Reports the local Moran Coefficient for each unit.
MI.local(x, W, alternative = "greater", na.rm = TRUE)Returns an object of class data.frame that contains the
following information for each variable:
Iiobserved value of local Moran's I
EIiexpected value of local Moran coefficients
VarIivariance of local Moran's I
zIistandardized local Moran coefficient
pIip-value of the test statistic
The calculation of the statistic and its moments follows Anselin (1995) and Sokal et al. (1998).
Anselin, Luc (1991): Local Indicators of Spatial Association-LISA. Geographical Analysis, 27 (2): pp. 93 - 115.
Bivand, Roger S. and David W. S. Wong (2018): Comparing Implementations of Global and Local Indicators of Spatial Association. TEST, 27: pp. 716 - 748.
Sokal, Robert R., Neal L. Oden, Barbara A. Thomson (1998): Local Spatial Autocorrelation in a Biological Model. Geographical Analysis, 30 (4): pp. 331 - 354.
data(fakedata)
x <- fakedataset$x2
(MIi <- MI.local(x = x, W = W, alternative = "greater"))
#> Ii EIi VarIi zIi pIi
#> 1 -0.1605244807 -0.02020202 1.943397 -0.1006575573 5.400888e-01
#> 2 -0.2045168571 -0.03030303 2.885612 -0.1025566146 5.408426e-01
#> 3 -0.1952635640 -0.03030303 2.885612 -0.0971093638 5.386802e-01
#> 4 -0.2006724317 -0.03030303 2.885612 -0.1002934690 5.399443e-01
#> 5 -0.1258476149 -0.03030303 2.885612 -0.0562454159 5.224268e-01
#> 6 3.2764878469 -0.03030303 2.885612 1.9466496080 2.578838e-02 *
#> 7 0.0449130519 -0.03030303 2.885612 0.0442783842 4.823413e-01
#> 8 6.7177964251 -0.03030303 2.885612 3.9724874199 3.556300e-05 ***
#> 9 4.5319624724 -0.03030303 2.885612 2.6857254306 3.618627e-03 **
#> 10 3.4070226935 -0.02020202 1.943397 2.4584522436 6.976867e-03 **
#> 11 -1.5989822781 -0.03030303 2.885612 -0.9234538731 8.221146e-01
#> 12 0.1420217092 -0.04040404 3.808170 0.0934819985 4.627603e-01
#> 13 0.4898396510 -0.04040404 3.808170 0.2717173430 3.929197e-01
#> 14 -0.0764245736 -0.04040404 3.808170 -0.0184583122 5.073634e-01
#> 15 -0.4892996972 -0.04040404 3.808170 -0.2300314688 5.909663e-01
#> 16 1.0365712215 -0.04040404 3.808170 0.5518837121 2.905140e-01
#> 17 0.6654888579 -0.04040404 3.808170 0.3617267795 3.587781e-01
#> 18 2.2578597838 -0.04040404 3.808170 1.1777191320 1.194543e-01
#> 19 -1.3571502901 -0.04040404 3.808170 -0.6747516251 7.500832e-01
#> 20 0.5045425431 -0.03030303 2.885612 0.3148541787 3.764362e-01
#> 21 -0.1383694593 -0.03030303 2.885612 -0.0636168054 5.253623e-01
#> 22 0.8470667658 -0.04040404 3.808170 0.4547743111 3.246358e-01
#> 23 -0.3795626483 -0.04040404 3.808170 -0.1737979674 5.689879e-01
#> 24 0.1254267971 -0.04040404 3.808170 0.0849781248 4.661394e-01
#> 25 0.9046200627 -0.04040404 3.808170 0.4842668429 3.140983e-01
#> 26 -4.1461523363 -0.04040404 3.808170 -2.1039439721 9.823083e-01
#> 27 0.0449570156 -0.04040404 3.808170 0.0437423014 4.825549e-01
#> 28 -0.0067201597 -0.04040404 3.808170 0.0172609212 4.931142e-01
#> 29 -0.6050902281 -0.04040404 3.808170 -0.2893670082 6.138497e-01
#> 30 -1.8434420401 -0.03030303 2.885612 -1.0673630338 8.570960e-01
#> 31 0.5838022344 -0.03030303 2.885612 0.3615129644 3.588580e-01
#> 32 0.0153829551 -0.04040404 3.808170 0.0285874107 4.885968e-01
#> 33 -0.6895735008 -0.04040404 3.808170 -0.3326594994 6.303043e-01
#> 34 5.7725515613 -0.04040404 3.808170 2.9787829201 1.446979e-03 **
#> 35 3.8178763177 -0.04040404 3.808170 1.9771318446 2.401336e-02 *
#> 36 -0.1301774683 -0.04040404 3.808170 -0.0460033711 5.183462e-01
#> 37 0.9035944687 -0.04040404 3.808170 0.4837412890 3.142847e-01
#> 38 0.0004932862 -0.04040404 3.808170 0.0209573694 4.916398e-01
#> 39 0.3611880285 -0.04040404 3.808170 0.2057912838 4.184770e-01
#> 40 0.0913618830 -0.03030303 2.885612 0.0716219938 4.714514e-01
#> 41 0.9804620721 -0.03030303 2.885612 0.5950196318 2.759152e-01
#> 42 0.9703849796 -0.04040404 3.808170 0.5179673259 3.022405e-01
