ihclust
Introduction
Drug utilization data have been widely explored by researchers as the patterns of the data are associated with various factors such as health outcomes and disparities, regulatory policies, and social issues. Despite the depth of the data and potential public health impact, drug utilization data are often analyzed using simple descriptive analyses (e.g., presentation of monthly utilization trend at the national level). Methods and software to explore the time trend of drug utilization across granular geographic units have been limited.
Therefore, we introduce ihclust, an R package to:
i) identify geographic areas with significant change over time in drug utilization, and
ii) characterize common change over time patterns among the time series for multiple geographic areas.
Methods
Step 1: Method to Identify Areas with Change Over Time
- We assume that prescription dispensing data are discrete observations from a smooth underlying function,
denoted as \(X_{i}(t)\), where \(i\) indicates a geographic area. - We identify a subset of geographic locations that change significantly with respect to time,
using hypothesis tests: \(H_{0}:X_{i}(t)=0\) vs. \(H_{a}:X_{i}(t)\neq0.\) - For each geographic location, p-values are obtained using a permutation test.
P-values are adjusted by using Benjamini-Hochberg method.
Step 2: Method to Characterize Temporal Change
We obtain clusters of geogrpahic areas that share similar temporal change patterns using Iterative Hiearchical Clustering (IHC).
IHC implements the following three steps to the estimated smooth function, \(\hat{X}_{i}(t)\):
1) Initialization: The initial clusters are determined by hiearchical clustering.
2) Merging: Clusters are re-assessed by examining the cluster centers. Any clusters with pairwise correlations greather than a pre-specified threshold \(\alpha\) are merged.
3) Pruning: Clustering membership is re-examined. Any cluster member with correlations between the cluster center and member less than \(\alpha\) is removed from each existing cluster and assigned into a single-element cluster.
4) Steps 2-3 are repeated until a pre-defined convergence criteria is satisfied.
Installation
ihclust can be installed using install.packages("ihclust").
The development version from GitHub can be installed using the following code:
# install.packages("devtools")
devtools::install_github("https://github.com/elincho/ihclust")Example
Following is an example illustrating usage of two main functions testchange and ihclust. A simulated data will be used in this example. An additional example using real data of opioid dispensings in the United States is provied in the Appendix at the end of this page.
library(ihclust)Data
We will use a simulated data generated by a function simcurve from the ihclust package. The following code randomly generates curves representing weekly prescription drug dispensing data from 900 areas over 52 weeks. p=0.05 represents a proportion of areas that had no significant change over time.
set.seed(1)
mydata <- simcurve(numareas = c(300, 300, 300), p=0.05, type="random")# create a function for plotting
plotsim <- function(curve){
if (curve$parameters[3] == "random"){
mysimdata <- curve$data
par(mfrow=c(1,3))
time=seq(1,52,1)
plot(time, mysimdata[1,],type='l', lwd = 0.2, ylim=c(-3.5,3.5),
ylab="Standardized number of prescriptions dispensed",
xlab="",
main="All Areas Over Time \n (n=900)",
cex.lab=1.2, cex.axis=0.8, cex.main=1, col = "red")
for(i in 2:45){lines(time,mysimdata[i,],ylim=c(-3.5,3.5), col = "red")}
for(i in 46:900){lines(time,mysimdata[i,],ylim=c(-3.5,3.5), col = "deepskyblue")}
plot(time, mysimdata[1,],type='l',ylim=c(-3.5,3.5),
ylab="",
xlab="Time (Weeks)",
main="Areas with Change Over Time \n (n=45)",
cex.lab=1.2, cex.axis=0.8, cex.main=1, col = "red")
for(i in 2:45){lines(time,mysimdata[i,],ylim=c(-3.5,3.5), col = "red")}
plot(time, mysimdata[46,],type='l',ylim=c(-3.5,3.5),
ylab="",
xlab="",
main="Areas with No Change \n (n=855)",
cex.lab=1.2, cex.axis=0.8, cex.main=1, col = "deepskyblue")
for(i in 47:900){lines(time,mysimdata[i,],ylim=c(-3.5,3.5), col = "deepskyblue")}
}
else if (curve$parameters[3] == "fixed"){
simulated_clusters <- curve$data
par(mfrow=c(1,3))
time <- seq(1,52,1)
plot(time, simulated_clusters[1,],type='l',ylim=c(-3.5,3.5),
ylab="Standardized number of prescriptions dispensed",
xlab = "",
main="Simulated data for cluster 1",
cex.lab=0.8, cex.axis=0.8, cex.main=1)
for(i in 2:300){lines(time,simulated_clusters[i,],ylim=c(-3.5,3.5))}
plot(time, simulated_clusters[301,],type='l',ylim=c(-3.5,3.5),
ylab = "",
xlab="Time (Weeks)",
main="Simulated data for cluster 2",
cex.lab=0.8, cex.axis=0.8, cex.main=1)
for(i in 301:600){lines(time,simulated_clusters[i,],ylim=c(-3.5,3.5))}
plot(time, simulated_clusters[601,],type='l',ylim=c(-3.5,3.5),
ylab = "",
xlab = "",
main="Simulated data for cluster 3",
cex.lab=0.8, cex.axis=0.8, cex.main=1)
for(i in 601:900){lines(time,simulated_clusters[i,],ylim=c(-3.5,3.5))}
}}
plotsim(mydata)
In the figure above, the red lines represent the areas that have disensing data with significant change over time. The blue lines represent the areas that have dispenisng data with no significant change over time. There are 45 areas with change, and 855 areas with no change.
Step 1: Identifying Areas with Change over Time
In the first step, testchange function below runs 100 permutation tests (nperm = 100) for each geograpghic area. The option time = seq(1,52,1) specifies the number of time points in the data, representing 52 weeks in this example.
The number of \(\geq10000\) permutations is recommended, but we recommend starting with a smaller size initially as it can be time-consuming to run permutation tests.
Adjusted p-values are measured against the significant level of 0.05 to sort out the areas that have significant change over time patterns in dispensing data. Among 900 areas, 40 areas were identified as having significant change (40 out of 45 areas correctly identified).
sim_change_results <- testchange(data=mydata$data,perm=TRUE, nperm=100,time=seq(1,52,1)) ## [1] "Performing permutation test.."sim_change <- mydata$data[sim_change_results$p.adjusted<.05, ]
nrow(sim_change) # 40 selected## [1] 40Step 2: Clustering Common Change over Time Patterns among the Time-series for Areas
In the second step, ihclust function performs Iterative Hiearchical Clustering to generate multiple clusters, each containing members with similar change over time patterns. The pre-specified correlation criteria is set as 0.75. The maximum number of iteration can be set as 100 to prevent the possible situation where merging and pruning steps keep repeating endlessly with two different final results.
sim_clust_results <- ihclust(data=sim_change, smooth = TRUE, cor_criteria = 0.75, max_iteration = 100, verbose = TRUE)## [1] 1
## [1] 1 2 3 4 5 6 7 8
## [1] 2
## [1] 1 2 3 4 5 6 7 8
## [1] 3
## [1] 1 2 3 4 5 6The numbers below represent clustering memberships of prescription drug dispensing data with change over time patterns for 40 geographic areas.
sim_clust_results[["Cluster_Label"]]## [1] 1 2 2 3 1 2 2 2 1 2 6 2 2 3 4 3 2 3 2 6 3 2 5 3 2 3 3 4 1 1 1 2 4 3 1 3 3 1
## [39] 5 3Clustering Results
A total of 6 clusters were identified by the IHC algorithm. The largest cluster (Cluster 2) identified 13 areas sharing similar change over time patterns. The second largest cluster (Cluster 3) identified 12 areas. All clusters are shown by figures below.
