Overview
Spatial Point Pattern Analysis is the evaluation of the pattern or distribution, of a set of points on a surface. The point can be location of:
- events such as crime, traffic accident and disease onset, or
- business services (coffee and fastfood outlets) or facilities such as childcare and eldercare.
In this hands-on exercise, you will gain hands-on experience on using appropriate functions of spatstat to perform. The case study aims to discover the spatial point processes of childecare centres in Singapore.
The research questions
The specific questions we would like to answer are as follows:
- are the childcare centres in Singapore randomly distributed throughout the country?
- if the answer is not, then the next logical question is where are the locations with higher concentration of childcare centres?
The data
To provide answers to the questions above, three data sets will be used. They are:
- CHILDCARE, a point feature data providing both location and attribute information of childcare centres. It is downloaded from www.data.gov.sg and is in ESRI shapefile format.
- MP14_SUBZONE_WEB_PL, a polygon feature data providing information of URA 2014 Master Plan Planning Subzone boundary data. It is in ESRI shapefile format.
- CostalOutline, a polygon feature data showing the national boundary of Singapore. It is provided by SLA and is in ESRI shapefile format.
Installing and Loading the R packages
In this hands-on exercise, five R packages will be used, they are:
-rgdal, which provides bindings to the ‘Geospatial’ Data Abstraction Library (GDAL) (>= 1.11.4) and access to projection/transformation operations from the PROJ library. In this exercise, rgdal will be used to import geospatial data in R and store as sp objects.
spatstat, which has a wide range of useful functions for point pattern analysis. In this hands-on exercise, it will be used to perform 1st- and 2nd-order spatial point patterns analysis and derive kernel density estimation (KDE) layer.
raster which reads, writes, manipulates, analyses and model of gridded spatial data (i.e. raster). In this hands-on exercise, it will be used to convert image output generate by spatstat into raster format.
maptools which provides a set of tools for manipulating geographic data. In this hands-on exercise, we mainly use it to convert Spatial objects into ppp format of spatstat.
tmap which provides functions for plotting cartographic quality static point patterns maps or interactive maps by using leaflet API.
Use the code chunk below to install and launch the five R packages.
packages = c('rgdal', 'maptools', 'raster','spatstat', 'tmap')
for (p in packages){
if(!require(p, character.only = T)){
install.packages(p)
}
library(p,character.only = T)
}
Spatial Data Wrangling
Importing the spatial data
In this section, readOGR() of rgdal package will be used to import the three geospatial data in R’s spatialpolygonsdataframe.
childcare <- readOGR(dsn = "data", layer="CHILDCARE")
OGR data source with driver: ESRI Shapefile
Source: "D:\tskam\GeoDSA\Hands-on_Ex\Hands-on_Ex04\data", layer: "CHILDCARE"
with 1312 features
It has 18 fieldssg <- readOGR(dsn = "data", layer="CostalOutline")
OGR data source with driver: ESRI Shapefile
Source: "D:\tskam\GeoDSA\Hands-on_Ex\Hands-on_Ex04\data", layer: "CostalOutline"
with 60 features
It has 4 fieldsmpsz <- readOGR(dsn = "data", layer="MP14_SUBZONE_WEB_PL")
OGR data source with driver: ESRI Shapefile
Source: "D:\tskam\GeoDSA\Hands-on_Ex\Hands-on_Ex04\data", layer: "MP14_SUBZONE_WEB_PL"
with 323 features
It has 15 fieldsBefore we can use these data for analysis, it is important for us to ensure that they are projected in same projection system. We can retrieve the information of these geospatial data by using the code chunk below.
crs(childcare)
CRS arguments:
+proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333
+k=1 +x_0=28001.642 +y_0=38744.572 +datum=WGS84 +units=m
+no_defs crs(mpsz)
CRS arguments:
+proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333
+k=1 +x_0=28001.642 +y_0=38744.572 +datum=WGS84 +units=m
+no_defs crs(sg)
CRS arguments:
+proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333
+k=1 +x_0=28001.642 +y_0=38744.572 +datum=WGS84 +units=m
+no_defs Next, we can examine the imported geospatial data by using plot().
Alternatively, we can also plotting these three geospatial data in one plot by using code chunk below.
We can also prepare an interactive pin map by using the code chunk below.
tmap_mode('view')
tm_shape(childcare)+
tm_dots()
tmap_mode('plot')
Lastly, let us examine the childcare SpatialPointsDataFrame.
childcare
class : SpatialPointsDataFrame
features : 1312
extent : 11203.01, 45404.24, 25667.6, 49300.88 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +datum=WGS84 +units=m +no_defs
variables : 18
names : OBJECTID, ADDRESSBLO, ADDRESSBUI, ADDRESSPOS, ADDRESSSTR, ADDRESSTYP, DESCRIPTIO, HYPERLINK, LANDXADDRE, LANDYADDRE, NAME, PHOTOURL, ADDRESSFLO, INC_CRC, FMEL_UPD_D, ...
min values : 1, NA, NA, 038983, 1 & 3 Stratton Road SINGAPORE 806787, NA, Child Care Services, http://www.childcarelink.gov.sg/ccls/chdcentpart/ChdCentPartLnk.jsp?centreCd=EB0001, 0, 0, 3-IN-1 FAMILY CENTRE, NA, NA, 000FD4E317754866, 2016/12/23, ...
max values : 1312, NA, NA, 829646, UPPER BASEMENT LEVEL WEST WING TERMINAL 1 SINGAPORE CHANGI AIRPORT SINGAPORE 819642, NA, Child Care Services, http://www.childcarelink.gov.sg/ccls/chdcentpart/ChdCentPartLnk.jsp?centreCd=YW0150, 0, 0, ZEE SCHOOLHOUSE PTE LTD, NA, NA, FFC5A1F137748668, 2017/03/16, ... Converting the spatial point data frame into generic sp format
spatstat requires the analytical data in ppp object form. There is no direct way to convert a SpatialDataFrame into ppp object. We need to convert the SpatialDataFrame into Spatial object first.
