spdep

A collection of functions to create spatial weights matrix objects from polygon 'contiguities', from point patterns by distance and tessellations, for summarizing these objects, and for permitting their use in spatial data analysis, including regional aggregation by minimum spanning tree; a collection of tests for spatial 'autocorrelation', including global 'Morans I' and 'Gearys C' proposed by 'Cliff' and 'Ord' (1973, ISBN: 0850860369) and (1981, ISBN: 0850860814), 'Hubert/Mantel' general cross product statistic, Empirical Bayes estimates and 'Assunção/Reis' (1999) doi:10.1002/(SICI)1097-0258(19990830)18:16%3C2147::AID-SIM179%3E3.0.CO;2-I Index, 'Getis/Ord' G ('Getis' and 'Ord' 1992) doi:10.1111/j.1538-4632.1992.tb00261.x and multicoloured join count statistics, 'APLE' ('Li 'et al.' ) doi:10.1111/j.1538-4632.2007.00708.x, local 'Moran's I', 'Gearys C' ('Anselin' 1995) doi:10.1111/j.1538-4632.1995.tb00338.x and 'Getis/Ord' G ('Ord' and 'Getis' 1995) doi:10.1111/j.1538-4632.1995.tb00912.x, 'saddlepoint' approximations ('Tiefelsdorf' 2002) doi:10.1111/j.1538-4632.2002.tb01084.x and exact tests for global and local 'Moran's I' ('Bivand et al.' 2009) doi:10.1016/j.csda.2008.07.021 and 'LOSH' local indicators of spatial heteroscedasticity ('Ord' and 'Getis') doi:10.1007/s00168-011-0492-y. The implementation of most of these measures is described in 'Bivand' and 'Wong' (2018) doi:10.1007/s11749-018-0599-x, with further extensions in 'Bivand' (2022) doi:10.1111/gean.12319. 'Lagrange' multiplier tests for spatial dependence in linear models are provided ('Anselin et al'. 1996) doi:10.1016/0166-0462(95)02111-6, as are 'Rao' score tests for hypothesised spatial 'Durbin' models based on linear models ('Koley' and 'Bera' 2023) doi:10.1080/17421772.2023.2256810. From 'spdep' and 'spatialreg' versions >= 1.2-1, the model fitting functions previously present in this package are defunct in 'spdep' and may be found in 'spatialreg'.