# center the data for plotting
sim_centered <- matrix(rep(NA,nrow(sim_change)*52),ncol=52)
for(i in 1:nrow(sim_centered)){
obsData.centered <- as.numeric(scale(sim_change[i,], center = TRUE, scale = TRUE))
sim_centered[i,] <- obsData.centered
rm(obsData.centered)
}
# merge centered data and clustering memberships
memb_sim <- sim_clust_results$Cluster_Label
clusters_sim <- cbind(sim_centered,memb_sim)
# sort clusters in decreasing order
memb_sim <- sort(table(memb_sim),decreasing=T)
# check number of members in each cluster
memb_sim## memb_sim
## 2 3 1 4 5 6
## 13 12 8 3 2 2par(mfrow=c(2,3))
for(i in 1:length(memb_sim)){
cluster_c <- clusters_sim[which(clusters_sim[,53]==names(memb_sim)[i]),]
time <- seq(1,52,1)
if(is.null(ncol(cluster_c))==F){
plot.title <- paste("Cluster: ",names(memb_sim)[i]," (",memb_sim[i]," Areas)",sep="")
plot(time, cluster_c[1,1:52],type='l',ylim=c(-5,5), xlab="Week",col='lightgrey',
ylab="",
cex.axis=0.8, main=plot.title,cex.lab=1,cex.main=1)
title(ylab="Standardized number of\nprescriptions dispensed", line=2, cex.lab=1)
for(i in 2:nrow(cluster_c)){lines(time,cluster_c[i,1:52],ylim=c(-5,5),col='lightgrey')}
lines(time,colMeans(cluster_c[,1:52]),col='red',lwd=2)
}
else{
plot.title <- paste("Cluster: ",names(memb_sim)[i]," (",memb_sim[i]," Area)",sep="")
plot(time, cluster_c[1:52],type='l',ylim=c(-5,5),xlab="Week",col='black',
ylab="",
cex.axis=0.8, main=plot.title,cex.lab=1,cex.main=1)
title(ylab="Standardized number of\nprescriptions dispensed", line=2, cex.lab=1)
}
}
The red line represents the average number (or rate) of prescription dispensings in each cluster, and the gray lines represent the numbers (or rates) of prescription dispenisngs in areas within each cluster.
Appendix
Example using a dataset opioidData within the package
The package includes a sample dataset from the CDC U.S.Opioid Dispensing Rate Maps (https://www.cdc.gov/drugoverdose/rxrate-maps/index.html). The data is publicly available and includes retail opioid prescription dispensing data at the state and county level from 2006 –2020. The data are obtained as rates of opioid dispensing per 100 persons. Further details about the data source are available from the CDC data resource page.
data(opioidData)
opioid_data_noNA <- opioidData[complete.cases(opioidData), ]
opioid_data <- as.matrix(opioid_data_noNA[,4:18])Step 1: Identifying Areas with Change over Time
opioid_change_results <- testchange(data=opioid_data,perm=TRUE,nperm=100,time=seq(1,15,1)) ## [1] "Performing permutation test.."opioid_change <- opioid_data[opioid_change_results$p.adjusted<.05, ] Step 2: Clustering Common Change over Time Patterns among the Time-series for Areas
opioid_clust_results <- ihclust(data=opioid_change, smooth = TRUE, cor_criteria = 0.75, max_iteration = 100, verbose = TRUE)## [1] 1
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
## [19] 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
## [37] 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
## [55] 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
## [73] 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
## [91] 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108
## [109] 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
## [127] 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144
## [145] 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162
## [163] 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180
## [181] 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198
## [199] 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216
## [217] 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234
## [235] 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252
## [253] 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270
## [271] 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288
## [289] 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306
## [307] 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324
## [325] 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342
## [343] 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360
## [361] 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378
## [379] 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396
## [397] 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414
## [415] 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432
## [433] 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450
## [451] 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468
## [469] 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486
## [487] 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504
## [505] 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522
## [523] 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540
## [541] 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558
## [559] 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576
## [577] 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594
## [595] 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612
## [613] 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630
## [631] 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648
## [649] 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666
## [667] 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684
## [685] 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702
## [703] 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720
## [721] 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738
## [739] 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756
## [757] 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774
## [775] 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792
## [793] 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810
## [811] 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828
## [829] 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846
## [847] 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864
## [865] 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882
## [883] 883 884 885
## [1] 2
## [1] 1 2 3 4 6 30 78 125 174 490 524 525 526 527 528 529 530 531
## [19] 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549
## [37] 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567
## [55] 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585
## [73] 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603
## [91] 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621
## [109] 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639
## [127] 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657
## [145] 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675
## [163] 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693
## [181] 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711
## [199] 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729
## [217] 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747
## [235] 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765
## [253] 766 767 768 769 770 771 772 773
## [1] 3
## [1] 1 2 4 6 30 78 125 490 524 526 527 540 541 542 543 544 545 546
## [19] 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564
## [37] 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582
## [55] 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600
## [73] 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618
## [91] 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634
## [1] 4
## [1] 1 2 4 30 125 490 524 526 527 540 541 545 595 596 597 598 599 600 601
## [20] 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620
## [39] 621
## [1] 5
## [1] 1 2 4 30 125 490 524 527 540 545 595 596 597 598 599 600 601 602 603
## [20] 604 605 606 607 608
## [1] 6
## [1] 1 2 4 30 125 490 524 527 540 545 595 597 598 600 606 607 608 609 610
## [20] 611 612
## [1] 7
## [1] 1 2 4 30 125 490 524 527 540 545 595 597 598 606 607 608 609
## [1] 8
## [1] 1 2 4 30 125 490 524 527 540 545 595 597 598 606 608Clustering Results
# center the data for plotting
opioid_centered <- matrix(rep(NA,nrow(opioid_change)*15),ncol=15)
for(i in 1:nrow(opioid_centered)){
obsData.centered <- as.numeric(scale(opioid_change[i,], center = TRUE, scale = TRUE))
opioid_centered[i,] <- obsData.centered
rm(obsData.centered)
}
# merge centered data and clustering memberships
memb_opioid <- opioid_clust_results$Cluster_Label
clusters_opioid <- cbind(opioid_centered,memb_opioid)
# sort clusters in decreasing order
memb_opioid_sorted <- sort(table(memb_opioid),decreasing=T)
# check number of members in each cluster
memb_opioid_sorted## memb_opioid
## 1 2 4 527 125 30 606 540 598 545 595 490 597 524 608
## 1570 466 260 69 40 13 9 6 6 5 4 2 2 1 1par(mfrow=c(3,5))
for(i in 1:length(memb_opioid_sorted)){
cluster_c <- clusters_opioid[which(clusters_opioid[,16]==names(memb_opioid_sorted)[i]),]
time <- seq(2006,2020,1)
if(is.null(ncol(cluster_c))==F){
plot.title <- paste("Cluster: ",names(memb_opioid_sorted)[i],"\n(",memb_opioid_sorted[i]," Counties)",sep="")
plot(time, cluster_c[1,1:15],type='l',ylim=c(-5,5), xlab="Week",col='lightgrey',
ylab="",
cex.axis=0.7, main=plot.title,cex.lab=1,cex.main=0.9,las=2)
title(ylab="Standardized Opioid\nDispensing Rate", line=2, cex.lab=0.7)
for(i in 2:nrow(cluster_c)){lines(time,cluster_c[i,1:15],ylim=c(-5,5),col='lightgrey')}
lines(time,colMeans(cluster_c[,1:15]),col='red',lwd=2)
}
else{
plot.title <- paste("Cluster: ",names(memb_opioid_sorted)[i],"\n(",memb_opioid_sorted[i]," County)",sep="")
plot(time, cluster_c[1:15],type='l',ylim=c(-5,5),xlab="Week",col='black',
ylab="",
cex.axis=0.7, main=plot.title,cex.lab=1,cex.main=0.9,las=2)
title(ylab="Standardized Opioid\nDispensing Rate", line=2, cex.lab=0.7)
}
}
The red line represents the average rate of opioid prescription dispensings in each cluster, and the gray lines represent the rates of prescription dispenisngs in counties within each cluster.