The codes below will convert the SpatialPoint and SpatialPolygon data frame into generic spatialpoints and spatialpolygons objects.
childcare_sp <- as(childcare, "SpatialPoints")
sg_sp <- as(sg, "SpatialPolygons")
Do you know what are the differences between SpatialPoints object and SpatialPointDataFrame object?
Let us plot the childcare_sp data by using the code chun below.
plot(childcare_sp)
Note that the output map look similar to the earlier plot.
How about we view the properties of childcare_sp data object by using the code chun below?
childcare_sp
class : SpatialPoints
features : 1312
extent : 11203.01, 45404.24, 25667.6, 49300.88 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +datum=WGS84 +units=m +no_defs Can you see the different now?
Converting the generic sp format into spatstat’s ppp format
Now, we will use as.ppp() function of spatstat to convert the spatial data into spatstat’s ppp object format.
childcare_ppp <- as(childcare_sp, "ppp")
childcare_ppp
Planar point pattern: 1312 points
window: rectangle = [11203.01, 45404.24] x [25667.6, 49300.88] unitsNow, let us plot childcare_ppp and examine the different.
plot(childcare_ppp)
You can take a quick look at the summary statistics of the newly created ppp object by using the code chunk below.
summary(childcare_ppp)
Planar point pattern: 1312 points
Average intensity 1.623186e-06 points per square unit
*Pattern contains duplicated points*
Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units
Window: rectangle = [11203.01, 45404.24] x [25667.6, 49300.88] units
(34200 x 23630 units)
Window area = 808287000 square unitsNotice the warning message about duplicates. In spatial point patterns analysis an issue of significant is the presence of duplicates. The statistical methodology used for spatial point patterns processes is based largely on the assumption that process are simple, that is, that the points cannot be coincident.
Handling duplicated points
We can check the duplication in a ppp object by using the code chunk below.
any(duplicated(childcare_ppp))
[1] TRUETo count the number of coindicence point, we will use the multiplicity() function as shown in the code chunk below.
multiplicity(childcare_ppp)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 1 4 1 1 1 1 1 1 1 1 1 1 1
15 16 17 18 19 20 21 22 23 24 25 26 27 28
1 1 1 1 1 1 1 1 1 1 1 1 1 1
29 30 31 32 33 34 35 36 37 38 39 40 41 42
1 1 1 1 1 1 1 1 1 1 1 1 1 1
43 44 45 46 47 48 49 50 51 52 53 54 55 56
3 1 1 1 1 1 1 1 1 1 1 1 1 1
57 58 59 60 61 62 63 64 65 66 67 68 69 70
1 2 1 1 1 1 1 1 1 1 2 1 1 1
71 72 73 74 75 76 77 78 79 80 81 82 83 84
1 1 1 7 1 1 1 1 1 1 1 1 1 1
85 86 87 88 89 90 91 92 93 94 95 96 97 98
2 1 1 1 1 1 1 1 1 1 1 1 2 1
99 100 101 102 103 104 105 106 107 108 109 110 111 112
1 1 1 1 1 2 1 1 1 1 1 1 1 1
113 114 115 116 117 118 119 120 121 122 123 124 125 126
1 1 1 1 1 1 2 1 1 1 1 5 1 1
127 128 129 130 131 132 133 134 135 136 137 138 139 140
1 1 2 1 1 1 1 1 1 2 1 1 1 1
141 142 143 144 145 146 147 148 149 150 151 152 153 154
1 1 1 1 1 1 1 1 1 1 1 1 1 2
155 156 157 158 159 160 161 162 163 164 165 166 167 168
1 1 1 1 1 1 1 1 1 1 1 1 1 1
169 170 171 172 173 174 175 176 177 178 179 180 181 182
1 1 1 1 1 1 1 1 1 1 1 1 1 1
183 184 185 186 187 188 189 190 191 192 193 194 195 196
1 1 7 1 1 1 1 1 1 1 1 1 1 1
197 198 199 200 201 202 203 204 205 206 207 208 209 210
5 1 1 1 1 1 1 2 1 1 1 1 1 1
211 212 213 214 215 216 217 218 219 220 221 222 223 224
1 1 1 1 1 1 1 1 1 1 2 1 1 1
225 226 227 228 229 230 231 232 233 234 235 236 237 238
1 1 2 1 1 1 1 1 1 1 1 1 1 1
239 240 241 242 243 244 245 246 247 248 249 250 251 252
1 1 1 1 1 1 1 1 1 1 1 2 1 1
253 254 255 256 257 258 259 260 261 262 263 264 265 266
1 1 2 2 1 2 1 1 3 1 1 1 1 1
267 268 269 270 271 272 273 274 275 276 277 278 279 280
2 1 1 1 1 1 1 1 7 1 1 1 1 2
281 282 283 284 285 286 287 288 289 290 291 292 293 294
1 2 1 1 2 1 1 1 1 1 1 1 1 1
295 296 297 298 299 300 301 302 303 304 305 306 307 308
1 1 1 1 1 1 1 1 1 1 1 1 1 1
309 310 311 312 313 314 315 316 317 318 319 320 321 322
1 1 1 1 1 1 1 1 1 1 1 1 1 1
323 324 325 326 327 328 329 330 331 332 333 334 335 336
1 1 1 1 1 1 1 1 1 1 1 1 1 1
337 338 339 340 341 342 343 344 345 346 347 348 349 350
1 1 1 1 1 1 1 1 1 1 1 1 1 1
351 352 353 354 355 356 357 358 359 360 361 362 363 364
1 1 4 1 1 1 1 1 1 2 1 1 1 1
365 366 367 368 369 370 371 372 373 374 375 376 377 378
1 1 1 1 1 1 1 2 1 1 1 1 1 1
379 380 381 382 383 384 385 386 387 388 389 390 391 392
1 1 1 1 1 1 1 1 1 1 1 1 1 1
393 394 395 396 397 398 399 400 401 402 403 404 405 406
1 1 1 1 1 1 1 1 1 1 1 1 1 1
