Ekonometria Przestrzenna
Kinga, Ola, Piotr
2024-05-25
Wczytanie danych, poĊÄ czenie danych z obiektem przestrzennym, usuniÄcie niepotrzebnych danych
data <- read_excel("DANE EP.xlsx")
polska <- st_read("NUTS_RG_20M_2021_3035.shp")## Reading layer `NUTS_RG_20M_2021_3035' from data source
## `C:\Users\LAB716-03\Desktop\25.05\NUTS_RG_20M_2021_3035.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 73 features and 10 fields
## Geometry type: POLYGON
## Dimension: XY
## Bounding box: xmin: 4598024 ymin: 2947340 xmax: 5311200 ymax: 3555563
## Projected CRS: ETRS89-extended / LAEA Europex <- st_read("Pol_NUTS3.shp")## Reading layer `Pol_NUTS3' from data source
## `C:\Users\LAB716-03\Desktop\25.05\Pol_NUTS3.shp' using driver `ESRI Shapefile'
## Simple feature collection with 66 features and 9 fields
## Geometry type: POLYGON
## Dimension: XY
## Bounding box: xmin: 1571260 ymin: 6268257 xmax: 2685070 ymax: 7321686
## CRS: NAspatial.data <- sp::merge(y = data, x = polska, by = "NUTS_ID")
rm(data, polska)Wykresy zmiennej objaĊniajÄ cej oraz potencjalnych zmiennych objaĊniajÄ cych
## Warning: Use of `spatial.data$P` is discouraged.
## âı Use `P` instead.
## Warning: Use of `spatial.data$SBR` is discouraged.
## âı Use `SBR` instead.## Warning in RColorBrewer::brewer.pal(n, pal): n too large, allowed maximum for palette RdBu is 11
## Returning the palette you asked for with that many colors## Warning: Use of `spatial.data$UBZM` is discouraged.
## âı Use `UBZM` instead.## Warning: Use of `spatial.data$R` is discouraged.
## âı Use `R` instead.## Warning: Use of `spatial.data$WWSP` is discouraged.
## âı Use `WWSP` instead.
## Warning: Use of `spatial.data$WF` is discouraged.
## âı Use `WF` instead.## Warning: Use of `spatial.data$WU` is discouraged.
## âı Use `WU` instead.## Warning: Use of `spatial.data$ABS` is discouraged.
## âı Use `ABS` instead.## Warning: Use of `spatial.data$PMWB` is discouraged.
## âı Use `PMWB` instead.## Warning: Use of `spatial.data$NIwP` is discouraged.
## âı Use `NIwP` instead.## Warning: Use of `spatial.data$SMO` is discouraged.
## âı Use `SMO` instead.
Macierz sÄ siedztwa I i II rzÄdu, macierz wag, macierz odlegĊoĊci euklidesowych, wykres macierzy sÄ siedztwa
queen1 <- poly2nb(spatial.data, queen = TRUE)
Wqueen1 <- nb2listw(queen1, style = "W")
Wqueen1## Characteristics of weights list object:
## Neighbour list object:
## Number of regions: 73
## Number of nonzero links: 358
## Percentage nonzero weights: 6.717958
## Average number of links: 4.90411
##
## Weights style: W
## Weights constants summary:
## n nn S0 S1 S2
## W 73 5329 73 35.47154 305.076queen2 <- read.gal("NUTS_RG_20M_2021_3035.gal")
Wqueen2 <- nb2listw(queen2)
Wqueen2## Characteristics of weights list object:
## Neighbour list object:
## Number of regions: 73
## Number of nonzero links: 702
## Percentage nonzero weights: 13.1732
## Average number of links: 9.616438
##
## Weights style: W
## Weights constants summary:
## n nn S0 S1 S2
## W 73 5329 73 17.02245 308.0344wm1 <- nb2mat(queen1, style='B')
wm2 <- nb2mat(queen1, style='W')
dist1 <- as.matrix(dist(coords))
print(dist1)## 1 2 3 4 5 6 7
## 1 0.0000000 0.5987183 0.5796856 0.7480069 1.0878333 1.2779137 1.2861008
## 2 0.5987183 0.0000000 0.7118774 0.3397537 0.9983315 1.5134864 0.7663780
## 3 0.5796856 0.7118774 0.0000000 0.5609564 0.5233702 0.8053411 1.0358386
## 4 0.7480069 0.3397537 0.5609564 0.0000000 0.6901508 1.3018772 0.5426392
## 5 1.0878333 0.9983315 0.5233702 0.6901508 0.0000000 0.7533395 0.8892323
## 6 1.2779137 1.5134864 0.8053411 1.3018772 0.7533395 0.0000000 1.6310201
## 7 1.2861008 0.7663780 1.0358386 0.5426392 0.8892323 1.6310201 0.0000000
## 8 1.0214864 0.6499968 0.6633281 0.3163691 0.5224120 1.2455216 0.3925755
## 9 1.6371347 1.6943600 1.0731708 1.4029704 0.7162096 0.5429878 1.5526974
## 10 2.0586952 2.2795588 1.5819226 2.0353307 1.3899528 0.7848150 2.2667553
## 11 1.3978539 1.1042094 0.9067805 0.7658901 0.4630569 1.1789185 0.6349622
## 12 1.4438023 1.0992023 0.9845431 0.7684627 0.5763426 1.3037745 0.5468501
## 13 1.4538083 1.0356624 1.0573470 0.7294520 0.7239657 1.4707319 0.3780000
## 14 1.5974486 1.1685996 1.1965492 0.8696555 0.8359545 1.5708875 0.4657036
## 15 1.6340467 1.4404255 1.0788304 1.1018978 0.5558526 1.0605767 1.0186160
## 16 1.7501686 1.4410222 1.2445264 1.1069687 0.7560518 1.3759110 0.8574593
## 17 2.4204709 2.5957888 1.9166350 2.3280211 1.6533005 1.1429039 2.4955318
## 18 1.8550280 1.4943689 1.3780333 1.1719335 0.9135117 1.5591997 0.8362579
## 19 1.7785063 1.3650540 1.3488001 1.0606787 0.9382606 1.6403182 0.6581090
## 20 2.5139710 2.5693436 1.9572519 2.2636089 1.5744947 1.2984474 2.3176714
## 21 2.4853598 2.0061925 2.0895253 1.7434279 1.6775909 2.3479036 1.2407370
## 22 2.0783756 2.0519624 1.5015805 1.7319652 1.0553854 1.0154041 1.7477415
## 23 2.7779420 2.9150313 2.2556375 2.6302859 1.9433243 1.5057368 2.7430289
## 24 2.0909517 1.7158730 1.6140066 1.3995221 1.1410623 1.7544255 1.0232688
## 25 1.9916915 1.7588426 1.4410855 1.4193456 