#> 43 -3.0341915102 -0.04040404 3.808170 -1.5341323059 9.375014e-01
#> 44 10.2889380939 -0.04040404 3.808170 5.2931537816 6.011237e-08 ***
#> 45 5.5887852776 -0.04040404 3.808170 2.8846139801 1.959469e-03 **
#> 46 -2.6082392885 -0.04040404 3.808170 -1.3158579392 9.058891e-01
#> 47 0.8829068593 -0.04040404 3.808170 0.4731401590 3.180566e-01
#> 48 -0.2914804624 -0.04040404 3.808170 -0.1286612541 5.511872e-01
#> 49 -0.5338129908 -0.04040404 3.808170 -0.2528417994 5.998048e-01
#> 50 -0.0441577625 -0.03030303 2.885612 -0.0081560371 5.032538e-01
#> 51 0.3489793975 -0.03030303 2.885612 0.2232768920 4.116600e-01
#> 52 0.1387332108 -0.04040404 3.808170 0.0917968450 4.634297e-01
#> 53 0.0120665538 -0.04040404 3.808170 0.0268879586 4.892745e-01
#> 54 3.1787312012 -0.04040404 3.808170 1.6496092061 4.951145e-02 *
#> 55 0.7343081456 -0.04040404 3.808170 0.3969924400 3.456865e-01
#> 56 -2.0088589009 -0.04040404 3.808170 -1.0087122832 8.434437e-01
#> 57 -2.7449247497 -0.04040404 3.808170 -1.3859008477 9.171114e-01
#> 58 -0.5565569290 -0.04040404 3.808170 -0.2644966716 6.043014e-01
#> 59 1.2903456623 -0.04040404 3.808170 0.6819275351 2.476424e-01
#> 60 0.1114650093 -0.03030303 2.885612 0.0834563506 4.667443e-01
#> 61 0.3992296196 -0.03030303 2.885612 0.2528583136 4.001889e-01
#> 62 2.4013985282 -0.04040404 3.808170 1.2512739274 1.054173e-01
#> 63 0.4041417277 -0.04040404 3.808170 0.2278024179 4.098999e-01
#> 64 0.6168416156 -0.04040404 3.808170 0.3367980540 3.681346e-01
#> 65 1.1530539797 -0.04040404 3.808170 0.6115739754 2.704098e-01
#> 66 1.1711181457 -0.04040404 3.808170 0.6208307516 2.673555e-01
#> 67 -0.2568922588 -0.04040404 3.808170 -0.1109369229 5.441668e-01
#> 68 0.3127401812 -0.04040404 3.808170 0.1809647360 4.281976e-01
#> 69 3.7130955098 -0.04040404 3.808170 1.9234381125 2.721253e-02 *
#> 70 2.1468121184 -0.03030303 2.885612 1.2816293828 9.998634e-02 .
#> 71 3.5948586370 -0.03030303 2.885612 2.1340688906 1.641857e-02 *
#> 72 2.5129080971 -0.04040404 3.808170 1.3084157365 9.536617e-02 .
#> 73 -2.7629337000 -0.04040404 3.808170 -1.3951293292 9.185116e-01
#> 74 0.3563326192 -0.04040404 3.808170 0.2033031845 4.194490e-01
#> 75 0.5290021064 -0.04040404 3.808170 0.2917856975 3.852252e-01
#> 76 0.5334557168 -0.04040404 3.808170 0.2940678994 3.843530e-01
#> 77 -0.0447420382 -0.04040404 3.808170 -0.0022229576 5.008868e-01
#> 78 -1.2542515800 -0.04040404 3.808170 -0.6220223525 7.330364e-01
#> 79 -0.0472950458 -0.04040404 3.808170 -0.0035312172 5.014087e-01
#> 80 -0.6302656115 -0.03030303 2.885612 -0.3531874155 6.380260e-01
#> 81 0.3269261797 -0.03030303 2.885612 0.2102945507 4.167189e-01
#> 82 -0.5160072696 -0.04040404 3.808170 -0.2437174602 5.962752e-01
#> 83 -0.2479933805 -0.04040404 3.808170 -0.1063767940 5.423583e-01
#> 84 -1.0131181663 -0.04040404 3.808170 -0.4984562799 6.909188e-01
#> 85 -0.0413517546 -0.04040404 3.808170 -0.0004856454 5.001937e-01
#> 86 1.2864978644 -0.04040404 3.808170 0.6799557749 2.482662e-01
#> 87 5.3442291716 -0.04040404 3.808170 2.7592939878 2.896320e-03 **
#> 88 1.1908375230 -0.04040404 3.808170 0.6309357220 2.640413e-01
#> 89 -0.1637798904 -0.04040404 3.808170 -0.0632225498 5.252054e-01
#> 90 -1.3882380495 -0.03030303 2.885612 -0.7993924536 7.879686e-01
#> 91 -0.0454833627 -0.02020202 1.943397 -0.0181350738 5.072345e-01
#> 92 0.0513870764 -0.03030303 2.885612 0.0480895285 4.808224e-01
#> 93 0.1655430040 -0.03030303 2.885612 0.1152911146 4.541072e-01
#> 94 -1.1189233191 -0.03030303 2.885612 -0.6408516103 7.391905e-01
#> 95 -1.3880973976 -0.03030303 2.885612 -0.7993096543 7.879446e-01
#> 96 -2.2690193864 -0.03030303 2.885612 -1.3178929297 9.062303e-01
#> 97 5.1597552628 -0.03030303 2.885612 3.0552960006 1.124193e-03 **
#> 98 3.1803457100 -0.03030303 2.885612 1.8900524236 2.937547e-02 *
#> 99 0.3915644846 -0.03030303 2.885612 0.2483459835 4.019334e-01
#> 100 0.1000864726 -0.02020202 1.943397 0.0862865845 4.656193e-01