407 408 409 410 411 412 413 414 415 416 417 418 419 420
1 1 1 1 1 1 1 1 1 1 1 1 1 1
421 422 423 424 425 426 427 428 429 430 431 432 433 434
1 1 1 1 1 1 1 1 1 1 1 1 1 7
435 436 437 438 439 440 441 442 443 444 445 446 447 448
1 2 1 1 1 1 1 1 1 1 1 1 1 1
449 450 451 452 453 454 455 456 457 458 459 460 461 462
1 3 1 1 1 1 1 1 1 1 1 2 2 2
463 464 465 466 467 468 469 470 471 472 473 474 475 476
1 1 1 1 1 1 1 1 1 2 1 1 1 1
477 478 479 480 481 482 483 484 485 486 487 488 489 490
4 1 1 1 1 1 1 1 1 1 3 1 1 1
491 492 493 494 495 496 497 498 499 500 501 502 503 504
1 1 1 1 1 1 1 1 1 1 1 1 1 1
505 506 507 508 509 510 511 512 513 514 515 516 517 518
1 1 3 1 1 1 1 1 1 1 1 1 1 1
519 520 521 522 523 524 525 526 527 528 529 530 531 532
1 1 4 1 4 1 1 1 2 1 1 1 1 1
533 534 535 536 537 538 539 540 541 542 543 544 545 546
1 1 1 1 1 1 1 1 1 1 1 1 1 1
547 548 549 550 551 552 553 554 555 556 557 558 559 560
1 1 1 1 1 1 1 3 1 1 1 1 1 1
561 562 563 564 565 566 567 568 569 570 571 572 573 574
1 1 1 1 4 1 1 1 1 1 1 1 1 1
575 576 577 578 579 580 581 582 583 584 585 586 587 588
1 1 1 1 1 1 1 1 1 1 1 1 1 1
589 590 591 592 593 594 595 596 597 598 599 600 601 602
1 2 1 1 1 1 1 1 1 1 1 1 1 1
603 604 605 606 607 608 609 610 611 612 613 614 615 616
2 1 1 1 1 1 1 1 1 1 1 1 1 1
617 618 619 620 621 622 623 624 625 626 627 628 629 630
1 1 1 2 1 1 1 1 1 1 1 1 1 1
631 632 633 634 635 636 637 638 639 640 641 642 643 644
1 1 1 1 2 1 1 7 1 1 1 1 4 1
645 646 647 648 649 650 651 652 653 654 655 656 657 658
1 1 2 1 1 1 1 1 1 1 1 1 1 1
659 660 661 662 663 664 665 666 667 668 669 670 671 672
1 1 1 1 1 1 1 1 1 1 1 2 1 3
673 674 675 676 677 678 679 680 681 682 683 684 685 686
1 1 1 1 1 1 1 1 1 1 1 1 1 1
687 688 689 690 691 692 693 694 695 696 697 698 699 700
1 1 2 1 1 1 1 1 1 1 1 1 1 1
701 702 703 704 705 706 707 708 709 710 711 712 713 714
1 1 1 1 1 1 1 1 1 1 1 1 1 1
715 716 717 718 719 720 721 722 723 724 725 726 727 728
1 1 1 1 1 1 1 1 1 1 1 1 1 1
729 730 731 732 733 734 735 736 737 738 739 740 741 742
1 1 1 1 1 1 1 1 4 1 1 1 1 1
743 744 745 746 747 748 749 750 751 752 753 754 755 756
1 7 1 1 1 1 1 1 1 1 1 1 1 1
757 758 759 760 761 762 763 764 765 766 767 768 769 770
1 1 1 1 1 4 1 2 2 1 1 1 1 1
771 772 773 774 775 776 777 778 779 780 781 782 783 784
2 1 1 1 2 1 1 1 1 1 1 1 2 1
785 786 787 788 789 790 791 792 793 794 795 796 797 798
1 1 1 1 1 1 1 1 1 1 1 1 1 1
799 800 801 802 803 804 805 806 807 808 809 810 811 812
1 1 1 1 1 1 5 1 1 1 1 1 1 1
813 814 815 816 817 818 819 820 821 822 823 824 825 826
1 1 1 1 1 1 1 1 1 1 1 1 1 1
827 828 829 830 831 832 833 834 835 836 837 838 839 840
1 1 1 1 1 1 1 1 2 1 1 1 1 1
841 842 843 844 845 846 847 848 849 850 851 852 853 854
1 1 1 1 1 1 1 1 3 1 1 1 1 1
855 856 857 858 859 860 861 862 863 864 865 866 867 868
1 1 1 1 2 1 1 1 1 1 1 1 1 1
869 870 871 872 873 874 875 876 877 878 879 880 881 882
1 1 1 1 1 1 1 1 1 1 1 1 1 1
883 884 885 886 887 888 889 890 891 892 893 894 895 896
1 1 1 1 1 1 1 1 1 1 1 1 1 1
897 898 899 900 901 902 903 904 905 906 907 908 909 910
1 1 1 1 1 1 1 1 1 1 1 1 1 1
911 912 913 914 915 916 917 918 919 920 921 922 923 924
1 1 1 1 1 1 1 1 1 1 1 1 1 1
925 926 927 928 929 930 931 932 933 934 935 936 937 938
1 1 1 1 1 1 1 1 1 1 1 1 1 1
939 940 941 942 943 944 945 946 947 948 949 950 951 952
1 1 1 1 1 3 1 1 1 1 1 2 1 1
953 954 955 956 957 958 959 960 961 962 963 964 965 966
1 1 1 1 1 1 1 1 1 1 1 1 1 1
967 968 969 970 971 972 973 974 975 976 977 978 979 980
1 1 1 1 1 1 2 1 1 1 1 1 1 1
981 982 983 984 985 986 987 988 989 990 991 992 993 994
1 1 1 1 1 1 1 1 1 1 1 1 1 1
995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008
1 5 1 1 1 1 1 1 1 1 1 1 1 1
1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064
1 1 5 1 1 1 1 1 1 1 1 1 1 1
1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078
1 1 1 1 4 1 1 1 1 1 1 1 1 1
1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162
1 1 1 1 2 1 1 1 1 1 1 1 1 1
1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190
1 1 1 1 1 1 1 1 1 1 4 1 1 1
1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204
1 1 1 1 2 1 1 1 1 1 1 1 1 1
1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260
1 1 2 1 1 1 1 4 2 1 1 1 1 1
1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274
1 1 1 1 1 1 2 1 1 1 1 1 1 1
1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302
1 2 1 1 1 1 1 1 1 1 1 1 1 2
1303 1304 1305 1306 1307 1308 1309 1310 1311 1312
1 1 1 1 1 1 1 1 7 2 If we want to know how many locations have more than one point event, we can use the code chunk below.
sum(multiplicity(childcare_ppp) > 1)
[1] 85The output shows that there are 85 duplicated point events.