List of counties in each cluster
opioid_county <- opioid_data_noNA[,3:18]
opioid_change_county <- opioid_county[opioid_change_results$p.adjusted<.05, ]
memb_county <- cbind(opioid_change_county,memb_opioid)
# make a list
clusters_list <- list()
for(i in 1:length(memb_opioid_sorted)){
county <- memb_county$County[which(memb_county$memb_opioid==names(memb_opioid_sorted)[i])]
clusters_list[[i]] <- county
names(clusters_list)[i] <- paste0("Cluster",names(memb_opioid_sorted)[i])
}
clusters_list## $Cluster1
## [1] "autauga" "baldwin" "barbour"
## [4] "blount" "butler" "calhoun"
## [7] "chambers" "cherokee" "chilton"
## [10] "choctaw" "clarke" "clay"
## [13] "coffee" "colbert" "coosa"
## [16] "crenshaw" "cullman" "dale"
## [19] "dallas" "elmore" "etowah"
## [22] "franklin" "hale" "houston"
## [25] "lauderdale" "lee" "limestone"
## [28] "macon" "madison" "marengo"
## [31] "marshall" "mobile" "montgomery"
## [34] "morgan" "pickens" "pike"
## [37] "russell" "st clair" "shelby"
## [40] "sumter" "talladega" "tallapoosa"
## [43] "tuscaloosa" "walker" "cochise"
## [46] "coconino" "gila" "graham"
## [49] "la paz" "maricopa" "mohave"
## [52] "navajo" "pima" "yavapai"
## [55] "yuma" "baxter" "benton"
## [58] "boone" "calhoun" "clark"
## [61] "cleburne" "columbia" "dallas"
## [64] "drew" "faulkner" "garland"
## [67] "greene" "hempstead" "hot spring"
## [70] "howard" "independence" "izard"
## [73] "jackson" "lonoke" "mississippi"
## [76] "montgomery" "perry" "phillips"
## [79] "pope" "prairie" "randolph"
## [82] "st francis" "saline" "sebastian"
## [85] "washington" "white" "amador"
## [88] "butte" "calaveras" "colusa"
## [91] "contra costa" "del norte" "fresno"
## [94] "imperial" "kern" "kings"
## [97] "lake" "lassen" "los angeles"
## [100] "madera" "mariposa" "mendocino"
## [103] "merced" "monterey" "napa"
## [106] "nevada" "plumas" "riverside"
## [109] "sacramento" "san benito" "san bernardino"
## [112] "san diego" "san joaquin" "san luis obispo"
## [115] "siskiyou" "solano" "stanislaus"
## [118] "tehama" "trinity" "tulare"
## [121] "tuolumne" "ventura" "yolo"
## [124] "yuba" "adams" "alamosa"
## [127] "arapahoe" "archuleta" "baca"
## [130] "broomfield" "chaffee" "cheyenne"
## [133] "crowley" "delta" "denver"
## [136] "douglas" "el paso" "fremont"
## [139] "garfield" "grand" "gunnison"
## [142] "huerfano" "jefferson" "kiowa"
## [145] "lake" "larimer" "las animas"
## [148] "logan" "moffat" "montezuma"
## [151] "montrose" "morgan" "otero"
## [154] "prowers" "pueblo" "summit"
## [157] "teller" "weld" "yuma"
## [160] "fairfield" "litchfield" "middlesex"
## [163] "new haven" "new london" "tolland"
## [166] "windham" "kent" "new castle"
## [169] "sussex" "bay" "bradford"
## [172] "brevard" "calhoun" "citrus"
## [175] "clay" "miami-dade" "de soto"
## [178] "duval" "escambia" "gadsden"
## [181] "gulf" "hendry" "hernando"
## [184] "highlands" "holmes" "indian river"
## [187] "lake" "levy" "liberty"
## [190] "nassau" "okeechobee" "osceola"
## [193] "putnam" "st lucie" "santa rosa"
## [196] "sumter" "suwannee" "taylor"
## [199] "union" "wakulla" "washington"
## [202] "appling" "atkinson" "baldwin"
## [205] "barrow" "bartow" "bibb"
## [208] "bleckley" "bulloch" "burke"
## [211] "butts" "carroll" "catoosa"
## [214] "chattooga" "clayton" "coffee"
## [217] "columbia" "cook" "coweta"
## [220] "crisp" "dade" "dawson"
## [223] "decatur" "de kalb" "dougherty"
## [226] "douglas" "effingham" "evans"
## [229] "fayette" "forsyth" "gilmer"
## [232] "gordon" "greene" "habersham"
## [235] "hall" "haralson" "hart"
## [238] "henry" "jackson" "jasper"
## [241] "lamar" "liberty" "lowndes"
## [244] "mcduffie" "mcintosh" "madison"
## [247] "murray" "newton" "peach"
## [250] "pickens" "polk" "rabun"
## [253] "randolph" "spalding" "stephens"
## [256] "sumter" "telfair" "toombs"
## [259] "towns" "troup" "union"
## [262] "walker" "walton" "washington"
## [265] "wayne" "whitfield" "wilkes"
## [268] "worth" "ada" "bannock"
## [271] "bear lake" "benewah" "bingham"
## [274] "bonner" "bonneville" "canyon"
## [277] "cassia" "clearwater" "custer"
## [280] "fremont" "gem" "idaho"
## [283] "jefferson" "jerome" "kootenai"
## [286] "latah" "lewis" "madison"
## [289] "minidoka" "shoshone" "teton"
## [292] "twin falls" "washington" "bond"
## [295] "boone" "champaign" "christian"
## [298] "clay" "coles" "cook"
## [301] "de kalb" "de witt" "du page"
## [304] "edgar" "fayette" "franklin"
## [307] "fulton" "grundy" "hardin"
## [310] "henry" "iroquois" "jackson"
## [313] "jefferson" "jersey" "jo daviess"
## [316] "kane" "kankakee" "kendall"
## [319] "knox" "lake" "la salle"
## [322] "lawrence" "lee" "livingston"
## [325] "logan" "mchenry" "mclean"
## [328] "macon" "macoupin" "madison"
## [331] "marion" "mason" "mercer"
## [334] "monroe" "montgomery" "morgan"
## [337] "moultrie" "ogle" "perry"
## [340] "randolph" "richland" "rock island"
## [343] "st clair" "saline" "sangamon"
## [346] "stephenson" "tazewell" "union"
## [349] "vermilion" "wabash" "warren"
## [352] "wayne" "white" "whiteside"
## [355] "will" "winnebago" "adams"
## [358] "bartholomew" "blackford" "boone"
## [361] "carroll" "cass" "clark"
## [364] "clay" "clinton" "crawford"
## [367] "decatur" "de kalb" "delaware"
## [370] "dubois" "elkhart" "fayette"
## [373] "fountain" "franklin" "fulton"
## [376] "gibson" "grant" "greene"
## [379] "hancock" "harrison" "hendricks"
## [382] "huntington" "jackson" "jasper"
## [385] "jay" "jefferson" "jennings"