0.9184695 1.3560917 1.2288137
## 26 2.0006731 1.8602727 1.4260475 1.5239963 0.9154081 1.1681296 1.4351289
## 27 2.3986187 2.3481593 1.8205037 2.0211452 1.3587985 1.3249431 1.9829492
## 28 2.4371851 2.2693788 1.8639584 1.9301784 1.3500910 1.5607256 1.7684671
## 29 2.3798366 2.1373230 1.8260311 1.7988632 1.3027026 1.6652266 1.5596391
## 30 2.4343008 2.1229775 1.9086240 1.7927905 1.3946817 1.8612006 1.4718270
## 31 3.1256777 2.5608200 2.8503807 2.3895086 2.5270257 3.2470045 1.8472739
## 32 3.1818417 3.2701961 2.6399959 2.9681816 2.2783667 1.9250564 3.0170175
## 33 2.6267679 2.5599919 2.0479339 2.2293217 1.5776401 1.5525468 2.1581848
## 34 3.1183364 2.6002479 2.7567407 2.3704339 2.3591718 3.0282695 1.8403144
## 35 2.8055607 2.6935312 2.2260279 2.3571617 1.7344185 1.7835324 2.2295913
## 36 3.4470055 2.8842836 3.1606669 2.7086728 2.8207710 3.5289146 2.1660803
## 37 2.7400887 2.4702963 2.1916866 2.1349527 1.6687976 2.0214809 1.8448187
## 38 2.7362185 2.5290351 2.1689607 2.1894853 1.6490140 1.8904337 1.9667313
## 39 3.9481582 3.3715488 3.6917180 3.2201176 3.3687821 4.0828766 2.6799341
## 40 3.3111158 3.3222905 2.7456929 3.0018048 2.3248435 2.1064565 2.9721052
## 41 3.5878355 3.6584017 3.0408134 3.3498297 2.6621997 2.3354964 3.3668713
## 42 3.5207825 2.9969114 3.1607611 2.7727785 2.7578713 3.4154250 2.2402085
## 43 2.9617120 2.7443357 2.3954848 2.4052718 1.8749839 2.1084228 2.1612061
## 44 3.0874641 2.9473427 2.5089731 2.6086274 2.0080191 2.0859009 2.4388026
## 45 3.2215095 2.9402923 2.6730240 2.6073683 2.1499457 2.4695057 2.2883406
## 46 3.9623092 3.3992410 3.6694418 3.2233040 3.3158113 4.0107665 2.6806665
## 47 3.9657538 3.9879546 3.4047643 3.6675108 2.9903000 2.7391948 3.6272949
## 48 3.2159933 2.9949492 2.6493303 2.6562653 2.1291372 2.3447174 2.3989701
## 49 3.4193877 3.2318201 2.8455141 2.8921406 2.3322141 2.4721207 2.6623293
## 8 9 10 11 12 13 14
## 1 1.0214864 1.6371347 2.0586952 1.3978539 1.4438023 1.4538083 1.5974486
## 2 0.6499968 1.6943600 2.2795588 1.1042094 1.0992023 1.0356624 1.1685996
## 3 0.6633281 1.0731708 1.5819226 0.9067805 0.9845431 1.0573470 1.1965492
## 4 0.3163691 1.4029704 2.0353307 0.7658901 0.7684627 0.7294520 0.8696555
## 5 0.5224120 0.7162096 1.3899528 0.4630569 0.5763426 0.7239657 0.8359545
## 6 1.2455216 0.5429878 0.7848150 1.1789185 1.3037745 1.4707319 1.5708875
## 7 0.3925755 1.5526974 2.2667553 0.6349622 0.5468501 0.3780000 0.4657036
## 8 0.0000000 1.2239873 1.9123505 0.4566323 0.4520965 0.4323702 0.5761486
## 9 1.2239873 0.0000000 0.7379648 0.9617853 1.0858477 1.2826807 1.3404230
## 10 1.9123505 0.7379648 0.0000000 1.6967869 1.8220398 2.0171676 2.0782800
## 11 0.4566323 0.9617853 1.6967869 0.0000000 0.1276276 0.3209097 0.3945969
## 12 0.4520965 1.0858477 1.8220398 0.1276276 0.0000000 0.2004320 0.2676712
## 13 0.4323702 1.2826807 2.0171676 0.3209097 0.2004320 0.0000000 0.1439476
## 14 0.5761486 1.3404230 2.0782800 0.3945969 0.2676712 0.1439476 0.0000000
## 15 0.8151436 0.6874161 1.4170339 0.3861979 0.4778414 0.6741276 0.6916275
## 16 0.7915088 1.0246784 1.7510487 0.3530782 0.3441575 0.4796116 0.4333241
## 17 2.1679013 0.9451279 0.3897826 1.8884146 2.0070358 2.2071043 2.2463511
## 18 0.8573127 1.2099904 1.9331488 0.4712647 0.4117584 0.4716071 0.3734514
## 19 0.7585755 1.3470058 2.0811813 0.4753227 0.3689763 0.3314289 0.1979661
## 20 2.0451433 0.8852794 0.7654518 1.6840497 1.7868085 1.9841897 1.9925273
## 21 1.4688071 1.9789150 2.6806428 1.2155016 1.1136667 1.0401445 0.8970297
## 22 1.4919877 0.4805815 0.8923967 1.1130520 1.2137154 1.4107195 1.4203089
## 23 2.4422472 1.2275275 0.7730302 2.1167633 2.2269193 2.4266785 2.4465193
## 24 1.0872405 1.3617944 2.0623278 0.7073782 0.6471522 0.6818421 0.5605150
## 25 1.1136834 0.8916319 1.5569979 0.6571941 0.6949337 0.8523425 0.8067597
## 26 1.2437651 0.6512158 1.2610008 0.8114898 0.8883810 1.0733799 1.0585918
## 27 1.7631470 0.8001129 1.0594132 1.3522849 1.4374939 1.6255246 1.6111571
## 28 1.6347804 1.0207208 1.4799585 1.1829449 1.2321781 1.3917897 1.3399366
## 29 1.4885816 1.1516841 1.7157528 1.0331281 1.0522698 1.1829430 1.1071652
## 30 1.4764615 1.3767834 1.9861738 1.0415762 1.0245383 1.1105409 1.0061985
## 31 2.1882304 2.9251175 3.6402141 2.0724193 1.9519909 1.8145787 1.6918250
## 32 2.7511011 1.5779468 1.2237799 2.3821903 2.4803677 2.6751501 2.6730453
## 33 1.9615004 1.0314400 1.2263548 1.5360444 1.6113923 1.7917548 1.7632588
## 34 2.1180407 2.6414791 3.3239303 1.8964360 1.7910612 1.6999623 1.5602409
## 35 2.0730091 1.2507447 1.4838407 1.6293841 1.6884227 1.8544753 1.8065884
## 36 2.5002575 3.1832615 3.8861109 2.3618098 2.2444509 2.1165909 1.9892094
## 37 1.8204410 1.4961865 1.9988502 1.3714437 1.3728797 1.4773256 1.3803075
## 38 1.8833777 1.3499705 1.7711864 1.4267454 1.4544839 1.5897869 1.5138376
## 39 3.0288531 3.7406567 4.4423399 2.9121358 2.7930219 2.6579732 2.5343893
## 40 2.7525682 1.6742954 1.5000027 2.3434909 2.4255831 2.6096774 2.5844151
## 41 3.1203646 1.9727024 1.6319475 2.7328754 2.8237628 3.0138912 2.9995080
## 42 