books, Springer, number 978-3-642-03647-7, March.
    4. David Wheeler & Michael Tiefelsdorf, 2005. "Multicollinearity and correlation among local regression coefficients in geographically weighted regression," Journal of Geographical Systems, Springer, vol. 7(2), pages 161-187, June.
    5. T J Fik & G F Mulligan, 1990. "Spatial Flows and Competing Central Places: Towards a General Theory of Hierarchical Interaction," Environment and Planning A, , vol. 22(4), pages 527-549, April.
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    Cited by:

    1. Oldřich Rypl & Karel Macků & Vít Pászto, 2024. "The quality of life in Czech rural and urban spaces," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-14, December.

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    More about this item

    Keywords

    Statistical inference in geography; Spatial analysis; Correlation; Geographically weighted regression; Internal migration; C31; R23;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • R23 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Household Analysis - - - Regional Migration; Regional Labor Markets; Population

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