To view the locations of these duplicate point events, we will plot childcare data by using the code chunk below.
tmap_mode("plot")
tm_shape(childcare) +
tm_dots(alpha=0.4, size=0.05)
tmap_mode("plot")
There are three ways to overcome this problem. The easiest way is to delete the duplicates. But, that will also mean that some useful point events will be lost.
The second solution is use jittering, which will add a small perturbation to the duplicate points so that they do not occupy the exact same space.
The third solution is to make each point “unique” and then attach the duplicates of the points to the patterns as marks, as attributes of the points. Then you would need analytical techniques that take into account these marks.
The code chunk below implements the jittering approach.
childcare_ppp_jit <- rjitter(childcare_ppp, retry=TRUE, nsim=1, drop=TRUE)
plot(childcare_ppp_jit)
any(duplicated(childcare_ppp_jit))
[1] FALSENotice the difference with the original plot. Can you see how the circumference do not overlap perfectly now?
Creating owin
When analysing spatial point patterns, it is a good practice to confine the analysis with a geographical area like Singapore boundary. In spatstat, an object called owin is specially designed to represent this polygonal region.
The code chunk below is used to covert sg SpatialPolygon object into owin object of spatstat.
sg_owin <- as(sg_sp, "owin")
The ouput object can be displayed by using plot() and summary() functions.
plot(sg_owin)
summary(sg_owin)
Window: polygonal boundary
60 separate polygons (no holes)
vertices area relative.area
polygon 1 38 1.56140e+04 2.09e-05
polygon 2 735 4.69093e+06 6.27e-03
polygon 3 49 1.66986e+04 2.23e-05
polygon 4 76 3.12332e+05 4.17e-04
polygon 5 5141 6.36179e+08 8.50e-01
polygon 6 42 5.58317e+04 7.46e-05
polygon 7 67 1.31354e+06 1.75e-03
polygon 8 15 4.46420e+03 5.96e-06
polygon 9 14 5.46674e+03 7.30e-06
polygon 10 37 5.26194e+03 7.03e-06
polygon 11 53 3.44003e+04 4.59e-05
polygon 12 74 5.82234e+04 7.78e-05
polygon 13 69 5.63134e+04 7.52e-05
polygon 14 143 1.45139e+05 1.94e-04
polygon 15 165 3.38736e+05 4.52e-04
polygon 16 130 9.40465e+04 1.26e-04
polygon 17 19 1.80977e+03 2.42e-06
polygon 18 16 2.01046e+03 2.69e-06
polygon 19 93 4.30642e+05 5.75e-04
polygon 20 90 4.15092e+05 5.54e-04
polygon 21 721 1.92795e+06 2.57e-03
polygon 22 330 1.11896e+06 1.49e-03
polygon 23 115 9.28394e+05 1.24e-03
polygon 24 37 1.01705e+04 1.36e-05
polygon 25 25 1.66227e+04 2.22e-05
polygon 26 10 2.14507e+03 2.86e-06
polygon 27 190 2.02489e+05 2.70e-04
polygon 28 175 9.25904e+05 1.24e-03
polygon 29 1993 9.99217e+06 1.33e-02
polygon 30 38 2.42492e+04 3.24e-05
polygon 31 24 6.35239e+03 8.48e-06
polygon 32 53 6.35791e+05 8.49e-04
polygon 33 41 1.60161e+04 2.14e-05
polygon 34 22 2.54368e+03 3.40e-06
polygon 35 30 1.08382e+04 1.45e-05
polygon 36 327 2.16921e+06 2.90e-03
polygon 37 111 6.62927e+05 8.85e-04
polygon 38 90 1.15991e+05 1.55e-04
polygon 39 98 6.26829e+04 8.37e-05
polygon 40 415 3.25384e+06 4.35e-03
polygon 41 222 1.51142e+06 2.02e-03
polygon 42 107 6.33039e+05 8.45e-04
polygon 43 7 2.48299e+03 3.32e-06
polygon 44 17 3.28303e+04 4.38e-05
polygon 45 26 8.34758e+03 1.11e-05
polygon 46 177 4.67446e+05 6.24e-04
polygon 47 16 3.19460e+03 4.27e-06
polygon 48 15 4.87296e+03 6.51e-06
polygon 49 66 1.61841e+04 2.16e-05
polygon 50 149 5.63430e+06 7.53e-03
polygon 51 609 2.62570e+07 3.51e-02
polygon 52 8 7.82256e+03 1.04e-05
polygon 53 976 2.33447e+07 3.12e-02
polygon 54 55 8.25379e+04 1.10e-04
polygon 55 976 2.33447e+07 3.12e-02
polygon 56 61 3.33449e+05 4.45e-04
polygon 57 6 1.68410e+04 2.25e-05
polygon 58 4 9.45963e+03 1.26e-05
polygon 59 46 6.99702e+05 9.35e-04
polygon 60 13 7.00873e+04 9.36e-05
enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
(53380 x 33890 units)
Window area = 748741000 square units
Fraction of frame area: 0.414Combining childcare points and the study area
By using the code below, we are able to extract childcare that is within the specific region to do our analysis later on.
