rm(list=ls())Propensity Score Matching in R (My first post in blogger)
My first post in blogger is about Propensity Score Matching (PSM) in R. In this post I will introduce the R packages MatchIt and Zelig. The first one is devoted to perform different PSM algorithms and the other one is used in order to estimate the average treatment effect (ATE) and the effect of the treatment on the treated (ATT). First of all, I will simulate a population where some individuals receive the treatment, and the remaining ones do not.
library(MatchIt)# Zelig is no longer available on CRAN; the equivalent analyses below use lm().N <- 1000x1 <- round(rnorm(N,20,4))x2 <- round(rnorm(N,80,10))f <- 1 + 1*x1 - 0.28*x2p <- exp(f)/(1+exp(f))
plot(p)
z <- rbinom(N,1, p)
table(z)| 0 | 1 |
|---|---|
| 634 | 366 |
y <- rep(0, times=N)# Different values for y over z# The mean difference for y is 5000y[z == 1] <- 9000 + 2*x1[z == 1] + 0.5*x2[z == 1]y[z == 0] <- 4000 + 2*x1[z == 0] + 0.5*x2[z == 0]y <- jitter(y, amount=1000,factor=2)Data <- data.frame(y=y, x1=x1, x2=x2, z)# The treatment populationTreats <- subset(Data, z == 1)colMeans(Treats) y x1 x2 z
9120.86681 22.78754 74.20397 1.00000 # The control populationControl <- subset(Data, z == 0)
colMeans(Control) y x1 x2 z
4091.96471 17.99691 83.44359 0.00000 # Computing the real effect of the treatmentmodel <- lm(y ~ z + x1 + x2,data=Data)Effect <- model$coeff[2]
Effect z
5026.857 Then I will run a logistic regression in order to estimate the propensity scores. That is the probability of receiving the treatment.
# The propensity scoresps.model <- glm(z ~ x1 + x2,family = binomial(link = "logit"),data = Data)plot(ps.model$fitted)
summary(ps.model)
Call:
glm(formula = z ~ x1 + x2, family = binomial(link = "logit"),
data = Data)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.28473 1.07836 1.191 0.234
x1 0.99640 0.07476 13.328 <2e-16 ***
x2 -0.28420 0.02246 -12.651 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 1298.57 on 999 degrees of freedom
Residual deviance: 470.03 on 997 degrees of freedom
AIC: 476.03
Number of Fisher Scoring iterations: 7Data$ps <- ps.model$fitted
table(Data$z)
0 1
647 353 hist(Data$ps[z==1])
hist(Data$ps[z==0])
After that, one may use different matching algorithms. Exact matching is a technique used to match individuals based on the exact values of covariates.
# Exact matchingm1.ps <- matchit(z ~ x1 + x2, method = "exact", data = Data)summary(m1.ps, covariates = T)
Call:
matchit(formula = z ~ x1 + x2, data = Data, method = "exact")
Summary of Balance for All Data:
Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean eCDF Max
x1 22.7875 17.9969 1.5648 0.8264 0.1993 0.5562
x2 74.2040 83.4436 -0.9872 1.0623 0.1589 0.3919
Summary of Balance for Matched Data:
Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean eCDF Max
x1 20.9794 20.9794 0 0.9907 0 0
x2 77.9897 77.9897 0 0.9907 0 0
Std. Pair Dist.
x1 0
x2 0
Sample Sizes:
Control Treated
All 647. 353
Matched (ESS) 51.16 97
Matched 95. 97
Unmatched 552. 256
Discarded 0. 0m1.data <- match.data(m1.ps)Nearest neighbour matching (NNM) is an algorithm that matches individuals with controls (it could be more two or more controls per treated unit) one by one based on a distance.
