localmoran_bv.RdGiven two continuous numeric variables, calculate the bivariate Local Moran's I.
localmoran_bv(x, y, listw, nsim = 199, scale = TRUE, alternative="two.sided",
iseed=1L, no_repeat_in_row=FALSE)a numeric vector of same length as y.
a numeric vector of same length as x.
a listw object for example as created by nb2listw().
the number of simulations to run.
default TRUE.
a character string specifying the alternative hypothesis, must be one of "greater" (default), "two.sided", or "less".
default NULL, used to set the seed for possible parallel RNGs.
default FALSE, if TRUE, sample conditionally in each row without replacements to avoid duplicate values, https://github.com/r-spatial/spdep/issues/124
a data.frame containing two columns Ib and p_sim containing the local bivariate Moran's I and simulated p-values respectively.
The Bivariate Local Moran, like its global counterpart, evaluates the value of x at observation i with its spatial neighbors' value of y. The value of \(I_i^B\) is xi * Wyi. Or, in simpler words, the local bivariate Moran is the result of multiplying x by the spatial lag of y. Formally it is defined as
\( I_i^B= cx_i\Sigma_j{w_{ij}y_j} \)
Anselin, Luc, Ibnu Syabri, and Oleg Smirnov. 2002. “Visualizing Multivariate Spatial Correlation with Dynamically Linked Windows.” In New Tools for Spatial Data Analysis: Proceedings of the Specialist Meeting, edited by Luc Anselin and Sergio Rey. University of California, Santa Barbara: Center for Spatially Integrated Social Science (CSISS).
# load columbus data
columbus <- st_read(system.file("shapes/columbus.shp", package="spData"))
#> Reading layer `columbus' from data source
#> `/home/rsb/lib/r_libs/spData/shapes/columbus.shp' using driver `ESRI Shapefile'
#> Simple feature collection with 49 features and 20 fields
#> Geometry type: POLYGON
#> Dimension: XY
#> Bounding box: xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245
#> CRS: NA
nb <- poly2nb(columbus)
listw <- nb2listw(nb)
set.seed(1)
(res <- localmoran_bv(columbus$CRIME, columbus$INC, listw, nsim = 499))
#> Ibvi E.Ibvi Var.Ibvi Z.Ibvi Pr(z != E(Ibvi))
#> [1,] -0.8578252210 -1.826370e-02 0.731541578 -0.98159654 3.262987e-01
#> [2,] 0.1802618568 2.554658e-02 0.334247968 0.26760782 7.890012e-01
#> [3,] 0.0118856298 7.791116e-03 0.017162929 0.03125407 9.750669e-01
#> [4,] -0.0163525887 -3.452848e-03 0.005852145 -0.16862558 8.660912e-01
#> [5,] -0.5037734606 1.811633e-02 0.101966376 -1.63436973 1.021812e-01
#> [6,] -0.0041841415 1.293651e-02 0.139142736 -0.04589760 9.633919e-01
#> [7,] 1.5201688711 -1.466392e-04 1.099034279 1.45020069 1.470026e-01
#> [8,] -0.2016456990 7.471406e-03 0.007231278 -2.45913301 1.392730e-02
#> [9,] 0.0297432891 1.600490e-03 0.009219518 0.29309821 7.694471e-01
#> [10,] -0.0374203146 1.218906e-03 0.001100110 -1.16495823 2.440359e-01
#> [11,] -1.2368494456 7.720869e-02 0.498286158 -1.86155199 6.266627e-02
#> [12,] -1.2010054212 4.055009e-02 0.266658169 -2.40430022 1.620346e-02
#> [13,] -0.5377131737 1.218864e-02 0.122363375 -1.57202494 1.159448e-01
#> [14,] -0.9879712511 3.048475e-02 0.320475271 -1.79905736 7.200961e-02
#> [15,] -0.6057303757 2.137030e-02 0.102916086 -1.95476986 5.061024e-02
#> [16,] -0.7878039284 1.378587e-02 0.161039891 -1.99749384 4.577156e-02
#> [17,] 0.1379508106 9.352179e-04 0.003351141 2.36686570 1.793944e-02
#> [18,] -0.3253226893 1.066349e-02 0.078469609 -1.19941831 2.303653e-01