childcareSG_ppp = childcare_ppp[sg_owin]
Here we plot the combined childcare point and Punggol region to prove that it works
plot(childcareSG_ppp)
summary(childcareSG_ppp)
Planar point pattern: 1312 points
Average intensity 1.752274e-06 points per square unit
*Pattern contains duplicated points*
Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units
Window: polygonal boundary
60 separate polygons (no holes)
vertices area relative.area
polygon 1 38 1.56140e+04 2.09e-05
polygon 2 735 4.69093e+06 6.27e-03
polygon 3 49 1.66986e+04 2.23e-05
polygon 4 76 3.12332e+05 4.17e-04
polygon 5 5141 6.36179e+08 8.50e-01
polygon 6 42 5.58317e+04 7.46e-05
polygon 7 67 1.31354e+06 1.75e-03
polygon 8 15 4.46420e+03 5.96e-06
polygon 9 14 5.46674e+03 7.30e-06
polygon 10 37 5.26194e+03 7.03e-06
polygon 11 53 3.44003e+04 4.59e-05
polygon 12 74 5.82234e+04 7.78e-05
polygon 13 69 5.63134e+04 7.52e-05
polygon 14 143 1.45139e+05 1.94e-04
polygon 15 165 3.38736e+05 4.52e-04
polygon 16 130 9.40465e+04 1.26e-04
polygon 17 19 1.80977e+03 2.42e-06
polygon 18 16 2.01046e+03 2.69e-06
polygon 19 93 4.30642e+05 5.75e-04
polygon 20 90 4.15092e+05 5.54e-04
polygon 21 721 1.92795e+06 2.57e-03
polygon 22 330 1.11896e+06 1.49e-03
polygon 23 115 9.28394e+05 1.24e-03
polygon 24 37 1.01705e+04 1.36e-05
polygon 25 25 1.66227e+04 2.22e-05
polygon 26 10 2.14507e+03 2.86e-06
polygon 27 190 2.02489e+05 2.70e-04
polygon 28 175 9.25904e+05 1.24e-03
polygon 29 1993 9.99217e+06 1.33e-02
polygon 30 38 2.42492e+04 3.24e-05
polygon 31 24 6.35239e+03 8.48e-06
polygon 32 53 6.35791e+05 8.49e-04
polygon 33 41 1.60161e+04 2.14e-05
polygon 34 22 2.54368e+03 3.40e-06
polygon 35 30 1.08382e+04 1.45e-05
polygon 36 327 2.16921e+06 2.90e-03
polygon 37 111 6.62927e+05 8.85e-04
polygon 38 90 1.15991e+05 1.55e-04
polygon 39 98 6.26829e+04 8.37e-05
polygon 40 415 3.25384e+06 4.35e-03
polygon 41 222 1.51142e+06 2.02e-03
polygon 42 107 6.33039e+05 8.45e-04
polygon 43 7 2.48299e+03 3.32e-06
polygon 44 17 3.28303e+04 4.38e-05
polygon 45 26 8.34758e+03 1.11e-05
polygon 46 177 4.67446e+05 6.24e-04
polygon 47 16 3.19460e+03 4.27e-06
polygon 48 15 4.87296e+03 6.51e-06
polygon 49 66 1.61841e+04 2.16e-05
polygon 50 149 5.63430e+06 7.53e-03
polygon 51 609 2.62570e+07 3.51e-02
polygon 52 8 7.82256e+03 1.04e-05
polygon 53 976 2.33447e+07 3.12e-02
polygon 54 55 8.25379e+04 1.10e-04
polygon 55 976 2.33447e+07 3.12e-02
polygon 56 61 3.33449e+05 4.45e-04
polygon 57 6 1.68410e+04 2.25e-05
polygon 58 4 9.45963e+03 1.26e-05
polygon 59 46 6.99702e+05 9.35e-04
polygon 60 13 7.00873e+04 9.36e-05
enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
(53380 x 33890 units)
Window area = 748741000 square units
Fraction of frame area: 0.414First-order Spatial Point Patterns Analysis
In this section, you will learn how to perform first-order SPPA by using spatstat package. The hands-on exercise will focus on:
- deriving kernel density estimation (KDE) layer for visualising and exploring the intensity of point processes,
- performing Confirmatory Spatial Point Patterns Analysis by using Nearest Neighbour statistics.
Kernel Density Estimation
In this section, you will learn how to compute the kernel density estimation of childcare services in Singapore.
Computing kernel density estimation using automatic bandwidth selection method
The code chunk below computes a kernel density by using the following configurations of density() of spatstat: - bw.diggle() automatic bandwidth selection method. Other recommended methods are bw.CvL(), bw.scott() or bw.ppl().
- The smoothing kernel used is gaussian, which is the default. Other smoothing methods are: “epanechnikov”, “quartic” or “disc”.
- The intensity estimate is corrected for edge effect bias by using method described by Jones (1993) and Diggle (2010, equation 18.9). The default is FALSE.
kde_childcareSG_bw <- density(childcareSG_ppp,
sigma=bw.diggle,
edge=TRUE,
kernel="gaussian")
bw <- bw.diggle(childcareSG_ppp)
bw
sigma
298.4095 The plot() function of Base R is then used to display the kernel density derived.
plot(kde_childcareSG_bw)
The density values of the output range from 0 to 0.000035 which is way too small to comprehend. This is because the default unit of measurement of svy21 is in meter. As a result, the density values computed is in “number of points per square meter”.
In the code chunk below, rescale() is used to covert the unit of measurement from meter to kilometer.
childcareSG_ppp.km <- rescale(childcareSG_ppp, 1000, "km")
Now, we can re-run density() using the resale data set and plot the output kde map.
kde_childcareSG.bw <- density(childcareSG_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(kde_childcareSG.bw)
Notice that output image looks identical to the earlier version, the only changes in the data values (refer to the legend).
Working with different automatic badwidth methods
Beside bw.diggle(), there are three other spatstat functions can be used to determine the bandwidth, they are: bw.CvL(), bw.scott(), and bw.ppl().
Let us take a look at the bandwidth return by these automatic bandwidth calculation methods by using the code chunk below.
bw.CvL(childcareSG_ppp.km)
sigma
3.080455 bw.scott(childcareSG_ppp.km)
sigma.x sigma.y
2.303178 1.492997 bw.ppl(childcareSG_ppp.km)
sigma
0.3310477 bw.diggle(childcareSG_ppp.km)
sigma
0.2984095 Baddeley et. (2016) suggested the use of the bw.ppl() algorithm because in ther experience it tends to produce the more appropriate values when the pattern consists predominantly of tight clusters. But they also insist that if the purpose of once study is to detect a single tight cluster in the midst of random noise then the bw.diggle() method seems to work best.