## [388] "johnson" "knox" "kosciusko"
## [391] "lagrange" "lake" "la porte"
## [394] "lawrence" "marshall" "martin"
## [397] "miami" "montgomery" "morgan"
## [400] "noble" "orange" "owen"
## [403] "perry" "pike" "porter"
## [406] "pulaski" "putnam" "randolph"
## [409] "ripley" "rush" "st joseph"
## [412] "shelby" "starke" "steuben"
## [415] "sullivan" "tippecanoe" "vermillion"
## [418] "wabash" "warrick" "washington"
## [421] "wayne" "wells" "white"
## [424] "whitley" "allamakee" "black hawk"
## [427] "buchanan" "cass" "cerro gordo"
## [430] "cherokee" "chickasaw" "clarke"
## [433] "clinton" "delaware" "des moines"
## [436] "dubuque" "fayette" "floyd"
## [439] "fremont" "hardin" "howard"
## [442] "linn" "marshall" "palo alto"
## [445] "pocahontas" "polk" "pottawattamie"
## [448] "scott" "wapello" "webster"
## [451] "wright" "allen" "atchison"
## [454] "barton" "butler" "cloud"
## [457] "crawford" "douglas" "finney"
## [460] "franklin" "geary" "graham"
## [463] "harvey" "jackson" "labette"
## [466] "leavenworth" "lyon" "marion"
## [469] "montgomery" "morton" "osborne"
## [472] "pratt" "reno" "riley"
## [475] "saline" "scott" "sedgwick"
## [478] "seward" "shawnee" "sherman"
## [481] "smith" "thomas" "adair"
## [484] "allen" "anderson" "ballard"
## [487] "barren" "breathitt" "breckinridge"
## [490] "bullitt" "butler" "carroll"
## [493] "cumberland" "daviess" "edmonson"
## [496] "estill" "fleming" "floyd"
## [499] "franklin" "grant" "grayson"
## [502] "harlan" "henderson" "jackson"
## [505] "jessamine" "knott" "larue"
## [508] "lee" "leslie" "letcher"
## [511] "lincoln" "logan" "madison"
## [514] "magoffin" "marion" "marshall"
## [517] "meade" "mercer" "muhlenberg"
## [520] "nelson" "oldham" "owsley"
## [523] "pendleton" "rockcastle" "shelby"
## [526] "spencer" "trigg" "union"
## [529] "webster" "whitley" "assumption"
## [532] "avoyelles" "beauregard" "calcasieu"
## [535] "east carroll" "evangeline" "franklin"
## [538] "iberia" "iberville" "jefferson davis"
## [541] "lafourche" "lincoln" "livingston"
## [544] "morehouse" "natchitoches" "ouachita"
## [547] "pointe coupee" "rapides" "sabine"
## [550] "st bernard" "st charles" "st landry"
## [553] "st martin:north" "st martin:south" "st mary"
## [556] "tangipahoa" "terrebonne" "washington"
## [559] "webster" "west baton rouge" "west carroll"
## [562] "androscoggin" "hancock" "kennebec"
## [565] "lincoln" "oxford" "sagadahoc"
## [568] "somerset" "washington" "york"
## [571] "allegany" "anne arundel" "baltimore"
## [574] "calvert" "caroline" "carroll"
## [577] "cecil" "charles" "dorchester"
## [580] "frederick" "garrett" "harford"
## [583] "howard" "kent" "montgomery"
## [586] "prince georges" "queen annes" "st marys"
## [589] "somerset" "talbot" "washington"
## [592] "wicomico" "bristol" "dukes"
## [595] "franklin" "hampden" "hampshire"
## [598] "plymouth" "alger" "allegan"
## [601] "alpena" "antrim" "arenac"
## [604] "bay" "benzie" "berrien"
## [607] "branch" "calhoun" "cass"
## [610] "charlevoix" "cheboygan" "chippewa"
## [613] "clare" "clinton" "dickinson"
## [616] "eaton" "emmet" "genesee"
## [619] "gogebic" "grand traverse" "gratiot"
## [622] "hillsdale" "huron" "ingham"
## [625] "ionia" "iosco" "iron"
## [628] "isabella" "jackson" "kalamazoo"
## [631] "kalkaska" "kent" "lapeer"
## [634] "lenawee" "livingston" "mackinac"
## [637] "macomb" "manistee" "marquette"
## [640] "mason" "mecosta" "menominee"
## [643] "midland" "monroe" "montcalm"
## [646] "montmorency" "muskegon" "newaygo"
## [649] "oakland" "ogemaw" "osceola"
## [652] "oscoda" "otsego" "ottawa"
## [655] "roscommon" "saginaw" "st clair"
## [658] "st joseph" "sanilac" "shiawassee"
## [661] "van buren" "wayne" "wexford"
## [664] "aitkin" "anoka" "becker"
## [667] "beltrami" "big stone" "blue earth"
## [670] "brown" "carlton" "carver"
## [673] "cass" "clay" "clearwater"
## [676] "crow wing" "dakota" "dodge"
## [679] "douglas" "faribault" "goodhue"
## [682] "grant" "hennepin" "hubbard"
## [685] "isanti" "itasca" "kandiyohi"
## [688] "lac qui parle" "le sueur" "lincoln"
## [691] "mcleod" "marshall" "martin"
## [694] "meeker" "mille lacs" "mower"
## [697] "nicollet" "nobles" "otter tail"
## [700] "polk" "ramsey" "red lake"
## [703] "redwood" "rice" "scott"
## [706] "sherburne" "stearns" "steele"
## [709] "swift" "wadena" "waseca"
## [712] "washington" "wilkin" "winona"
## [715] "wright" "adams" "alcorn"
## [718] "amite" "attala" "benton"
## [721] "bolivar" "chickasaw" "claiborne"
## [724] "clay" "copiah" "de soto"
## [727] "forrest" "franklin" "george"
## [730] "grenada" "hancock" "harrison"
## [733] "jefferson davis" "jones" "lamar"
## [736] "lawrence" "lincoln" "lowndes"
## [739] "marion" "monroe" "neshoba"
## [742] "noxubee" "panola" "pearl river"
## [745] "pike" "pontotoc" "prentiss"
## [748] "rankin" "simpson" "sunflower"
## [751] "tate" "tippah" "union"
## [754] "warren" "washington" "wayne"
## [757] "winston" "yalobusha" "yazoo"
## [760] "adair" "audrain" "buchanan"
## [763] "butler" "camden" "cape girardeau"
## [766] "cass" "clay" "cole"
## [769] "crawford" "dent" "dunklin"
## [772] "franklin" "jackson" "jasper"
## [775] "jefferson" "johnson" "lincoln"
## [778] "linn" "livingston" "mcdonald"
## [781] "madison" "miller" "montgomery"
## [784] "morgan" "pemiscot" "pettis"
## [787] "phelps" "platte" "polk"
## [790] "pulaski" "randolph" "ripley"
## [793] "st charles" "st francois" "st louis"
## [796] "scott" "shelby" "stone"
## [799] "vernon" "warren" "wayne"