2.5223775 3.0112612 3.6763664 2.2958161 2.1924853 2.1042284 1.9642122
## 43 2.0965613 1.5663333 1.9466265 1.6403886 1.6611697 1.7867251 1.7020509
## 44 2.3148255 1.5517285 1.7662720 1.8628754 1.9087516 2.0608821 1.9972756
## 45 2.2916521 1.9333382 2.3568190 1.8472192 1.8410999 1.9307880 1.8228928
## 46 3.0107939 3.6411366 4.3272481 2.8542601 2.7399996 2.6203189 2.4897037
## 47 3.4164691 2.3317484 2.0715141 3.0023410 3.0804520 3.2607134 3.2279184
## 48 2.3463093 1.8017483 2.1346328 1.8907426 1.9077014 2.0269617 1.9367041
## 49 2.5869302 1.9327434 2.1707552 2.1303077 2.1572137 2.2871717 2.2037525
## 15 16 17 18 19 20 21
## 1 1.6340467 1.7501686 2.4204709 1.8550280 1.7785063 2.5139710 2.4853598
## 2 1.4404255 1.4410222 2.5957888 1.4943689 1.3650540 2.5693436 2.0061925
## 3 1.0788304 1.2445264 1.9166350 1.3780333 1.3488001 1.9572519 2.0895253
## 4 1.1018978 1.1069687 2.3280211 1.1719335 1.0606787 2.2636089 1.7434279
## 5 0.5558526 0.7560518 1.6533005 0.9135117 0.9382606 1.5744947 1.6775909
## 6 1.0605767 1.3759110 1.1429039 1.5591997 1.6403182 1.2984474 2.3479036
## 7 1.0186160 0.8574593 2.4955318 0.8362579 0.6581090 2.3176714 1.2407370
## 8 0.8151436 0.7915088 2.1679013 0.8573127 0.7585755 2.0451433 1.4688071
## 9 0.6874161 1.0246784 0.9451279 1.2099904 1.3470058 0.8852794 1.9789150
## 10 1.4170339 1.7510487 0.3897826 1.9331488 2.0811813 0.7654518 2.6806428
## 11 0.3861979 0.3530782 1.8884146 0.4712647 0.4753227 1.6840497 1.2155016
## 12 0.4778414 0.3441575 2.0070358 0.4117584 0.3689763 1.7868085 1.1136667
## 13 0.6741276 0.4796116 2.2071043 0.4716071 0.3314289 1.9841897 1.0401445
## 14 0.6916275 0.4333241 2.2463511 0.3734514 0.1979661 1.9925273 0.8970297
## 15 0.0000000 0.3375278 1.5580040 0.5237030 0.6653201 1.3100769 1.3034848
## 16 0.3375278 0.0000000 1.8728634 0.1868856 0.3457514 1.5787841 0.9734932
## 17 1.5580040 1.8728634 0.0000000 2.0432572 2.2163370 0.5165470 2.7395624
## 18 0.5237030 0.1868856 2.0432572 0.0000000 0.2134260 1.7269228 0.7887654
## 19 0.6653201 0.3457514 2.2163370 0.2134260 0.0000000 1.9224050 0.7446981
## 20 1.3100769 1.5787841 0.5165470 1.7269228 1.9224050 0.0000000 2.3494551
## 21 1.3034848 0.9734932 2.7395624 0.7887654 0.7446981 2.3494551 0.0000000
## 22 0.7365922 1.0128342 0.8926952 1.1702433 1.3582766 0.5735564 1.8468690
## 23 1.7565428 2.0432876 0.3834687 2.1981607 2.3886568 0.4820481 2.8315029
## 24 0.6963560 0.3885234 2.1334693 0.2370461 0.3651606 1.7708923 0.6188642
## 25 0.3627414 0.3754163 1.6121276 0.4800217 0.6886754 1.2579178 1.1306303
## 26 0.4294629 0.6322074 1.2988955 0.7742618 0.9720390 0.9526670 1.4414942
## 27 0.9660925 1.1819402 0.9351178 1.3102498 1.5155550 0.4660747 1.8906877
## 28 0.8298781 0.9133406 1.4010602 0.9890963 1.2025189 0.9352262 1.4545087
## 29 0.7475876 0.7104608 1.6828162 0.7375701 0.9462658 1.2408866 1.1340935
## 30 0.8518662 0.6893807 1.9716935 0.6389945 0.8195293 1.5351966 0.8539182
## 31 2.2394480 1.9021376 3.7093491 1.7157558 1.6069959 3.3158611 0.9701038
## 32 2.0025331 2.2486048 0.8367687 2.3813526 2.5856527 0.7061802 2.9262651
## 33 1.1520993 1.3299917 1.0391983 1.4377692 1.6489062 0.5263962 1.9432410
## 34 1.9770990 1.6524363 3.3480076 1.4695376 1.4228194 2.9195701 0.6829388
## 35 1.2582628 1.3779413 1.2853560 1.4561768 1.6695628 0.7689806 1.8626397
## 36 2.5028543 2.1678079 3.9325245 1.9809706 1.8903244 3.5172745 1.2059454
## 37 1.1129546 1.0294707 1.9096900 1.0086807 1.1975560 1.4235365 1.1579446
## 38 1.1074197 1.1151953 1.6470573 1.1429264 1.3492598 1.1476006 1.4278696
## 39 3.0600613 2.7247245 4.4830133 2.5378537 2.4429686 4.0595649 1.7629440
## 40 1.9573376 2.1512465 1.1408505 2.2574464 2.4692993 0.8082099 2.7074421
## 41 2.3482760 2.5685768 1.2431239 2.6862776 2.8958830 1.0894598 3.1646783
## 42 2.3587381 2.0404513 3.6762244 1.8603164 1.8237269 3.2270846 1.0803338
## 43 1.3307945 1.3186423 1.7896553 1.3287167 1.5284524 1.2775963 1.5145402
## 44 1.5069180 1.5813470 1.5378253 1.6322093 1.8425632 1.0250684 1.9239915
## 45 1.5941978 1.5004139 2.2057523 1.4591850 1.6316077 1.6932978 1.4165306
## 46 2.9699224 2.6394423 4.3465879 2.4537420 2.3798029 3.9074941 1.6665608
## 47 2.6166969 2.7948952 1.6871916 2.8890953 3.1023230 1.4523395 3.2696403
## 48 1.5849916 1.5641035 1.9441390 1.5634877 1.7576805 1.4275952 1.6701699
## 49 1.8028495 1.8163280 1.9337501 1.8304469 2.0298229 1.4248599 1.9621624
## 22 23 24 25 26 27 28
## 1 2.0783756 2.7779420 2.0909517 1.9916915 2.0006731 2.3986187 2.4371851
## 2 2.0519624 2.9150313 1.7158730 1.7588426 1.8602727 2.3481593 2.2693788
## 3 1.5015805 2.2556375 1.6140066 1.4410855 1.4260475 1.8205037 1.8639584
## 4 1.7319652 2.6302859 1.3995221 1.4193456 1.5239963 2.0211452 1.9301784
## 5 1.0553854 1.9433243 1.1410623 0.9184695 0.9154081 1.3587985 1.3500910
## 6 1.0154041 1.5057368 1.7544255 1.3560917 1.1681296 1.3249431 1.5607256
## 7 1.7477415 2.7430289 1.0232688 1.2288137 1.4351289 1.9829492 1.7684671
## 8 1.4919877 2.4422472 1.0872405 1.1136834 1.2437651 1.7631470 1.6347804
## 9 0.4805815 1.2275275 