The code chunk beow will be used to compare the output of using bw.diggle and bw.ppl methods.
kde_childcareSG.ppl <- density(childcareSG_ppp.km, sigma=bw.ppl, edge=TRUE, kernel="gaussian")
par(mfrow=c(1,2))
plot(kde_childcareSG.bw, main = "bw.diggle")
plot(kde_childcareSG.ppl, main = "bw.ppl")
Working with different kernel methods
By default, the kernel method used in density.ppp() is gaussian. But there are three other options, namely: Epanechnikov, Quartic and Dics.
The code chunk below will be used to compute three more kernel density estimations by using these three kernel function.
par(mfrow=c(1,2))
plot(density(childcareSG_ppp.km, sigma=bw.ppl, edge=TRUE, kernel="gaussian"), main="Gaussian")
plot(density(childcareSG_ppp.km, sigma=bw.ppl, edge=TRUE, kernel="epanechnikov"), main="Epanechnikov")
par(mfrow=c(1,2))
plot(density(childcareSG_ppp.km, sigma=bw.ppl, edge=TRUE, kernel="quartic"), main="Quartic")
plot(density(childcareSG_ppp.km, sigma=bw.ppl, edge=TRUE, kernel="disc"), main="Disc")
Fixed and Adaptive KDE
Computing KDE by using fixed bandwidth
Next, you will compute a density map by defining a bandwidth of 600 meter. Notice that in the code chunk below, the sigma value used is 0.6. This is because the unit of measurement of childcareSG_ppp.km object is in kilometer, hence the 600m is 0.6km.
kde_childcareSG_600 <- density(childcareSG_ppp.km, sigma=0.6, edge=TRUE, kernel="gaussian")
plot(kde_childcareSG_600)
Computing KDE by using adaptive bandwidth
Fixed bandwidth method is very sensitive to highly skew distribution of spatial point patterns over geographical units for example urban versus rural. One way to overcome this problem is by using adaptive bandwidth instead.
In this section, you will learn how to derive adaptive kernel density estimation by using density.adaptive() of spatstat.
kde_childcareSG_adaptive <- adaptive.density(childcareSG_ppp.km, method="kernel")
plot(kde_childcareSG_adaptive)
We can compare the fixed and adaptive kernel density estimation outputs by using the code chunk below.
par(mfrow=c(1,2))
plot(kde_childcareSG.bw, main = "Fixed bandwidth")
plot(kde_childcareSG_adaptive, main = "Adaptive bandwidth")
Converting KDE output into grid object.
The result is the same, we just convert it so that it is suitable for mapping purposes
gridded_kde_childcareSG_bw <- as.SpatialGridDataFrame.im(kde_childcareSG.bw)
spplot(gridded_kde_childcareSG_bw)
Converting gridded output into raster
Next, we will convert the gridded kernal density objects into RasterLayer object by using raster() of raster package.
kde_childcareSG_bw_raster <- raster(gridded_kde_childcareSG_bw)
Let us take a look at the properties of kde_childcareSG_bw_raster RasterLayer.
kde_childcareSG_bw_raster
class : RasterLayer
dimensions : 128, 128, 16384 (nrow, ncol, ncell)
resolution : 0.4170614, 0.2647348 (x, y)
extent : 2.663926, 56.04779, 16.35798, 50.24403 (xmin, xmax, ymin, ymax)
crs : NA
source : memory
names : v
values : -6.052971e-15, 28.01036 (min, max)Notice that the crs property is NA.
Assigning projection systems
The code chunk below will be used to include the CRS information on kde_childcareSG_bw_raster RasterLayer.
projection(kde_childcareSG_bw_raster) <- CRS("+init=EPSG:3414")
kde_childcareSG_bw_raster
class : RasterLayer
dimensions : 128, 128, 16384 (nrow, ncol, ncell)
resolution : 0.4170614, 0.2647348 (x, y)
extent : 2.663926, 56.04779, 16.35798, 50.24403 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +units=m +no_defs
source : memory
names : v
values : -6.052971e-15, 28.01036 (min, max)Notice that the crs property is completed.
Visualising the output in tmap
Finally, we will display the raster in cartographic quality map using tmap package.
tm_shape(kde_childcareSG_bw_raster) +
tm_raster("v") +
tm_layout(legend.position = c("right", "bottom"), frame = FALSE)
Notice that the raster values are encoded explicitly onto the raster pixel using the values in “v”" field.
Comparing Spatial Point Patterns using KDE
In this section, you will learn how to compare KDE of childcare at Ponggol, Tampines, Chua Chu Kang and Jurong West planning areas.
Extracting study area
The code chunk below will be used to extract the target planning areas.
pg = mpsz[mpsz@data$PLN_AREA_N == "PUNGGOL",]
tm = mpsz[mpsz@data$PLN_AREA_N == "TAMPINES",]
ck = mpsz[mpsz@data$PLN_AREA_N == "CHOA CHU KANG",]
jw = mpsz[mpsz@data$PLN_AREA_N == "JURONG WEST",]
Plotting target planning areas
par(mfrow=c(2,2))
plot(pg, main = "Ponggol")
plot(tm, main = "Tampines")
plot(ck, main = "Choa Chu Kang")
plot(jw, main = "Jurong West")
Converting the spatial point data frame into generic sp format
Next, we will convert these SpatialPolygonsDataFrame layers into generic spatialpolygons layers.
pg_sp = as(pg, "SpatialPolygons")
tm_sp = as(tm, "SpatialPolygons")
ck_sp = as(ck, "SpatialPolygons")
jw_sp = as(jw, "SpatialPolygons")
Creating owin object
Now, we will convert these SpatialPolygons objects into owin objects that is required by spatstat.
pg_owin = as(pg_sp, "owin")
tm_owin = as(tm_sp, "owin")
ck_owin = as(ck_sp, "owin")
jw_owin = as(jw_sp, "owin")
Combining childcare points and the study area
By using the code chunk below, we are able to extract childcare that is within the specific region to do our analysis later on.