#Nearest neighbor matchingm3.ps <- matchit(z ~ x1 + x2, method = "nearest", ratio = 1, data = Data)summary(m3.ps, covariates = T)
Call:
matchit(formula = z ~ x1 + x2, data = Data, method = "nearest",
ratio = 1)
Summary of Balance for All Data:
Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
distance 0.7919 0.1135 2.6166 1.6655 0.4027
x1 22.7875 17.9969 1.5648 0.8264 0.1993
x2 74.2040 83.4436 -0.9872 1.0623 0.1589
eCDF Max
distance 0.7901
x1 0.5562
x2 0.3919
Summary of Balance for Matched Data:
Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
distance 0.7919 0.2063 2.2586 1.2210 0.2663
x1 22.7875 19.7309 0.9984 1.3338 0.1274
x2 74.2040 80.6997 -0.6940 1.1994 0.1120
eCDF Max Std. Pair Dist.
distance 0.6969 2.2586
x1 0.4193 1.2020
x2 0.2861 1.1850
Sample Sizes:
Control Treated
All 647 353
Matched 353 353
Unmatched 294 0
Discarded 0 0plot(m3.ps)
plot(m3.ps, type="jitter")
To identify the units, use first mouse button; to stop, use second.plot(m3.ps, type="hist")
m3.data <- match.data(m3.ps)m3.ps$match.matrix [,1]
3 "687"
5 "316"
10 "101"
11 "623"
16 "252"
17 "274"
18 "389"
21 "845"
23 "592"
25 "997"
29 "629"
31 "614"
33 "979"
35 "731"
47 "481"
51 "591"
55 "908"
60 "125"
61 "423"
63 "750"
64 "181"
66 "710"
67 "878"
73 "691"
74 "972"
75 "581"
77 "677"
79 "529"
81 "888"
84 "802"
85 "19"
88 "365"
89 "327"
90 "595"
92 "701"
96 "456"
97 "363"
99 "443"
100 "850"
109 "478"
112 "627"
113 "510"
114 "530"
115 "319"
116 "108"
117 "607"
118 "727"
119 "909"
120 "500"
123 "298"
126 "337"
130 "276"
139 "457"
140 "106"
142 "398"
154 "630"
155 "72"
156 "603"
163 "187"
164 "590"
166 "401"
167 "95"
168 "557"
174 "650"
177 "579"
184 "735"
185 "386"
189 "986"
192 "488"
194 "572"
196 "157"
198 "876"
205 "970"
213 "982"
215 "268"
216 "915"
217 "366"
219 "358"
220 "856"
221 "822"
222 "195"
223 "233"
227 "434"
230 "995"
231 "279"
236 "545"
237 "188"
238 "757"
241 "50"
242 "618"
246 "823"
247 "361"
249 "773"
250 "475"
255 "248"
256 "98"
269 "463"
271 "874"
278 "507"
284 "415"
286 "391"
289 "416"
290 "28"
291 "576"
293 "209"
297 "345"
304 "452"
305 "54"
306 "924"
309 "333"
310 "105"
311 "9"
313 "172"
315 "936"
318 "699"
321 "159"
324 "904"
343 "641"
347 "129"
348 "368"
351 "906"
354 "957"
357 "431"
359 "883"
362 "718"
364 "424"
367 "462"
369 "245"
373 "76"
378 "679"
379 "751"
382 "153"
387 "604"
392 "534"
394 "913"
395 "490"
399 "978"
402 "825"
403 "160"
405 "826"
406 "244"
409 "325"
411 "445"
413 "839"
414 "593"
421 "797"
422 "542"
427 "503"
428 "208"
429 "183"
430 "270"
435 "326"
436 "151"
437 "994"
438 "146"
441 "330"
444 "133"
446 "955"
447 "835"
450 "334"
455 "36"
461 "568"
464 "111"
465 "763"
466 "285"
468 "776"
470 "383"
471 "528"
472 "8"
473 "388"
477 "301"
480 "990"
483 "320"
484 "296"
485 "884"
487 "384"
491 "26"
494 "175"
504 "454"
506 "143"
508 "624"
509 "141"
516 "719"
517 "857"
521 "818"
523 "102"
525 "846"
527 "65"
537 "752"
538 "127"