1.3617944 0.8916319 0.6512158 0.8001129 1.0207208
## 10 0.8923967 0.7730302 2.0623278 1.5569979 1.2610008 1.0594132 1.4799585
## 11 1.1130520 2.1167633 0.7073782 0.6571941 0.8114898 1.3522849 1.1829449
## 12 1.2137154 2.2269193 0.6471522 0.6949337 0.8883810 1.4374939 1.2321781
## 13 1.4107195 2.4266785 0.6818421 0.8523425 1.0733799 1.6255246 1.3917897
## 14 1.4203089 2.4465193 0.5605150 0.8067597 1.0585918 1.6111571 1.3399366
## 15 0.7365922 1.7565428 0.6963560 0.3627414 0.4294629 0.9660925 0.8298781
## 16 1.0128342 2.0432876 0.3885234 0.3754163 0.6322074 1.1819402 0.9133406
## 17 0.8926952 0.3834687 2.1334693 1.6121276 1.2988955 0.9351178 1.4010602
## 18 1.1702433 2.1981607 0.2370461 0.4800217 0.7742618 1.3102498 0.9890963
## 19 1.3582766 2.3886568 0.3651606 0.6886754 0.9720390 1.5155550 1.2025189
## 20 0.5735564 0.4820481 1.7708923 1.2579178 0.9526670 0.4660747 0.9352262
## 21 1.8468690 2.8315029 0.6188642 1.1306303 1.4414942 1.8906877 1.4545087
## 22 0.0000000 1.0304569 1.2429579 0.7211987 0.4072794 0.3235728 0.6023657
## 23 1.0304569 0.0000000 2.2507924 1.7349105 1.4257077 0.9450872 1.4087946
## 24 1.2429579 2.2507924 0.0000000 0.5217642 0.8356829 1.3269787 0.9408979
## 25 0.7211987 1.7349105 0.5217642 0.0000000 0.3139376 0.8309532 0.5396543
## 26 0.4072794 1.4257077 0.8356829 0.3139376 0.0000000 0.5531913 0.4385274
## 27 0.3235728 0.9450872 1.3269787 0.8309532 0.5531913 0.0000000 0.4714840
## 28 0.6023657 1.4087946 0.9408979 0.5396543 0.4385274 0.4714840 0.0000000
## 29 0.8237583 1.7194622 0.6444817 0.3884715 0.5007690 0.7749413 0.3205252
## 30 1.0994526 2.0138154 0.4644089 0.5076375 0.7360418 1.0693040 0.6105077
## 31 2.8167060 3.7976996 1.5807242 2.0987400 2.4107813 2.8542572 2.4063351
## 32 1.2693294 0.4565880 2.3904213 1.9021359 1.6164513 1.0711959 1.4718615
## 33 0.5551652 0.9611063 1.4192938 0.9611541 0.7247040 0.2317736 0.4890121
## 34 2.4614868 3.3972779 1.2824216 1.7672801 2.0664934 2.4535593 1.9894394
## 35 0.7703344 1.1683797 1.3955228 1.0027297 0.8332785 0.4622931 0.4674055
## 36 3.0413985 3.9969451 1.8248076 2.3324779 2.6397725 3.0519877 2.5919897
## 37 1.1157306 1.8792049 0.8453545 0.7506633 0.8534938 0.9745723 0.5190740
## 38 0.9178589 1.5915966 1.0280814 0.7702133 0.7550260 0.7191208 0.3297557
## 39 3.5932845 4.5373917 2.3817780 2.8874777 3.1933330 3.5935960 3.1293639
## 40 1.2704707 0.8045146 2.2247617 1.7823538 1.5373348 0.9917476 1.2838715
## 41 1.6288052 0.8599494 2.6681129 2.2072243 1.9422753 1.3890911 1.7290443
## 42 2.8001182 3.6980201 1.6624005 2.1263880 2.4153716 2.7623601 2.2918585
## 43 1.1203986 1.6913113 1.1888784 0.9869908 0.9816939 0.8872225 0.5513975
## 44 1.0718127 1.3677667 1.5331404 1.2138705 1.0949338 0.7645939 0.6801209
## 45 1.5105665 2.0994185 1.2677307 1.2321983 1.3101853 1.2982609 0.9152863
## 46 3.4628422 4.3812520 2.2796382 2.7704913 3.0695112 3.4417754 2.9729900
## 47 1.9362303 1.3084345 2.8343997 2.4216579 2.1926381 1.6537074 1.9019443
## 48 1.3434706 1.8021011 1.4082393 1.2394808 1.2325301 1.0831179 0.7978623
## 49 1.4569628 1.7379111 1.6869624 1.4734197 1.4194690 1.1608500 0.9822101
## 29 30 31 32 33 34 35
## 1 2.3798366 2.4343008 3.1256777 3.1818417 2.6267679 3.1183364 2.8055607
## 2 2.1373230 2.1229775 2.5608200 3.2701961 2.5599919 2.6002479 2.6935312
## 3 1.8260311 1.9086240 2.8503807 2.6399959 2.0479339 2.7567407 2.2260279
## 4 1.7988632 1.7927905 2.3895086 2.9681816 2.2293217 2.3704339 2.3571617
## 5 1.3027026 1.3946817 2.5270257 2.2783667 1.5776401 2.3591718 1.7344185
## 6 1.6652266 1.8612006 3.2470045 1.9250564 1.5525468 3.0282695 1.7835324
## 7 1.5596391 1.4718270 1.8472739 3.0170175 2.1581848 1.8403144 2.2295913
## 8 1.4885816 1.4764615 2.1882304 2.7511011 1.9615004 2.1180407 2.0730091
## 9 1.1516841 1.3767834 2.9251175 1.5779468 1.0314400 2.6414791 1.2507447
## 10 1.7157528 1.9861738 3.6402141 1.2237799 1.2263548 3.3239303 1.4838407
## 11 1.0331281 1.0415762 2.0724193 2.3821903 1.5360444 1.8964360 1.6293841
## 12 1.0522698 1.0245383 1.9519909 2.4803677 1.6113923 1.7910612 1.6884227
## 13 1.1829430 1.1105409 1.8145787 2.6751501 1.7917548 1.6999623 1.8544753
## 14 1.1071652 1.0061985 1.6918250 2.6730453 1.7632588 1.5602409 1.8065884
## 15 0.7475876 0.8518662 2.2394480 2.0025331 1.1520993 1.9770990 1.2582628
## 16 0.7104608 0.6893807 1.9021376 2.2486048 1.3299917 1.6524363 1.3779413
## 17 1.6828162 1.9716935 3.7093491 0.8367687 1.0391983 3.3480076 1.2853560
## 18 0.7375701 0.6389945 1.7157558 2.3813526 1.4377692 1.4695376 1.4561768
## 19 0.9462658 0.8195293 1.6069959 2.5856527 1.6489062 1.4228194 1.6695628
## 20 1.2408866 1.5351966 3.3158611 0.7061802 0.5263962 2.9195701 0.7689806
## 21 1.1340935 0.8539182 0.9701038 2.9262651 1.9432410 0.6829388 1.8626397
## 22 0.8237583 1.0994526 2.8167060 1.2693294 0.5551652 2.4614868 0.7703344
## 23 1.7194622 2.0138154 3.7976996 0.4565880 0.9611063 3.3972779 1.1683797
## 24 0.6444817 0.4644089 1.5807242 2.3904213 1.4192938 1.2824216 1.3955228
## 25 0.3884715 0.5076375 2.0987400 1.9021359 0.9611541 1.7672801 