childcare_pg_ppp = childcare_ppp_jit[pg_owin]
childcare_tm_ppp = childcare_ppp_jit[tm_owin]
childcare_ck_ppp = childcare_ppp_jit[ck_owin]
childcare_jw_ppp = childcare_ppp_jit[jw_owin]
Next, rescale() function is used to trasnform the unit of measurement from metre to kilometre.
childcare_pg_ppp.km = rescale(childcare_pg_ppp, 1000, "km")
childcare_tm_ppp.km = rescale(childcare_tm_ppp, 1000, "km")
childcare_ck_ppp.km = rescale(childcare_ck_ppp, 1000, "km")
childcare_jw_ppp.km = rescale(childcare_jw_ppp, 1000, "km")
The code chunk below is used to plot these four study areas and the locations of the childcare centres.
par(mfrow=c(2,2))
plot(childcare_pg_ppp.km, main="Punggol")
plot(childcare_tm_ppp.km, main="Tampines")
plot(childcare_ck_ppp.km, main="Choa Chu Kang")
plot(childcare_jw_ppp.km, main="Jurong West")
Computing KDE
The code chunk below will be used to compute the KDE of these four planning area. bw.diggle method is used to derive the bandwidth of each
kde_childcare_pg_bw <- density(childcare_pg_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(kde_childcare_pg_bw)
kde_childcare_tm_bw <- density(childcare_tm_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(kde_childcare_tm_bw)
kde_childcare_ck_bw <- density(childcare_ck_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(kde_childcare_ck_bw)
kde_childcare_jw_bw <- density(childcare_jw_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(kde_childcare_jw_bw)
Computing fixed bandwidth KDE
For comparison purposes, we will use 250m as the bandwidth.
kde_childcare_ck_250 <- density(childcare_ck_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_childcare_ck_250)
kde_childcare_jw_250 <- density(childcare_jw_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_childcare_jw_250)
kde_childcare_pg_250 <- density(childcare_pg_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_childcare_pg_250)
kde_childcare_tm_250 <- density(childcare_tm_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_childcare_tm_250)
Nearest Neighbour Analysis
In this section, we will perform the Clark-Evans test of aggregation for a spatial point pattern by using clarkevans.test() of statspat.
The test hypotheses are:
Ho = The distribution of childcare services are randomly distributed.
H1= The distribution of childcare services are not randomly distributed.
The 95% confident interval will be used.
Testing spatial point patterns using Clark and Evans Test
clarkevans.test(childcareSG_ppp,
correction="none",
clipregion="sg_owin",
alternative=c("clustered"),
nsim=99)
Clark-Evans test
No edge correction
Monte Carlo test based on 99 simulations of CSR with fixed n
data: childcareSG_ppp
R = 0.55696, p-value = 0.01
alternative hypothesis: clustered (R < 1)What conclusion can you draw from the test result?
Clark and Evans Test: Choa Chu Kang planning area
In the code chunk below, clarkevans.test() of spatstat is used to performs Clark-Evans test of aggregation for childcare centre in Choa Chu Kang planning area.
clarkevans.test(childcare_ck_ppp,
correction="none",
clipregion=NULL,
alternative=c("two.sided"),
nsim=999)
Clark-Evans test
No edge correction
Monte Carlo test based on 999 simulations of CSR with fixed n
data: childcare_ck_ppp
R = 0.98402, p-value = 0.298
alternative hypothesis: two-sidedClark and Evans Test: Tampines planning area
In the code chunk below, the similar test is used to analyse the spatial point patterns of childcare centre in Tampines planning area.
clarkevans.test(childcare_tm_ppp,
correction="none",
clipregion=NULL,
alternative=c("two.sided"),
nsim=999)
Clark-Evans test
No edge correction
Monte Carlo test based on 999 simulations of CSR with fixed n
data: childcare_tm_ppp
R = 0.77079, p-value = 0.002
alternative hypothesis: two-sidedSecond-order Spatial Point Patterns Analysis
Analysing Spatial Point Process Using G-Function
The G function measures the distribution of the distances from an arbitrary event to its nearest event. In this section, you will learn how to compute G-function estimation by using Gest() of spatstat package. You will also learn how to perform monta carlo simulation test using envelope() of spatstat package.
Choa Chu Kang planning area
Computing G-function estimation
The code chunk below is used to compute G-function using Gest() of spatat package.
Performing Complete Spatial Randomness Test
To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:
Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.
H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
Monte Carlo test with G-fucntion
G_CK.csr <- envelope(childcare_ck_ppp, Gest, nsim = 999)
Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60
.........70.........80.........90.........100.........110.........120
.........130.........140.........150.........160.........170.........180
.........190.........200.........210.........220.........230.........240
.........250.........260.........270.........280.........290.........300
.........310.........320.........330.........340.........350.........360
.........370.........380.........390.........400.........410.........420
.........430.........440.........450.........460.........470.........480
.........490.........500.........510.........520.........530.........540
.........550.........560.........570.........580.........590.........600
.........610.........620.........630.........640.........650.........660
.........670.........680.........690.........700.........710.........720
.........730.........740.........750.........760.........770.........780
.........790.........800.........810.........820.........830.........840
.........850.........860.........870.........880.........890.........900
.........910.........920.........930.........940.........950.........960
.........970.........980.........990........ 999.
Done.plot(G_CK.csr)
Tampines planning area
Computing G-function estimation
G_tm = Gest(childcare_tm_ppp, correction = "best")
plot(G_tm)
Performing Complete Spatial Randomness Test
To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:
Ho = The distribution of childcare services at Tampines are randomly distributed.
H1= The distribution of childcare services at Tampines are not randomly distributed.
The null hypothesis will be rejected is p-value is smaller than alpha value of 0.001.
The code chunk below is used to perform the hypothesis testing.
G_tm.csr <- envelope(childcare_tm_ppp, Gest, correction = "all", nsim = 999)
Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60
.........70.........80.........90.........100.........110.........120
.........130.........140.........150.........160.........170.........180
.........190.........200.........210.........220.........230.........240
.........250.........260.........270.........280.........290.........300
.........310.........320.........330.........340.........350.........360
.........370.........380.........390.........400.........410.........420
.........430.........440.........450.........460.........470.........480
.........490.........500.........510.........520.........530.........540
.........550.........560.........570.........580.........590.........600
.........610.........620.........630.........640.........650.........660
.........670.........680.........690.........700.........710.........720
.........730.........740.........750.........760.........770.........780
.........790.........800.........810.........820.........830.........840
.........850.........860.........870.........880.........890.........900
.........910.........920.........930.........940.........950.........960
.........970.........980.........990........ 999.