540 "170"
543 "329"
544 "27"
548 "968"
550 "779"
553 "169"
558 "738"
559 "39"
560 "775"
561 "355"
569 "68"
570 "493"
577 "94"
578 "193"
582 "197"
584 "786"
588 "774"
594 "754"
597 "336"
598 "684"
600 "328"
601 "815"
605 "791"
606 "397"
609 "721"
610 "535"
611 "32"
615 "121"
619 "573"
620 "149"
628 "70"
631 "229"
635 "621"
636 "199"
638 "661"
640 "840"
643 "659"
644 "877"
645 "235"
647 "13"
652 "349"
654 "780"
655 "862"
657 "486"
658 "404"
660 "58"
662 "520"
663 "283"
664 "182"
665 "927"
666 "695"
668 "335"
669 "844"
671 "150"
674 "206"
675 "949"
676 "272"
680 "41"
682 "967"
683 "795"
685 "939"
686 "962"
689 "400"
692 "863"
693 "905"
694 "810"
700 "69"
715 "225"
716 "396"
717 "812"
723 "602"
730 "801"
733 "998"
734 "356"
739 "267"
741 "549"
745 "107"
746 "965"
747 "743"
748 "40"
753 "809"
758 "940"
759 "744"
761 "59"
769 "469"
771 "253"
777 "616"
778 "678"
781 "617"
783 "161"
787 "519"
792 "410"
796 "985"
799 "374"
803 "372"
807 "891"
811 "260"
814 "993"
817 "377"
819 "78"
821 "224"
824 "203"
827 "867"
832 "322"
834 "138"
836 "533"
837 "875"
838 "346"
842 "46"
849 "622"
851 "782"
852 "926"
853 "847"
854 "152"
855 "869"
858 "370"
859 "190"
860 "790"
864 "898"
865 "564"
866 "724"
868 "755"
870 "281"
872 "331"
873 "670"
885 "999"
887 "562"
892 "302"
894 "637"
897 "264"
899 "765"
900 "265"
902 "612"
903 "459"
911 "907"
920 "344"
922 "353"
928 "2"
929 "554"
930 "134"
931 "261"
932 "62"
938 "262"
941 "793"
943 "749"
944 "482"
945 "698"
946 "536"
948 "412"
950 "890"
951 "433"
961 "340"
963 "259"
969 "43"
973 "772"
975 "639"
976 "228"
977 "186"
984 "93"
989 "44"
992 "385"
996 "12"
1000 "460"Pairs <- cbind(Data[row.names(m3.ps$match.matrix),], Data[m3.ps$match.matrix,])Pairs y x1 x2 z ps y x1 x2 z ps
3 10063.205 23 76 1 0.931027491 3160.657 21 86 0 0.096892912
5 9705.856 26 70 1 0.999322883 4548.612 22 80 0 0.615235752
10 8759.264 20 73 1 0.614433803 3306.336 20 87 0 0.028949215
11 8789.761 20 78 1 0.277876327 4613.367 19 86 0 0.014414046
16 8433.025 23 69 1 0.989968995 3257.432 21 81 0 0.307629262
17 8823.235 26 72 1 0.998805205 3735.166 19 70 0 0.579858911
18 9172.051 19 76 1 0.200525046 3964.997 18 83 0 0.012507663
21 8189.328 28 74 1 0.999712207 3459.289 20 72 0 0.679220102
23 8248.042 23 85 1 0.511189473 3418.535 20 88 0 0.021944768
25 8988.314 24 80 1 0.921447105 4065.890 17 72 0 0.096301872
29 8276.923 22 76 1 0.832880575 5052.542 14 63 0 0.064743360
31 9489.524 20 78 1 0.277876327 3421.752 19 86 0 0.014414046
33 8236.849 27 68 1 0.999858319 3452.033 22 78 0 0.738421072
35 9715.245 23 58 1 0.999555543 5082.799 28 101 0 0.617637828
47 8581.192 20 69 1 0.832408685 3654.491 17 74 0 0.056925008
51 8121.518 23 82 1 0.710408842 3588.038 17 75 0 0.043454549
55 9021.084 20 72 1 0.679220102 3362.499 18 79 0 0.037978361
60 8619.468 20 70 1 0.788947598 4420.698 18 78 0 0.049839708
61 8516.199 26 88 1 0.898562905 3795.357 20 83 0 0.085018977