1.0027297
## 26 0.5007690 0.7360418 2.4107813 1.6164513 0.7247040 2.0664934 0.8332785
## 27 0.7749413 1.0693040 2.8542572 1.0711959 0.2317736 2.4535593 0.4622931
## 28 0.3205252 0.6105077 2.4063351 1.4718615 0.4890121 1.9894394 0.4674055
## 29 0.0000000 0.2943815 2.0869078 1.7921752 0.8091623 1.6786964 0.7533389
## 30 0.2943815 0.0000000 1.7964052 2.0772050 1.0952736 1.3844810 1.0099907
## 31 2.0869078 1.7964052 0.0000000 3.8719290 2.8914064 0.5304089 2.7845989
## 32 1.7921752 2.0772050 3.8719290 0.0000000 0.9830290 3.4311512 1.1060138
## 33 0.8091623 1.0952736 2.8914064 0.9830290 0.0000000 2.4620814 0.2575780
## 34 1.6786964 1.3844810 0.5304089 3.4311512 2.4620814 0.0000000 2.3296974
## 35 0.7533389 1.0099907 2.7845989 1.1060138 0.2575780 2.3296974 0.0000000
## 36 2.2775985 1.9833729 0.3241293 4.0404105 3.0686156 0.6106209 2.9399871
## 37 0.3695523 0.3809616 2.0397261 1.8637613 0.9192560 1.5729331 0.7584434
## 38 0.4071918 0.5916563 2.3319535 1.5641864 0.6307369 1.8713583 0.4588884
## 39 2.8186801 2.5243815 0.8434429 4.5632891 3.5997180 1.1401181 3.4584883
## 40 1.5909418 1.8546719 3.6229387 0.4328110 0.8214540 3.1553961 0.8448254
## 41 2.0416849 2.3110045 4.0843258 0.4115650 1.2509531 3.6172391 1.3029159
## 42 1.9941717 1.7047003 0.6558511 3.6947469 2.7464172 0.4044439 2.5888352
## 43 0.6090223 0.7295537 2.3712241 1.6032058 0.7512789 1.8850930 0.5229936
## 44 0.8969576 1.0993258 2.7987445 1.2100329 0.5503008 2.3146913 0.3026538
## 45 0.8480652 0.8205737 2.1581844 1.9797418 1.1671535 1.6425795 0.9328745
## 46 2.6693866 2.3768450 0.8384248 4.3851939 3.4333322 1.0033304 3.2792008
## 47 2.1908432 2.4309659 4.1426835 0.8518466 1.4692728 3.6486782 1.4391820
## 48 0.8577322 0.9439223 2.4706802 1.6508853 0.9125195 1.9641354 0.6593280
## 49 1.1059054 1.2242621 2.7507782 1.5182518 0.9534740 2.2384499 0.7000914
## 36 37 38 39 40 41 42
## 1 3.4470055 2.7400887 2.7362185 3.9481582 3.3111158 3.5878355 3.5207825
## 2 2.8842836 2.4702963 2.5290351 3.3715488 3.3222905 3.6584017 2.9969114
## 3 3.1606669 2.1916866 2.1689607 3.6917180 2.7456929 3.0408134 3.1607611
## 4 2.7086728 2.1349527 2.1894853 3.2201176 3.0018048 3.3498297 2.7727785
## 5 2.8207710 1.6687976 1.6490140 3.3687821 2.3248435 2.6621997 2.7578713
## 6 3.5289146 2.0214809 1.8904337 4.0828766 2.1064565 2.3354964 3.4154250
## 7 2.1660803 1.8448187 1.9667313 2.6799341 2.9721052 3.3668713 2.2402085
## 8 2.5002575 1.8204410 1.8833777 3.0288531 2.7525682 3.1203646 2.5223775
## 9 3.1832615 1.4961865 1.3499705 3.7406567 1.6742954 1.9727024 3.0112612
## 10 3.8861109 1.9988502 1.7711864 4.4423399 1.5000027 1.6319475 3.6763664
## 11 2.3618098 1.3714437 1.4267454 2.9121358 2.3434909 2.7328754 2.2958161
## 12 2.2444509 1.3728797 1.4544839 2.7930219 2.4255831 2.8237628 2.1924853
## 13 2.1165909 1.4773256 1.5897869 2.6579732 2.6096774 3.0138912 2.1042284
## 14 1.9892094 1.3803075 1.5138376 2.5343893 2.5844151 2.9995080 1.9642122
## 15 2.5028543 1.1129546 1.1074197 3.0600613 1.9573376 2.3482760 2.3587381
## 16 2.1678079 1.0294707 1.1151953 2.7247245 2.1512465 2.5685768 2.0404513
## 17 3.9325245 1.9096900 1.6470573 4.4830133 1.1408505 1.2431239 3.6762244
## 18 1.9809706 1.0086807 1.1429264 2.5378537 2.2574464 2.6862776 1.8603164
## 19 1.8903244 1.1975560 1.3492598 2.4429686 2.4692993 2.8958830 1.8237269
## 20 3.5172745 1.4235365 1.1476006 4.0595649 0.8082099 1.0894598 3.2270846
## 21 1.2059454 1.1579446 1.4278696 1.7629440 2.7074421 3.1646783 1.0803338
## 22 3.0413985 1.1157306 0.9178589 3.5932845 1.2704707 1.6288052 2.8001182
## 23 3.9969451 1.8792049 1.5915966 4.5373917 0.8045146 0.8599494 3.6980201
## 24 1.8248076 0.8453545 1.0280814 2.3817780 2.2247617 2.6681129 1.6624005
## 25 2.3324779 0.7506633 0.7702133 2.8874777 1.7823538 2.2072243 2.1263880
## 26 2.6397725 0.8534938 0.7550260 3.1933330 1.5373348 1.9422753 2.4153716
## 27 3.0519877 0.9745723 0.7191208 3.5935960 0.9917476 1.3890911 2.7623601
## 28 2.5919897 0.5190740 0.3297557 3.1293639 1.2838715 1.7290443 2.2918585
## 29 2.2775985 0.3695523 0.4071918 2.8186801 1.5909418 2.0416849 1.9941717
## 30 1.9833729 0.3809616 0.5916563 2.5243815 1.8546719 2.3110045 1.7047003
## 31 0.3241293 2.0397261 2.3319535 0.8434429 3.6229387 4.0843258 0.6558511
## 32 4.0404105 1.8637613 1.5641864 4.5632891 0.4328110 0.4115650 3.6947469
## 33 3.0686156 0.9192560 0.6307369 3.5997180 0.8214540 1.2509531 2.7464172
## 34 0.6106209 1.5729331 1.8713583 1.1401181 3.1553961 3.6172391 0.4044439
## 35 2.9399871 0.7584434 0.4588884 3.4584883 0.8448254 1.3029159 2.5888352
## 36 0.0000000 2.1835291 2.4818205 0.5574022 3.7658028 4.2275967 0.5100927
## 37 2.1835291 0.0000000 0.2996231 2.7000464 1.5849185 2.0468069 1.8331578
## 38 2.4818205 0.2996231 0.0000000 2.9996421 1.2910206 1.7523905 2.1318510
## 39 0.5574022 2.7000464 2.9996421 0.0000000 4.2718325 4.7322666 0.8945394
## 40 3.7658028 1.5849185 1.2910206 4.2718325 0.0000000 0.4619413 3.3890638
## 41 4.2275967 2.0468069 1.7523905 4.7322666 0.4619413 0.0000000 3.8479291
## 42 0.5100927 1.8331578 