#> [19,] -0.3888822685 -7.104732e-06 0.432305953 -0.59144532 5.542221e-01
#> [20,] -0.4544889957 1.367811e-01 0.355060554 -0.99228105 3.210604e-01
#> [21,] -0.0006014046 3.919068e-03 0.031597455 -0.02543067 9.797114e-01
#> [22,] -0.0068813684 -3.664201e-03 0.001242910 -0.09125440 9.272904e-01
#> [23,] -0.8788967496 1.189579e-02 0.289002627 -1.65701209 9.751703e-02
#> [24,] -0.1256865340 -3.048451e-03 0.004692164 -1.79035349 7.339710e-02
#> [25,] -0.9307459211 4.509269e-02 0.303474056 -1.77140234 7.649382e-02
#> [26,] -0.2252775788 1.039843e-02 0.019527743 -1.68651169 9.169728e-02
#> [27,] 0.1413018326 -1.409345e-02 0.236810168 0.31932848 7.494774e-01
#> [28,] -0.7804482928 3.200178e-02 0.184987862 -1.88897002 5.889585e-02
#> [29,] -0.7654416689 5.928648e-02 0.364667175 -1.36572255 1.720261e-01
#> [30,] -0.9074829015 7.597435e-03 0.737090639 -1.06585659 2.864885e-01
#> [31,] -0.5510119267 -1.377557e-03 0.388899970 -0.88136323 3.781213e-01
#> [32,] -1.9581476375 2.561515e-02 0.239115219 -4.05682367 4.974461e-05
#> [33,] 0.0907015890 3.048227e-02 0.043681309 0.28812970 7.732475e-01
#> [34,] -0.4297843082 2.130996e-02 0.104683121 -1.39421250 1.632534e-01
#> [35,] 0.1181174820 6.746380e-04 0.008393054 1.28193663 1.998649e-01
#> [36,] -0.9901007017 2.760845e-02 0.278368628 -1.92891697 5.374117e-02
#> [37,] -0.2195812498 -7.723065e-03 0.032151838 -1.18152344 2.373948e-01
#> [38,] -0.3096268627 3.401135e-02 0.205499338 -0.75804717 4.484227e-01
#> [39,] -0.6090192229 1.689079e-02 0.308320019 -1.12722610 2.596469e-01
#> [40,] -1.2709838927 6.528265e-02 0.216905961 -2.86917707 4.115413e-03
#> [41,] -1.3940681427 9.430182e-02 0.304439982 -2.69749131 6.986411e-03
#> [42,] -0.4820987026 3.961324e-02 0.632999863 -0.65573592 5.119941e-01
#> [43,] -0.0064402410 2.939096e-03 0.001385154 -0.25201308 8.010310e-01
#> [44,] 0.0761664412 2.162964e-02 0.054095662 0.23448142 8.146113e-01
#> [45,] -0.0560342555 7.788766e-03 0.029796273 -0.36973996 7.115763e-01
#> [46,] -0.8249832451 -2.301643e-02 0.673531467 -0.97718648 3.284768e-01
#> [47,] -0.8915318222 2.294960e-02 0.095247718 -2.96310881 3.045489e-03
#> [48,] -0.1282863305 -9.674295e-03 0.061579149 -0.47798241 6.326627e-01
#> [49,] 0.0094888641 -4.828535e-03 0.222107368 0.03037964 9.757643e-01
#> Pr(z != E(Ibvi)) Sim Pr(folded) Sim
#> [1,] 0.324 0.162
#> [2,] 0.880 0.440
#> [3,] 0.976 0.488
#> [4,] 0.800 0.400
#> [5,] 0.112 0.056
#> [6,] 0.864 0.430
#> [7,] 0.096 0.048
#> [8,] 0.004 0.002
#> [9,] 0.852 0.426
#> [10,] 0.260 0.130
#> [11,] 0.056 0.028
#> [12,] 0.008 0.004
#> [13,] 0.084 0.042
#> [14,] 0.064 0.032
#> [15,] 0.052 0.026
#> [16,] 0.028 0.014
#> [17,] 0.028 0.014
#> [18,] 0.192 0.096
#> [19,] 0.608 0.304
#> [20,] 0.368 0.184
#> [21,] 0.936 0.468
#> [22,] 0.928 0.464
#> [23,] 0.120 0.060
#> [24,] 0.040 0.020
#> [25,] 0.044 0.022
#> [26,] 0.076 0.038
#> [27,] 0.736 0.368
#> [28,] 0.032 0.016
#> [29,] 0.140 0.070
#> [30,] 0.284 0.142
#> [31,] 0.408 0.204
#> [32,] 0.004 0.002
#> [33,] 0.724 0.362
#> [34,] 0.188 0.094
#> [35,] 0.216 0.108
#> [36,] 0.084 0.042
#> [37,] 0.232 0.116
#> [38,] 0.464 0.232
#> [39,] 0.268 0.134
#> [40,] 0.004 0.002
#> [41,] 0.020 0.010
#> [42,] 0.468 0.234
#> [43,] 0.884 0.442
#> [44,] 0.904 0.452
#> [45,] 0.672 0.336
#> [46,] 0.344 0.172
#> [47,] 0.012 0.006
#> [48,] 0.544 0.272
#> [49,] 0.896 0.448
#> attr(,"class")
#> [1] "localmoran" "matrix" "array"