## [802] "webster" "wright" "blaine"
## [805] "cascade" "custer" "dawson"
## [808] "glacier" "hill" "lake"
## [811] "lewis and clark" "lincoln" "meagher"
## [814] "powell" "ravalli" "richland"
## [817] "rosebud" "sanders" "silver bow"
## [820] "teton" "yellowstone" "adams"
## [823] "antelope" "butler" "cedar"
## [826] "cheyenne" "dawson" "dodge"
## [829] "dundy" "gage" "hall"
## [832] "holt" "howard" "kearney"
## [835] "keith" "lincoln" "merrick"
## [838] "otoe" "platte" "polk"
## [841] "red willow" "saline" "sarpy"
## [844] "saunders" "scotts bluff" "washington"
## [847] "york" "churchill" "clark"
## [850] "douglas" "elko" "humboldt"
## [853] "lincoln" "lyon" "mineral"
## [856] "nye" "washoe" "white pine"
## [859] "belknap" "carroll" "cheshire"
## [862] "coos" "grafton" "merrimack"
## [865] "rockingham" "strafford" "sullivan"
## [868] "bergen" "burlington" "camden"
## [871] "cape may" "cumberland" "essex"
## [874] "gloucester" "hudson" "hunterdon"
## [877] "mercer" "middlesex" "monmouth"
## [880] "ocean" "passaic" "salem"
## [883] "somerset" "sussex" "union"
## [886] "warren" "bernalillo" "chaves"
## [889] "curry" "dona ana" "eddy"
## [892] "grant" "lea" "lincoln"
## [895] "los alamos" "otero" "quay"
## [898] "rio arriba" "sandoval" "san juan"
## [901] "san miguel" "santa fe" "socorro"
## [904] "taos" "torrance" "valencia"
## [907] "allegany" "bronx" "broome"
## [910] "cattaraugus" "chautauqua" "chemung"
## [913] "chenango" "columbia" "delaware"
## [916] "dutchess" "fulton" "genesee"
## [919] "greene" "kings" "livingston"
## [922] "monroe" "montgomery" "niagara"
## [925] "oneida" "ontario" "orange"
## [928] "orleans" "otsego" "putnam"
## [931] "queens" "rensselaer" "richmond"
## [934] "rockland" "saratoga" "schenectady"
## [937] "steuben" "tioga" "ulster"
## [940] "washington" "wayne" "westchester"
## [943] "wyoming" "alamance" "alexander"
## [946] "alleghany" "ashe" "beaufort"
## [949] "brunswick" "burke" "cabarrus"
## [952] "caldwell" "carteret" "catawba"
## [955] "chatham" "cherokee" "clay"
## [958] "cleveland" "columbus" "craven"
## [961] "cumberland" "dare" "davidson"
## [964] "davie" "duplin" "franklin"
## [967] "gaston" "granville" "halifax"
## [970] "harnett" "henderson" "johnston"
## [973] "lee" "lenoir" "lincoln"
## [976] "mcdowell" "madison" "mecklenburg"
## [979] "nash" "new hanover" "onslow"
## [982] "pasquotank" "pender" "person"
## [985] "polk" "randolph" "richmond"
## [988] "rockingham" "rowan" "sampson"
## [991] "stanly" "stokes" "surry"
## [994] "transylvania" "union" "vance"
## [997] "wake" "watauga" "wayne"
## [1000] "wilson" "yadkin" "adams"
## [1003] "barnes" "bottineau" "bowman"
## [1006] "burleigh" "dickey" "dunn"
## [1009] "emmons" "grand forks" "kidder"
## [1012] "la moure" "mckenzie" "mclean"
## [1015] "mercer" "morton" "pembina"
## [1018] "pierce" "ransom" "stark"
## [1021] "stutsman" "williams" "allen"
## [1024] "ashland" "ashtabula" "athens"
## [1027] "auglaize" "belmont" "brown"
## [1030] "butler" "champaign" "clinton"
## [1033] "columbiana" "coshocton" "cuyahoga"
## [1036] "darke" "defiance" "erie"
## [1039] "fulton" "geauga" "greene"
## [1042] "guernsey" "hancock" "hardin"
## [1045] "harrison" "henry" "highland"
## [1048] "hocking" "holmes" "huron"
## [1051] "jefferson" "knox" "lake"
## [1054] "licking" "logan" "lorain"
## [1057] "lucas" "madison" "mahoning"
## [1060] "marion" "medina" "mercer"
## [1063] "miami" "monroe" "montgomery"
## [1066] "morrow" "ottawa" "paulding"
## [1069] "perry" "pike" "portage"
## [1072] "preble" "putnam" "sandusky"
## [1075] "seneca" "shelby" "stark"
## [1078] "summit" "trumbull" "tuscarawas"
## [1081] "union" "van wert" "warren"
## [1084] "washington" "wayne" "williams"
## [1087] "wood" "wyandot" "atoka"
## [1090] "beckham" "bryan" "caddo"
## [1093] "canadian" "carter" "cherokee"
## [1096] "cimarron" "craig" "creek"
## [1099] "custer" "delaware" "garfield"
## [1102] "garvin" "grady" "hughes"
## [1105] "jackson" "kay" "le flore"
## [1108] "logan" "mcclain" "murray"
## [1111] "nowata" "oklahoma" "okmulgee"
## [1114] "osage" "ottawa" "pawnee"
## [1117] "payne" "pittsburg" "pontotoc"
## [1120] "pottawatomie" "rogers" "stephens"
## [1123] "woods" "woodward" "baker"
## [1126] "clackamas" "columbia" "coos"
## [1129] "crook" "curry" "deschutes"
## [1132] "douglas" "harney" "jackson"
## [1135] "josephine" "klamath" "lake"
## [1138] "lane" "lincoln" "linn"
## [1141] "marion" "polk" "tillamook"
## [1144] "umatilla" "wallowa" "wasco"
## [1147] "allegheny" "armstrong" "beaver"
## [1150] "bedford" "berks" "blair"
## [1153] "bradford" "bucks" "butler"
## [1156] "cambria" "cameron" "carbon"
## [1159] "chester" "clarion" "clearfield"
## [1162] "clinton" "columbia" "crawford"
## [1165] "cumberland" "dauphin" "delaware"
## [1168] "elk" "erie" "fayette"
## [1171] "forest" "franklin" "greene"
## [1174] "indiana" "jefferson" "juniata"
## [1177] "lackawanna" "lancaster" "lawrence"
## [1180] "lebanon" "lehigh" "luzerne"
## [1183] "lycoming" "mckean" "mercer"
## [1186] "mifflin" "monroe" "montgomery"
## [1189] "northampton" "northumberland" "perry"
## [1192] "philadelphia" "pike" "potter"
## [1195] "schuylkill" "snyder" "somerset"
## [1198] "sullivan" "susquehanna" "tioga"
## [1201] "union" "venango" "washington"
## [1204] "wayne" "westmoreland" "wyoming"
## [1207] "york" "bristol" "abbeville"
## [1210] "aiken" "barnwell" "beaufort"
## [1213] "berkeley" "cherokee" "chesterfield"
## [1216] "colleton" "dorchester" "georgetown"
