Local Correlation, Spatial Inequalities, Geographically Weighted Regression and Other Tools

The main purpose of the R package lctools is to provide researchers and educators with easy-to-learn user friendly tools for calculating key spatial statistics and to apply simple as well as advanced methods of spatial analysis in real data. These include: Local Pearson and
Geographically Weighted Pearson Correlation Coefficients, Spatial Inequality Measures (Gini, Spatial Gini, LQ, Focal LQ), Spatial Autocorrelation (Global and Local Moran’s I), several Geographically Weighted Regression techniques and other Spatial Analysis tools (other geographically weighted statistics). This package also contains functions for measuring the significance of each statistic calculated, mainly based on Monte Carlo simulations.

Available in CRAN @


Version: 0.2-8 (6 April 2020)

Code: Bug fixes, update dependencies with other packages and data directory to comply with CRAN policies

Version: 0.2-7 (23 April 2019)

Code: Bug fixes, checks to comply with CRAN policies

Version: 0.2-6 (5 August 2017) Significance test for the spatial variation of the GGWR local parameter estimates

Documentation: Mistake corrections, improved equations

Contact: New website with contact form and new email

Version: 0.2-5 (3 September 2016)

moransI.v: Computes a vector of Moran’s I statistics (using a set of bandwidths; fixed or adaptive spatial kernels)

l.moransI: updated to draw a Moran’s I Scatter Plot

Code: Bug fixes

Vignettes: Updated Spatial Autocorrelation vignette

References: Updated broken links and list of references

Version: 0.2-4 (20 December 2015) Optimal bandwidth estimation for Generalised Geographically Weighted Regression (GGWR)

gw.glm: Generalised Geographically Weighted Regression (GGWR) Optimal bandwidth estimation for Geographically Weighted Zero Inflated Poisson Regression (GWZIPR) Significance test for the spatial variation of the GWZIPR local parameter estimates

gw.zi: Geographically Weighted Zero Inflated Poisson Regression (GWZIPR) Optimal bandwidth estimation for Geographically Weighted Regression (GWR)

gwr: Geographically Weighted Regression (GWR) Radmom data generator

spg.sim.test: Simulation test (Rey & Smith, 2013)

lat2w: Contiguity-based weights matrix for a regular grid

Version: 0.2-3 (5 July 2015)

moransI.w: Moran’s I classic statistic for assessing spatial autocorrelation using a ready made weights matrix

spGini.w: Spatial Gini coefficient with a given weights matrix

w.matrix: Weights Matrix based on a fixed number of nearest neighbours

Code: Bug fixes

Version: 0.2-2 (15 April 2015)

Documentation: Vignettes on spatial autocorrelation and spatial inequalities

Code: Bug fixes, somewhat improved code efficiency (and thus speed)

Version: 0.2 (5 April 2015)

l.moransI: Local Moran’s I classic statistic for assessing spatial autocorrelation

GR.Municipalities: Municipalities in Greece in 2011 (data from 2001 Census).

Datasets removed: GreeceNew, GreeceLAs

Version: 0.1-3 (29 July 2014)

mc.lcorrel: Monte Carlo simulation for the significance of the local correlation coeficients

mc.spGini: Monte Carlo simulation for the significance of the Spatial Gini coefficient

moransI: Moran’s I classic statistic for assessing spatial autocorrelation

Version: 0.1-2 (24 April 2014)

spGini: spatial decomposition of the Gini (Rey and Smith, 2013)

FLQ: Location Quotients and Focal Location Quotients (Cromley and Hanink, 2012)

VotesGR: New Democracy and Total Votes in Greece in 2012 at NUTS III level of geography

Version: 0.1-1 (23 January 2014)

The main purpose of the R package lctools is to help testing the existence of local multi-collinearity among the explanatory variables of local regression models. The main function (lcorrel) allows the computation of Local Pearson and Geographically Weighted Pearson Correlation Coefficients and tests for their significance.

lctools has also two other tools that help computing variables for Spatial Interaction Models (SIM):

gw_variable: the calculation of the regional or geographically weighted version of a variable (Fotheringham et al., 2002; 2004)

acc: the calculation of the destination accessibility (or centrality) measure necessary for the Competing Destinations Model in SIM

Download lctools

lctools is available at the Comprehensive R Archive Network (CRAN): A reference manual for lctools is available here…


Cromley, R. G. and Hanink, D. M. (2012), Focal Location Quotients: Specification and Application, Geographical Analysis, 44 (4), pp. 398-410. doi: 10.1111/j.1538-4632.2012.00852.x

Fotheringham, A.S., Barmby, T., Brunsdon, C., Champion, T., Charlton, M., Kalogirou, S., Tremayne, A., Rees, P., Eyre, H., Macgill, J., Stillwell, J., Bramley, G., and Hollis, J., 2002, Development of a Migration Model: Analytical and Practical Enhancements, Office of the Deputy Prime Minister. URL:

Fotheringham, A.S., Rees, P., Champion, T., Kalogirou, S., and Tremayne, A.R., 2004, The Development of a Migration Model for England and Wales: Overview and Modelling Out-migration, Environment and Planning A, 36, pp. 1633 – 1672. doi:10.1068/a36136. URL:

Kalogirou, S., 2003, The Statistical Analysis And Modelling Of Internal Migration Flows Within England And Wales, PhD Thesis, School of Geography, Politics and Sociology, University of Newcastle upon Tyne, UK. URL:

Kalogirou, S., 2012, Testing local versions of correlation coefficients, Review of Regional Research – Jahrbuch fur Regionalwissenschaft, 32, 1, pp. 45 – 61, doi: 10.1007/s10037-011-0061-y. Url:

Kalogirou, S., 2013, Testing geographically weighted multicollinearity diagnostics, GISRUK 2013, Department of Geography and Planning, School of Environmental Sciences, University of Liverpool, Liverpool, UK, 3-5 April 2013. Url:

Kalogirou, S. (2015) Spatial Analysis: Methodology and Applications with R. [ebook] Athens: Hellenic Academic Libraries Link. ISBN: 978-960-603-285-1 (in Greek).

Kalogirou, S. (2016) Destination Choice of Athenians: an application of geographically weighted versions of standard and zero inflated Poisson spatial interaction models, Geographical Analysis, 48(2),pp. 191-230. DOI: 10.1111/gean.12092

Rey, S.J., Smith J.S., 2013, A spatial decomposition of the Gini coefficient, Letters in Spatial and Resource Sciences, 6 (2), pp. 55-70.