2.1318510 0.8945394 3.3890638 3.8479291 0.0000000
## 43 2.4936547 0.3608405 0.2270989 2.9925403 1.2803273 1.7398780 2.1087560
## 44 2.9232119 0.7677780 0.5082726 3.4199808 0.8584833 1.3146457 2.5336577
## 45 2.2349239 0.4816757 0.5928215 2.7003580 1.6222729 2.0698210 1.8062649
## 46 0.5153946 2.5226952 2.8217532 0.2723395 4.0792838 4.5376578 0.6908810
## 47 4.2525450 2.1158996 1.8431222 4.7296722 0.6657740 0.4695714 3.8358840
## 48 2.5634827 0.5630065 0.4803749 3.0380822 1.2826405 1.7275254 2.1449479
## 49 2.8318759 0.8454588 0.7036867 3.2930850 1.1148967 1.5334206 2.3985481
## 43 44 45 46 47 48 49
## 1 2.9617120 3.0874641 3.2215095 3.9623092 3.9657538 3.2159933 3.4193877
## 2 2.7443357 2.9473427 2.9402923 3.3992410 3.9879546 2.9949492 3.2318201
## 3 2.3954848 2.5089731 2.6730240 3.6694418 3.4047643 2.6493303 2.8455141
## 4 2.4052718 2.6086274 2.6073683 3.2233040 3.6675108 2.6562653 2.8921406
## 5 1.8749839 2.0080191 2.1499457 3.3158113 2.9903000 2.1291372 2.3322141
## 6 2.1084228 2.0859009 2.4695057 4.0107665 2.7391948 2.3447174 2.4721207
## 7 2.1612061 2.4388026 2.2883406 2.6806665 3.6272949 2.3989701 2.6623293
## 8 2.0965613 2.3148255 2.2916521 3.0107939 3.4164691 2.3463093 2.5869302
## 9 1.5663333 1.5517285 1.9333382 3.6411366 2.3317484 1.8017483 1.9327434
## 10 1.9466265 1.7662720 2.3568190 4.3272481 2.0715141 2.1346328 2.1707552
## 11 1.6403886 1.8628754 1.8472192 2.8542601 3.0023410 1.8907426 2.1303077
## 12 1.6611697 1.9087516 1.8410999 2.7399996 3.0804520 1.9077014 2.1572137
## 13 1.7867251 2.0608821 1.9307880 2.6203189 3.2607134 2.0269617 2.2871717
## 14 1.7020509 1.9972756 1.8228928 2.4897037 3.2279184 1.9367041 2.2037525
## 15 1.3307945 1.5069180 1.5941978 2.9699224 2.6166969 1.5849916 1.8028495
## 16 1.3186423 1.5813470 1.5004139 2.6394423 2.7948952 1.5641035 1.8163280
## 17 1.7896553 1.5378253 2.2057523 4.3465879 1.6871916 1.9441390 1.9337501
## 18 1.3287167 1.6322093 1.4591850 2.4537420 2.8890953 1.5634877 1.8304469
## 19 1.5284524 1.8425632 1.6316077 2.3798029 3.1023230 1.7576805 2.0298229
## 20 1.2775963 1.0250684 1.6932978 3.9074941 1.4523395 1.4275952 1.4248599
## 21 1.5145402 1.9239915 1.4165306 1.6665608 3.2696403 1.6701699 1.9621624
## 22 1.1203986 1.0718127 1.5105665 3.4628422 1.9362303 1.3434706 1.4569628
## 23 1.6913113 1.3677667 2.0994185 4.3812520 1.3084345 1.8021011 1.7379111
## 24 1.1888784 1.5331404 1.2677307 2.2796382 2.8343997 1.4082393 1.6869624
## 25 0.9869908 1.2138705 1.2321983 2.7704913 2.4216579 1.2394808 1.4734197
## 26 0.9816939 1.0949338 1.3101853 3.0695112 2.1926381 1.2325301 1.4194690
## 27 0.8872225 0.7645939 1.2982609 3.4417754 1.6537074 1.0831179 1.1608500
## 28 0.5513975 0.6801209 0.9152863 2.9729900 1.9019443 0.7978623 0.9822101
## 29 0.6090223 0.8969576 0.8480652 2.6693866 2.1908432 0.8577322 1.1059054
## 30 0.7295537 1.0993258 0.8205737 2.3768450 2.4309659 0.9439223 1.2242621
## 31 2.3712241 2.7987445 2.1581844 0.8384248 4.1426835 2.4706802 2.7507782
## 32 1.6032058 1.2100329 1.9797418 4.3851939 0.8518466 1.6508853 1.5182518
## 33 0.7512789 0.5503008 1.1671535 3.4333322 1.4692728 0.9125195 0.9534740
## 34 1.8850930 2.3146913 1.6425795 1.0033304 3.6486782 1.9641354 2.2384499
## 35 0.5229936 0.3026538 0.9328745 3.2792008 1.4391820 0.6593280 0.7000914
## 36 2.4936547 2.9232119 2.2349239 0.5153946 4.2525450 2.5634827 2.8318759
## 37 0.3608405 0.7677780 0.4816757 2.5226952 2.1158996 0.5630065 0.8454588
## 38 0.2270989 0.5082726 0.5928215 2.8217532 1.8431222 0.4803749 0.7036867
## 39 2.9925403 3.4199808 2.7003580 0.2723395 4.7296722 3.0380822 3.2930850
## 40 1.2803273 0.8584833 1.6222729 4.0792838 0.6657740 1.2826405 1.1148967
## 41 1.7398780 1.3146457 2.0698210 4.5376578 0.4695714 1.7275254 1.5334206
## 42 2.1087560 2.5336577 1.8062649 0.6908810 3.8358840 2.1449479 2.3985481
## 43 0.0000000 0.4296062 0.4161024 2.7991020 1.7721328 0.2543169 0.5017429
## 44 0.4296062 0.0000000 0.7706765 3.2231013 1.3483483 0.4427949 0.4047973
## 45 0.4161024 0.7706765 0.0000000 2.4879573 2.0297001 0.3431703 0.5969628
## 46 2.7991020 3.2231013 2.4879573 0.0000000 4.5167649 2.8288274 3.0755500
## 47 1.7721328 1.3483483 2.0297001 4.5167649 0.0000000 1.6920305 1.4431672
## 48 0.2543169 0.4427949 0.3431703 2.8288274 1.6920305 0.0000000 0.2921347
## 49 0.5017429 0.4047973 0.5969628 3.0755500 1.4431672 0.2921347 0.0000000coords <- coordinates(as(spatial.data, "Spatial"))
plot(st_geometry(spatial.data), border="grey")
plot(queen1, coords, add=TRUE)
points(coords, col="red", pch=20)
Wyznaczenie globalnych i lokalnych statystyk, wykres rozproszenia Morana
moran.test(spatial.data$P, Wqueen1)##
## Moran I test under randomisation
##
## data: spatial.data$P
## weights: Wqueen1
##
## Moran I statistic standard deviate = 2.815, p-value = 0.002439
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic Expectation Variance
## 0.168137769 -0.013888889 0.004181322moran.plot(spatial.data$P, listw = Wqueen1)
lisa = localmoran(spatial.data$P, Wqueen2)
summary(lisa)## Ii E.Ii Var.Ii Z.Ii