## [1219] "greenwood" "horry" "lancaster"
## [1222] "laurens" "lexington" "marlboro"
## [1225] "newberry" "oconee" "orangeburg"
## [1228] "pickens" "richland" "saluda"
## [1231] "spartanburg" "sumter" "union"
## [1234] "williamsburg" "york" "beadle"
## [1237] "brown" "clay" "codington"
## [1240] "davison" "douglas" "grant"
## [1243] "hughes" "lawrence" "mccook"
## [1246] "mcpherson" "miner" "pennington"
## [1249] "turner" "bedford" "bradley"
## [1252] "campbell" "cannon" "carter"
## [1255] "chester" "claiborne" "clay"
## [1258] "cocke" "cumberland" "decatur"
## [1261] "de kalb" "dickson" "dyer"
## [1264] "fayette" "fentress" "franklin"
## [1267] "grainger" "grundy" "hamilton"
## [1270] "hardeman" "hardin" "hawkins"
## [1273] "henderson" "humphreys" "jefferson"
## [1276] "johnson" "lawrence" "loudon"
## [1279] "mcminn" "mcnairy" "macon"
## [1282] "marshall" "maury" "monroe"
## [1285] "montgomery" "overton" "pickett"
## [1288] "putnam" "rhea" "roane"
## [1291] "robertson" "rutherford" "sequatchie"
## [1294] "sevier" "smith" "stewart"
## [1297] "sumner" "trousdale" "union"
## [1300] "warren" "wayne" "white"
## [1303] "wilson" "anderson" "angelina"
## [1306] "aransas" "atascosa" "austin"
## [1309] "bailey" "bastrop" "bee"
## [1312] "bell" "bexar" "brazoria"
## [1315] "brazos" "brewster" "brown"
## [1318] "burnet" "caldwell" "calhoun"
## [1321] "cherokee" "childress" "collin"
## [1324] "colorado" "comal" "comanche"
## [1327] "cooke" "coryell" "crane"
## [1330] "dallam" "dawson" "deaf smith"
## [1333] "denton" "de witt" "dimmit"
## [1336] "duval" "ector" "ellis"
## [1339] "el paso" "erath" "falls"
## [1342] "fort bend" "frio" "gaines"
## [1345] "gonzales" "gray" "grayson"
## [1348] "guadalupe" "hale" "hardin"
## [1351] "harrison" "hays" "henderson"
## [1354] "hockley" "hood" "hopkins"
## [1357] "hunt" "jim wells" "johnson"
## [1360] "kaufman" "kendall" "kimble"
## [1363] "kleberg" "lamar" "liberty"
## [1366] "limestone" "llano" "mcculloch"
## [1369] "mclennan" "matagorda" "maverick"
## [1372] "midland" "milam" "montague"
## [1375] "nacogdoches" "navarro" "nolan"
## [1378] "nueces" "ochiltree" "orange"
## [1381] "palo pinto" "panola" "parker"
## [1384] "randall" "reeves" "rockwall"
## [1387] "rusk" "san patricio" "scurry"
## [1390] "stephens" "tarrant" "taylor"
## [1393] "titus" "tom green" "uvalde"
## [1396] "val verde" "van zandt" "victoria"
## [1399] "walker" "ward" "washington"
## [1402] "webb" "wharton" "wichita"
## [1405] "williamson" "wilson" "winkler"
## [1408] "young" "beaver" "carbon"
## [1411] "garfield" "grand" "iron"
## [1414] "juab" "kane" "sevier"
## [1417] "summit" "uintah" "washington"
## [1420] "weber" "rutland" "windsor"
## [1423] "accomack:main" "accomack:chincoteague" "amherst"
## [1426] "appomattox" "bedford" "botetourt"
## [1429] "brunswick" "charlotte" "chesterfield"
## [1432] "culpeper" "fauquier" "floyd"
## [1435] "fluvanna" "franklin" "frederick"
## [1438] "giles" "gloucester" "grayson"
## [1441] "halifax" "hanover" "henrico"
## [1444] "henry" "james city" "king william"
## [1447] "lancaster" "loudoun" "louisa"
## [1450] "mecklenburg" "suffolk" "new kent"
## [1453] "northampton" "northumberland" "nottoway"
## [1456] "orange" "page" "pittsylvania"
## [1459] "powhatan" "prince edward" "prince william"
## [1462] "roanoke" "rockingham" "shenandoah"
## [1465] "smyth" "spotsylvania" "stafford"
## [1468] "tazewell" "warren" "westmoreland"
## [1471] "wise" "wythe" "york"
## [1474] "hampton" "newport news" "virginia beach"
## [1477] "asotin" "benton" "cowlitz"
## [1480] "douglas" "ferry" "grays harbor"
## [1483] "island" "jefferson" "kittitas"
## [1486] "lewis" "mason" "stevens"
## [1489] "walla walla" "yakima" "barbour"
## [1492] "berkeley" "boone" "braxton"
## [1495] "brooke" "calhoun" "doddridge"
## [1498] "hampshire" "hancock" "hardy"
## [1501] "jackson" "kanawha" "lincoln"
## [1504] "marion" "marshall" "mineral"
## [1507] "nicholas" "pendleton" "pleasants"
## [1510] "putnam" "ritchie" "roane"
## [1513] "summers" "taylor" "tucker"
## [1516] "wetzel" "wirt" "wood"
## [1519] "wyoming" "adams" "ashland"
## [1522] "barron" "brown" "burnett"
## [1525] "chippewa" "columbia" "crawford"
## [1528] "dane" "dodge" "dunn"
## [1531] "eau claire" "fond du lac" "forest"
## [1534] "grant" "green" "green lake"
## [1537] "iowa" "jackson" "jefferson"
## [1540] "kenosha" "lincoln" "manitowoc"
## [1543] "marathon" "marinette" "marquette"
## [1546] "milwaukee" "monroe" "oneida"
## [1549] "ozaukee" "portage" "price"
## [1552] "racine" "rock" "st croix"
## [1555] "sauk" "sheboygan" "vernon"
## [1558] "vilas" "walworth" "washington"
## [1561] "waukesha" "waupaca" "winnebago"
## [1564] "wood" "albany" "big horn"
## [1567] "carbon" "fremont" "laramie"
## [1570] "park"
##
## $Cluster2
## [1] "bibb" "bullock" "conecuh"
## [4] "marion" "santa cruz" "logan"
## [7] "scott" "alameda" "el dorado"
## [10] "glenn" "humboldt" "inyo"
## [13] "marin" "modoc" "orange"
## [16] "placer" "san francisco" "san mateo"
## [19] "santa barbara" "santa clara" "santa cruz"
## [22] "shasta" "sonoma" "sutter"
## [25] "boulder" "clear creek" "la plata"
## [28] "mesa" "routt" "san miguel"
## [31] "hartford" "baker" "broward"
## [34] "charlotte" "collier" "columbia"
## [37] "flagler" "franklin" "gilchrist"
## [40] "hamilton" "hardee" "hillsborough"
## [43] "jefferson" "lee" "leon"
## [46] "manatee" "marion" "martin"
## [49] "monroe" "okaloosa:main" "okaloosa:spit"