Done.plot(G_tm.csr)
Analysing Spatial Point Process Using F-Function
The F function estimates the empty space function F(r) or its hazard rate h(r) from a point pattern in a window of arbitrary shape. In this section, you will learn how to compute F-function estimation by using Fest() of spatstat package. You will also learn how to perform monta carlo simulation test using envelope() of spatstat package.
Choa Chu Kang planning area
Computing F-function estimation
The code chunk below is used to compute F-function using Fest() of spatat package.
F_CK = Fest(childcare_ck_ppp)
plot(F_CK)
Performing Complete Spatial Randomness Test
To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:
Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.
H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
Monte Carlo test with F-fucntion
F_CK.csr <- envelope(childcare_ck_ppp, Fest, nsim = 999)
Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60
.........70.........80.........90.........100.........110.........120
.........130.........140.........150.........160.........170.........180
.........190.........200.........210.........220.........230.........240
.........250.........260.........270.........280.........290.........300
.........310.........320.........330.........340.........350.........360
.........370.........380.........390.........400.........410.........420
.........430.........440.........450.........460.........470.........480
.........490.........500.........510.........520.........530.........540
.........550.........560.........570.........580.........590.........600
.........610.........620.........630.........640.........650.........660
.........670.........680.........690.........700.........710.........720
.........730.........740.........750.........760.........770.........780
.........790.........800.........810.........820.........830.........840
.........850.........860.........870.........880.........890.........900
.........910.........920.........930.........940.........950.........960
.........970.........980.........990........ 999.
Done.plot(F_CK.csr)
Tampines planning area
Computing F-function estimation
Monte Carlo test with F-fucntion
F_tm = Fest(childcare_tm_ppp, correction = "best")
plot(F_tm)
Performing Complete Spatial Randomness Test
To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:
Ho = The distribution of childcare services at Tampines are randomly distributed.
H1= The distribution of childcare services at Tampines are not randomly distributed.
The null hypothesis will be rejected is p-value is smaller than alpha value of 0.001.
The code chunk below is used to perform the hypothesis testing.
F_tm.csr <- envelope(childcare_tm_ppp, Fest, correction = "all", nsim = 999)
Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60
.........70.........80.........90.........100.........110.........120
.........130.........140.........150.........160.........170.........180
.........190.........200.........210.........220.........230.........240
.........250.........260.........270.........280.........290.........300
.........310.........320.........330.........340.........350.........360
.........370.........380.........390.........400.........410.........420
.........430.........440.........450.........460.........470.........480
.........490.........500.........510.........520.........530.........540
.........550.........560.........570.........580.........590.........600
.........610.........620.........630.........640.........650.........660
.........670.........680.........690.........700.........710.........720
.........730.........740.........750.........760.........770.........780
.........790.........800.........810.........820.........830.........840
.........850.........860.........870.........880.........890.........900
.........910.........920.........930.........940.........950.........960
.........970.........980.........990........ 999.
Done.plot(F_tm.csr)
Analysing Spatial Point Process Using K-Function
K-function measures the number of events found up to a given distance of any particular event. In this section, you will learn how to compute K-function estimates by using Kest() of spatstat package. You will also learn how to perform monta carlo simulation test using envelope() of spatstat package.
Choa Chu Kang planning area
Computing K-fucntion estimate
K_ck = Kest(childcare_ck_ppp, correction = "Ripley")
plot(K_ck, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")
Performing Complete Spatial Randomness Test
To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:
Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.
H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
The code chunk below is used to perform the hypothesis testing.
K_ck.csr <- envelope(childcare_ck_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)
Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70,
71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99.
Done.plot(K_ck.csr, . - r ~ r, xlab="d", ylab="K(d)-r")
Tampines planning area
Computing K-fucntion estimation
K_tm = Kest(childcare_tm_ppp, correction = "Ripley")
plot(K_tm, . -r ~ r,
ylab= "K(d)-r", xlab = "d(m)",
xlim=c(0,1000))
Performing Complete Spatial Randomness Test
To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:
Ho = The distribution of childcare services at Tampines are randomly distributed.
H1= The distribution of childcare services at Tampines are not randomly distributed.
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
The code chunk below is used to perform the hypothesis testing.
K_tm.csr <- envelope(childcare_tm_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)
Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70,
71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99.
Done.
Analysing Spatial Point Process Using L-Function
In this section, you will learn how to compute L-function estimation by using Lest() of spatstat package. You will also learn how to perform monta carlo simulation test using envelope() of spatstat package.
Choa Chu Kang planning area
Computing L Fucntion estimation
L_ck = Lest(childcare_ck_ppp, correction = "Ripley")
plot(L_ck, . -r ~ r,
ylab= "L(d)-r", xlab = "d(m)")
Performing Complete Spatial Randomness Test
To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:
Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.
H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.
The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.
The code chunk below is used to perform the hypothesis testing.
L_ck.csr <- envelope(childcare_ck_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)
Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70,
71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99.
Done.plot(L_ck.csr, . - r ~ r, xlab="d", ylab="L(d)-r")
Tampines planning area
Computing L-fucntion estimate
L_tm = Lest(childcare_tm_ppp, correction = "Ripley")
plot(L_tm, . -r ~ r,
ylab= "L(d)-r", xlab = "d(m)",
xlim=c(0,1000))
Performing Complete Spatial Randomness Test
To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:
Ho = The distribution of childcare services at Tampines are randomly distributed.
H1= The distribution of childcare services at Tampines are not randomly distributed.
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
The code chunk below will be used to perform the hypothesis testing.
L_tm.csr <- envelope(childcare_tm_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)
Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70,
71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99.
Done.Then, plot the model output by using the code chun below.
library(pagedown)
pagedown::chrome_print("Hands-on_Ex04_SPPA_spatstat.html")