## Min. :-1.70408 Min. :-0.5943176 Min. :0.0000921 Min. :-3.1129
## 1st Qu.:-0.06332 1st Qu.:-0.0070347 1st Qu.:0.0054240 1st Qu.:-0.5931
## Median : 0.02510 Median :-0.0035852 Median :0.0170778 Median : 0.2447
## Mean : 0.01991 Mean :-0.0138889 Mean :0.0855946 Mean : 0.1632
## 3rd Qu.: 0.13412 3rd Qu.:-0.0010224 3rd Qu.:0.0572744 3rd Qu.: 0.9372
## Max. : 0.76555 Max. :-0.0000162 Max. :2.3018900 Max. : 2.7856
## Pr(z != E(Ii))
## Min. :0.001853
## 1st Qu.:0.251059
## Median :0.415843
## Mean :0.458918
## 3rd Qu.:0.672804
## Max. :0.966671Model przyczynowo-skutkowy bez interakcji przestrzennych
spatial.data$log_P <- log(spatial.data$P)
spatial.data$log_WWSP <- log(spatial.data$WWSP)
spatial.data$log_WF <- log(spatial.data$WF)
spatial.data$log_PMWB <- log(spatial.data$PMWB)
spatial.data$log_SBR <- log(spatial.data$SBR)
spatial.data$log_UBZM <- log(spatial.data$UBZM)
spatial.data$log_R <- log(spatial.data$R)
spatial.data$log_WU <- log(spatial.data$WU)
spatial.data$log_ABS <- log(spatial.data$ABS)
spatial.data$log_NIwP <- log(spatial.data$NIwP)
spatial.data$log_SMO <- log(spatial.data$SMO)## Warning in log(spatial.data$SMO): wyprodukowano wartoĊci NaNmodel_log <- lm(log_P ~ log_WWSP + log_WF + log_PMWB, data = spatial.data)
reslog = residuals(model_log)
summary(model_log)##
## Call:
## lm(formula = log_P ~ log_WWSP + log_WF + log_PMWB, data = spatial.data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.37787 -0.14266 -0.01692 0.13117 0.68364
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -34.0554 6.2399 -5.458 7.1e-07 ***
## log_WWSP 1.1158 0.2777 4.019 0.000147 ***
## log_WF 4.2011 1.3812 3.042 0.003325 **
## log_PMWB 1.4606 0.3397 4.300 5.5e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2246 on 69 degrees of freedom
## Multiple R-squared: 0.479, Adjusted R-squared: 0.4563
## F-statistic: 21.15 on 3 and 69 DF, p-value: 8.009e-10bptest(model_log, studentize = FALSE)##
## Breusch-Pagan test
##
## data: model_log
## BP = 6.0052, df = 3, p-value = 0.1114jarque.bera.test(reslog)##
## Jarque Bera Test
##
## data: reslog
## X-squared = 4.5452, df = 2, p-value = 0.103shapiro.test(reslog)##
## Shapiro-Wilk normality test
##
## data: reslog
## W = 0.97098, p-value = 0.09027Test I Morana
lm.morantest(model_log, listw=Wqueen1)##
## Global Moran I for regression residuals
##
## data:
## model: lm(formula = log_P ~ log_WWSP + log_WF + log_PMWB, data =
## spatial.data)
## weights: Wqueen1
##
## Moran I statistic standard deviate = 2.6009, p-value = 0.004649
## alternative hypothesis: greater
## sample estimates:
## Observed Moran I Expectation Variance
## 0.180537670 -0.022917873 0.006119172moran.plot(reslog, listw=Wqueen1)
p.lagrange <- lm.LMtests(model_log, listw=Wqueen1, test=c("LMerr","RLMerr","LMlag","RLMlag","SARMA"))## Please update scripts to use lm.RStests in place of lm.LMtestssummary(p.lagrange)## Rao's score (a.k.a Lagrange multiplier) diagnostics for spatial
## dependence
## data:
## model: lm(formula = log_P ~ log_WWSP + log_WF + log_PMWB, data =
## spatial.data)
## test weights: listw
##
## statistic parameter p.value
## RSerr 4.896676 1 0.026908 *
## RSlag 6.700522 1 0.009638 **
## adjRSerr 0.026971 1 0.869552
## adjRSlag 1.830816 1 0.176031
## SARMA 6.727492 2 0.034605 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1SEM
model.SEM.W1 <- errorsarlm(log_P ~ log_WWSP + log_WF + log_PMWB, data = spatial.data, listw = Wqueen1)
summary(model.SEM.W1)##
## Call:
## errorsarlm(formula = log_P ~ log_WWSP + log_WF + log_PMWB, data = spatial.data,
## listw = Wqueen1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.371718 -0.142508 -0.012987 0.137479 0.672791
##
## Type: error
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -36.59605 6.07858 -6.0205 1.739e-09
## log_WWSP 1.17369 0.27474 4.2720 1.937e-05
## log_WF 5.45346 1.35787 4.0162 5.915e-05
## log_PMWB 1.05410 0.33460 3.1504 0.001631
##
## Lambda: 0.40088, LR test value: 5.7636, p-value: 0.016362
## Asymptotic standard error: 0.13723
## z-value: 2.9212, p-value: 0.0034868
## Wald statistic: 8.5334, p-value: 0.0034868
##
## Log likelihood: 10.38466 for error model
## ML residual variance (sigma squared): 0.042423, (sigma: 0.20597)
## Number of observations: 73
## Number of parameters estimated: 6
## AIC: -8.7693, (AIC for lm: -5.0057)moran.test(model.SEM.W1$residuals, Wqueen1, alternative = "greater")##
## Moran I test under randomisation
##
## data: model.SEM.W1$residuals
## weights: Wqueen1
##
## Moran I statistic standard deviate = 0.1725, p-value = 0.4315
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic Expectation Variance
## -0.0003329914 -0.0138888889 0.0061755351spatial.data$res.sem <- model.SEM.W1$residuals
moran.plot(spatial.data$res.sem, Wqueen1, pch = 20, col = "cornflowerblue")
## SAR
SAR <- lagsarlm(log_P ~ log_WWSP + log_WF + log_PMWB, data=spatial.data, listw = Wqueen1)
summary(SAR)##