## [52] "orange" "palm beach" "pasco"
## [55] "pinellas" "polk" "st johns"
## [58] "sarasota" "seminole" "volusia"
## [61] "walton" "berrien" "camden"
## [64] "chatham" "cherokee" "clay"
## [67] "cobb" "franklin" "glynn"
## [70] "gwinnett" "houston" "irwin"
## [73] "jeff davis" "jenkins" "laurens"
## [76] "miller" "oconee" "paulding"
## [79] "rockdale" "stewart" "tattnall"
## [82] "ware" "blaine" "franklin"
## [85] "gooding" "nez perce" "valley"
## [88] "cass" "effingham" "jasper"
## [91] "pike" "schuyler" "shelby"
## [94] "williamson" "brown" "daviess"
## [97] "dearborn" "floyd" "hamilton"
## [100] "henry" "howard" "madison"
## [103] "marion" "monroe" "newton"
## [106] "parke" "posey" "scott"
## [109] "switzerland" "tipton" "union"
## [112] "vigo" "buena vista" "butler"
## [115] "clayton" "ida" "jasper"
## [118] "sac" "barber" "cowley"
## [121] "decatur" "ellis" "ford"
## [124] "greeley" "johnson" "republic"
## [127] "sumner" "bell" "boone"
## [130] "bourbon" "boyd" "boyle"
## [133] "calloway" "campbell" "carter"
## [136] "christian" "clay" "crittenden"
## [139] "garrard" "graves" "green"
## [142] "greenup" "hardin" "harrison"
## [145] "hart" "henry" "hickman"
## [148] "hopkins" "jefferson" "johnson"
## [151] "kenton" "knox" "laurel"
## [154] "lawrence" "lewis" "mccreary"
## [157] "mason" "menifee" "monroe"
## [160] "montgomery" "ohio" "owen"
## [163] "pike" "powell" "pulaski"
## [166] "rowan" "russell" "scott"
## [169] "simpson" "taylor" "warren"
## [172] "washington" "wayne" "woodford"
## [175] "acadia" "ascension" "bossier"
## [178] "concordia" "east baton rouge" "east feliciana"
## [181] "jefferson" "lafayette" "st tammany"
## [184] "vermilion" "aroostook" "cumberland"
## [187] "franklin" "knox" "penobscot"
## [190] "piscataquis" "waldo" "worcester"
## [193] "barnstable" "berkshire" "essex"
## [196] "middlesex" "nantucket" "norfolk"
## [199] "worcester" "baraga" "crawford"
## [202] "luce" "presque isle" "benton"
## [205] "freeborn" "koochiching" "lyon"
## [208] "mahnomen" "norman" "pennington"
## [211] "st louis" "todd" "traverse"
## [214] "yellow medicine" "calhoun" "jackson"
## [217] "lafayette" "lee" "madison"
## [220] "montgomery" "callaway" "carroll"
## [223] "christian" "dade" "greene"
## [226] "laclede" "marion" "perry"
## [229] "taney" "washington" "chouteau"
## [232] "deer lodge" "flathead" "gallatin"
## [235] "missoula" "park" "valley"
## [238] "yellowstone national" "custer" "lancaster"
## [241] "nemaha" "nuckolls" "richardson"
## [244] "thurston" "carson city" "hillsborough"
## [247] "atlantic" "morris" "mckinley"
## [250] "union" "erie" "nassau"
## [253] "suffolk" "yates" "avery"
## [256] "buncombe" "currituck:knotts" "currituck:main"
## [259] "currituck:spit" "graham" "greene"
## [262] "guilford" "macon" "perquimans"
## [265] "wilkes" "yancey" "cass"
## [268] "hettinger" "mcintosh" "mountrail"
## [271] "ramsey" "richland" "rolette"
## [274] "walsh" "adams" "carroll"
## [277] "clark" "clermont" "crawford"
## [280] "delaware" "fairfield" "fayette"
## [283] "franklin" "gallia" "hamilton"
## [286] "jackson" "lawrence" "meigs"
## [289] "morgan" "muskingum" "noble"
## [292] "pickaway" "richland" "ross"
## [295] "scioto" "choctaw" "cleveland"
## [298] "comanche" "greer" "mccurtain"
## [301] "noble" "seminole" "texas"
## [304] "tulsa" "clatsop" "hood river"
## [307] "jefferson" "multnomah" "washington"
## [310] "yamhill" "centre" "kent"
## [313] "newport" "providence" "washington"
## [316] "anderson" "fairfield" "greenville"
## [319] "lee" "custer" "meade"
## [322] "anderson" "bledsoe" "blount"
## [325] "carroll" "coffee" "davidson"
## [328] "gibson" "greene" "hamblen"
## [331] "haywood" "henry" "knox"
## [334] "lauderdale" "lewis" "lincoln"
## [337] "marion" "morgan" "obion"
## [340] "shelby" "sullivan" "unicoi"
## [343] "washington" "williamson" "andrews"
## [346] "bosque" "bowie" "brooks"
## [349] "cameron" "camp" "dallas"
## [352] "eastland" "galveston:main" "galveston:spit"
## [355] "gillespie" "gregg" "hardeman"
## [358] "harris" "hidalgo" "hill"
## [361] "howard" "jackson" "jasper"
## [364] "jefferson" "kerr" "lamb"
## [367] "lavaca" "madison" "montgomery"
## [370] "pecos" "robertson" "shelby"
## [373] "somervell" "travis" "waller"
## [376] "wheeler" "wilbarger" "cache"
## [379] "davis" "duchesne" "emery"
## [382] "millard" "salt lake" "san juan"
## [385] "tooele" "utah" "wasatch"
## [388] "bennington" "chittenden" "grand isle"
## [391] "windham" "albemarle" "amelia"
## [394] "campbell" "carroll" "dickenson"
## [397] "dinwiddie" "fairfax" "goochland"
## [400] "montgomery" "nelson" "patrick"
## [403] "pulaski" "richmond" "russell"
## [406] "sussex" "washington" "chelan"
## [409] "clallam" "clark" "franklin"
## [412] "grant" "king" "kitsap"
## [415] "okanogan" "pacific" "pend oreille"
## [418] "pierce:main" "pierce:penrose" "skagit"
## [421] "skamania" "snohomish" "spokane"
## [424] "thurston" "whatcom" "whitman"
## [427] "cabell" "clay" "fayette"
## [430] "gilmer" "grant" "greenbrier"
## [433] "harrison" "lewis" "logan"
## [436] "mcdowell" "mason" "mercer"
## [439] "mingo" "monongalia" "morgan"
## [442] "ohio" "pocahontas" "raleigh"
## [445] "randolph" "upshur" "wayne"
## [448] "buffalo" "douglas" "iron"
## [451] "kewaunee" "la crosse" "oconto"
## [454] "outagamie" "pepin" "pierce"
## [457] "shawano" "taylor" "trempealeau"
## [460] "campbell" "converse" "goshen"
## [463] "natrona" "sheridan" "sublette"
## [466] "teton"
##
## $Cluster4
## [1] "cleburne" "de kalb" "escambia"
## [4] "geneva" "jackson" "lamar"
## [7] "lawrence" "randolph" "wilcox"
## [10] "winston" "apache" "arkansas"
## [13] "ashley" "carroll" "clay"
## [16] "conway" "crawford" "cross"
## [19] "desha" "fulton" "grant"
## [22] "johnson" "lincoln" "marion"
## [25] "miller" "ouachita" "sevier"
## [28] "van buren" "bent" "elbert"
## [31] "rio grande" "jackson" "lafayette"
## [34] "madison" "banks" "ben hill"
## [37] "bryan" "candler" "charlton"
## [40] "clinch" "early" "elbert"
## [43] "fannin" "grady" "jefferson"
## [46] "jones" "lee" "lumpkin"
## [49] "macon" "meriwether" "mitchell"
## [52] "morgan" "pierce" "pulaski"
## [55] "putnam" "seminole" "upson"
## [58] "white" "elmore" "lemhi"
## [61] "adams" "carroll" "clinton"
## [64] "crawford" "mcdonough" "massac"
## [67] "piatt" "benton" "adair"
## [70] "appanoose" "boone" "bremer"
## [73] "carroll" "clay" "crawford"
## [76] "davis" "dickinson" "greene"
## [79] "hamilton" "henry" "humboldt"
## [82] "jackson" "jefferson" "jones"
## [85] "kossuth" "lee" "louisa"
## [88] "lucas" "madison" "marion"
## [91] "monona" "muscatine" "page"
## [94] "plymouth" "poweshiek" "ringgold"
## [97] "shelby" "sioux" "story"
## [100] "union" "warren" "washington"
## [103] "winnebago" "winneshiek" "woodbury"
## [106] "bourbon" "gray" "mcpherson"
## [109] "nemaha" "norton" "pawnee"
## [112] "rice" "trego" "casey"
## [115] "lyon" "mclean" "metcalfe"
## [118] "la salle" "st john the baptist" "union"
## [121] "vernon" "west feliciana" "barry"
## [124] "delta" "missaukee" "tuscola"
## [127] "chippewa" "chisago" "fillmore"
## [130] "kittson" "morrison" "murray"
## [133] "pine" "pipestone" "roseau"
## [136] "sibley" "clarke" "coahoma"
## [139] "covington" "humphreys" "leake"
## [142] "marshall" "walthall" "bates"
## [145] "benton" "clinton" "cooper"
## [148] "dallas" "douglas" "grundy"
## [151] "harrison" "howell" "mercer"
## [154] "new madrid" "newton" "nodaway"
## [157] "oregon" "pike" "ste genevieve"
## [160] "stoddard" "texas" "beaverhead"
## [163] "phillips" "cass" "dakota"
## [166] "dawes" "dixon" "garden"
## [169] "hamilton" "jefferson" "wayne"
## [172] "luna" "cayuga" "cortland"
## [175] "herkimer" "madison" "oswego"
## [178] "schuyler" "anson" "bladen"
## [181] "chowan" "edgecombe" "hertford"
## [184] "hoke" "jackson" "martin"
## [187] "mitchell" "pamlico" "robeson"
## [190] "rutherford" "scotland" "washington"
## [193] "benson" "ward" "haskell"
## [196] "mcintosh" "marshall" "mayes"
## [199] "wagoner" "washington" "malheur"
## [202] "union" "huntingdon" "warren"
## [205] "allendale" "bamberg" "chester"
## [208] "clarendon" "darlington" "dillon"
## [211] "edgefield" "hampton" "kershaw"
## [214] "marion" "brookings" "edmunds"
## [217] "fall river" "gregory" "hutchinson"
## [220] "minnehaha" "tripp" "walworth"
## [223] "yankton" "benton" "cheatham"
## [226] "giles" "hancock" "hickman"
## [229] "houston" "tipton" "weakley"
## [232] "fannin" "hutchinson" "jones"
## [235] "karnes" "medina" "moore"
## [238] "polk" "runnels" "starr"
## [241] "terry" "upshur" "willacy"
## [244] "morgan" "franklin" "alleghany"
## [247] "essex" "isle of wight" "king george"
## [250] "preston" "calumet" "clark"
## [253] "door" "juneau" "langlade"
## [256] "polk" "rusk" "sawyer"
## [259] "uinta" "washakie"
##
## $Cluster527
## [1] "covington" "monroe" "pinal" "crittenden" "sharp"
## [6] "mono" "ouray" "dixie" "dodge" "emanuel"
## [11] "monroe" "screven" "turner" "boundary" "dallas"
## [16] "harrison" "lyon" "mahaska" "montgomery" "hamilton"
## [21] "caldwell" "fulton" "allen" "catahoula" "gladwin"
## [26] "schoolcraft" "cottonwood" "kanabec" "pope" "stevens"
## [31] "itawamba" "newton" "perry" "scott" "stone"
## [36] "tishomingo" "barry" "henry" "ozark" "fergus"
## [41] "brown" "cuming" "harlan" "seward" "haywood"
## [46] "iredell" "montgomery" "warren" "kiowa" "muskogee"
## [51] "sequoyah" "adams" "jasper" "lake" "marshall"
## [56] "crockett" "grimes" "wood" "box elder" "sanpete"
## [61] "washington" "caroline" "lee" "adams" "jefferson"
## [66] "johnson" "platte" "sweetwater" "weston"
##
## $Cluster125
## [1] "little river" "poinsett"
## [3] "yell" "colquitt"
## [5] "thomas" "tift"
## [7] "washington" "calhoun"
## [9] "grundy" "iowa"
## [11] "mills" "obrien"
## [13] "tama" "brown"
## [15] "cheyenne" "marshall"
## [17] "miami" "washington"
## [19] "richland" "saline"
## [21] "box butte" "cibola"
## [23] "colfax" "clinton"
## [25] "franklin" "jefferson"
## [27] "lewis" "st lawrence"
## [29] "adair" "lincoln"
## [31] "haakon" "lincoln"
## [33] "roberts" "union"
## [35] "cass" "lampasas"
## [37] "wise" "san juan:lopez island"
## [39] "san juan:orcas island" "san juan:san juan island"
##
## $Cluster30
## [1] "alachua" "wayne" "dickinson" "neosho" "clark"
## [6] "fayette" "suffolk" "lewis" "toole" "durham"
## [11] "bland" "webster" "hot springs"
##
## $Cluster606
## [1] "emmet" "lawrence" "macon" "phelps" "schoharie" "caledonia"
## [7] "richland" "waushara" "lincoln"
##
## $Cluster540
## [1] "bureau" "johnson" "perry" "orleans" "olmsted" "renville"
##
## $Cluster598
## [1] "madison" "stone" "douglas" "de soto" "jackson" "winn"
##
## $Cluster545
## [1] "franklin" "eagle" "muscogee" "madison" "smith"
##
## $Cluster595
## [1] "pierce" "orange" "kingfisher" "montour"
##
## $Cluster490
## [1] "roosevelt" "knox"
##
## $Cluster597
## [1] "payette" "woodford"
##
## $Cluster524
## [1] "roosevelt"
##
## $Cluster608
## [1] "carlisle"