## Call:
## lagsarlm(formula = log_P ~ log_WWSP + log_WF + log_PMWB, data = spatial.data,
## listw = Wqueen1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.432380 -0.137710 -0.024975 0.115128 0.638642
##
## Type: lag
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -33.62230 5.84274 -5.7545 8.688e-09
## log_WWSP 1.02955 0.26072 3.9488 7.854e-05
## log_WF 4.37139 1.28700 3.3966 0.0006824
## log_PMWB 1.25306 0.31418 3.9884 6.653e-05
##
## Rho: 0.31781, LR test value: 6.3193, p-value: 0.011943
## Asymptotic standard error: 0.11765
## z-value: 2.7012, p-value: 0.0069089
## Wald statistic: 7.2965, p-value: 0.0069089
##
## Log likelihood: 10.66255 for lag model
## ML residual variance (sigma squared): 0.042726, (sigma: 0.2067)
## Number of observations: 73
## Number of parameters estimated: 6
## AIC: -9.3251, (AIC for lm: -5.0057)
## LM test for residual autocorrelation
## test value: 0.021186, p-value: 0.88427SARMA/SARAR
SARMA<- sacsarlm(log_P ~ log_WWSP + log_WF + log_PMWB, data=spatial.data, listw = Wqueen1)
summary(SARMA) ##
## Call:
## sacsarlm(formula = log_P ~ log_WWSP + log_WF + log_PMWB, data = spatial.data,
## listw = Wqueen1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.423212 -0.136428 -0.016846 0.123079 0.641928
##
## Type: sac
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -34.77995 6.00496 -5.7919 6.961e-09
## log_WWSP 1.07308 0.27114 3.9576 7.570e-05
## log_WF 4.67101 1.33051 3.5107 0.0004470
## log_PMWB 1.22319 0.32124 3.8077 0.0001402
##
## Rho: 0.2628
## Asymptotic standard error: 0.20915
## z-value: 1.2565, p-value: 0.20893
## Lambda: 0.092549
## Asymptotic standard error: 0.27833
## z-value: 0.33252, p-value: 0.7395
##
## LR test value: 6.3674, p-value: 0.041433
##
## Log likelihood: 10.68656 for sac model
## ML residual variance (sigma squared): 0.042943, (sigma: 0.20723)
## Number of observations: 73
## Number of parameters estimated: 7
## AIC: -7.3731, (AIC for lm: -5.0057)Spatial Durbin Model
DURBIN <- lagsarlm(log_P ~ log_WWSP + log_WF + log_PMWB, data=spatial.data, listw = Wqueen1, type="mixed");
summary(DURBIN) ##
## Call:
## lagsarlm(formula = log_P ~ log_WWSP + log_WF + log_PMWB, data = spatial.data,
## listw = Wqueen1, type = "mixed")
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.327732 -0.144441 -0.014583 0.129672 0.635804
##
## Type: mixed
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -20.03994 10.74381 -1.8653 0.062146
## log_WWSP 1.30633 0.26833 4.8684 0.000001125
## log_WF 5.90435 1.30117 4.5377 0.000005687
## log_PMWB 0.76701 0.33418 2.2952 0.021723
## lag.log_WWSP -0.90152 0.60459 -1.4911 0.135929
## lag.log_WF -6.33589 2.36381 -2.6804 0.007354
## lag.log_PMWB 1.82414 0.69135 2.6385 0.008327
##
## Rho: 0.26508, LR test value: 2.9417, p-value: 0.08632
## Asymptotic standard error: 0.14644
## z-value: 1.8102, p-value: 0.070267
## Wald statistic: 3.2768, p-value: 0.070267
##
## Log likelihood: 15.89154 for mixed model
## ML residual variance (sigma squared): 0.037293, (sigma: 0.19311)
## Number of observations: 73
## Number of parameters estimated: 9
## AIC: -13.783, (AIC for lm: -12.841)
## LM test for residual autocorrelation
## test value: 0.12956, p-value: 0.71889SLX model/SCM - Spatial Cross-Regressive Model
SCM<- lmSLX(log_P ~ log_WWSP + log_WF + log_PMWB, data=spatial.data, listw = Wqueen1, Durbin = TRUE);
summary(SCM) ##
## Call:
## lm(formula = formula(paste("y ~ ", paste(colnames(x)[-1], collapse = "+"))),
## data = as.data.frame(x), weights = weights)
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -27.64713001 10.00063714 -2.76453686 0.00738223
## log_WWSP 1.30589491 0.29020409 4.49991912 0.00002827
## log_WF 5.59584071 1.40354546 3.98693229 0.00017000
## log_PMWB 0.84285185 0.35874841 2.34942321 0.02180415
## lag.log_WWSP -0.58622364 0.63415421 -0.92441812 0.35863624
## lag.log_WF -5.84256535 2.45058395 -2.38415229 0.02000167
## lag.log_PMWB 2.45992851 0.69471099 3.54093798 0.00073679SDEM - Spatial Durbin Error Model
SEDM <- errorsarlm(log_P ~ log_WWSP + log_WF + log_PMWB, data=spatial.data, listw = Wqueen1, etype="mixed");
summary(SEDM) ##
## Call:
## errorsarlm(formula = log_P ~ log_WWSP + log_WF + log_PMWB, data = spatial.data,
## listw = Wqueen1, etype = "mixed")
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.32936 -0.13014 -0.02157 0.13525 0.63687
##
## Type: error
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -30.16631 11.03643 -2.7333 0.006270
## log_WWSP 1.30672 0.26264 4.9753 6.514e-07
## log_WF 5.71866 1.28178 4.4615 8.139e-06
## log_PMWB 0.85163 0.32810 2.5957 0.009441
## lag.log_WWSP -0.65294 0.62174 -1.0502 0.293630
## lag.log_WF -4.83011 2.31745 -2.0842 0.037139
## lag.log_PMWB 2.16583 0.67862 3.1915 0.001415
##
## Lambda: 0.25736, LR test value: 2.2852, p-value: 0.13061
## Asymptotic standard error: 0.15151
## z-value: 1.6986, p-value: 0.089388
## Wald statistic: 2.8854, p-value: 0.089388
##
## Log likelihood: 15.5633 for error model
## ML residual variance (sigma squared): 0.037665, (sigma: 0.19408)
## Number of observations: 73
## Number of parameters estimated: 9
## AIC: -13.127, (AIC for lm: -12.841)