63 9327.283 19 65 1 0.851093425 5049.109 18 77 0 0.065154678
64 8694.914 22 74 1 0.897943907 3969.973 20 83 0 0.085018977
66 9850.745 22 85 1 0.278556361 4430.712 21 93 0 0.014462234
67 9595.795 19 57 1 0.982308420 3690.397 20 79 0 0.224571440
73 9816.380 24 74 1 0.984743618 4447.631 18 71 0 0.277197315
74 8472.126 19 78 1 0.124398661 4657.404 17 80 0 0.010850639
75 9324.843 22 78 1 0.738421072 3173.394 21 89 0 0.043736943
77 8703.039 24 75 1 0.979829980 4142.515 25 97 0 0.202158682
79 8760.662 26 63 1 0.999907333 4076.043 24 85 0 0.739074650
81 9699.242 19 73 1 0.370421056 3322.930 22 96 0 0.016661501
84 9117.942 31 91 1 0.998186622 4561.407 18 67 0 0.544482128
85 9459.019 22 70 1 0.964817558 3459.873 19 77 0 0.158795476
88 9524.842 20 75 1 0.474418575 3255.879 16 74 0 0.021799870
89 8576.767 30 105 1 0.791753158 3670.894 20 85 0 0.050000319
90 9108.723 19 70 1 0.579858911 3685.462 21 91 0 0.025252745
92 8301.088 24 85 1 0.739074650 3657.659 16 71 0 0.049679585
96 8781.966 22 65 1 0.991271548 3382.339 23 88 0 0.308351017
97 8190.420 25 83 1 0.931244634 4106.513 23 93 0 0.097189644
99 8350.664 31 92 1 0.997591998 4347.073 20 75 0 0.474418575
100 8893.035 21 74 1 0.764621449 4715.693 16 71 0 0.049679585
109 8710.371 23 76 1 0.931027491 3429.858 21 86 0 0.096892912
112 9323.273 21 77 1 0.580683696 3813.462 21 91 0 0.025252745
113 8983.719 24 82 1 0.869184755 4608.771 17 73 0 0.074247052
114 9217.271 20 81 1 0.140925361 3430.843 19 87 0 0.010887046
115 8134.586 21 79 1 0.439590841 4135.298 21 92 0 0.019125067
116 8270.879 24 83 1 0.833351401 3725.726 16 70 0 0.064948716
117 9256.702 19 71 1 0.509496988 4977.148 18 81 0 0.021872202
118 10052.430 20 76 1 0.404531992 4893.147 19 85 0 0.019061644
119 8729.021 20 70 1 0.788947598 3582.514 16 71 0 0.049679585
120 8856.850 22 76 1 0.832880575 4709.535 23 95 0 0.057472865
123 9688.339 21 76 1 0.647891157 3852.608 21 90 0 0.033277126
126 9861.592 17 58 1 0.850663742 4306.987 16 70 0 0.064948716
130 8684.901 30 74 1 0.999960760 3766.032 24 84 0 0.790073132
139 9704.264 21 71 1 0.883992214 4396.007 21 87 0 0.074713924
140 8536.793 25 84 1 0.910663678 3291.898 15 65 0 0.096007562
142 8156.267 21 67 1 0.959596552 4107.493 18 74 0 0.140515881
154 9310.721 19 65 1 0.851093425 4115.816 18 77 0 0.065154678
155 8139.426 29 85 1 0.997583850 4531.086 20 75 0 0.474418575
156 8773.188 21 71 1 0.883992214 3692.977 19 80 0 0.074480152
163 9368.322 29 68 1 0.999980685 3831.602 27 93 0 0.852801965
164 9036.764 26 84 1 0.965046737 4587.618 21 84 0 0.159248355
166 8996.454 22 68 1 0.979762945 3914.979 23 90 0 0.201613035
167 9553.791 23 69 1 0.989968995 3743.188 21 81 0 0.307629262
168 8230.864 22 84 1 0.339072068 3729.481 20 89 0 0.016606109
174 9799.736 18 69 1 0.403716516 3904.217 19 85 0 0.019061644
177 8315.752 27 77 1 0.998174321 3474.498 25 92 0 0.512035622
184 8937.535 26 93 1 0.681429563 4308.630 20 86 0 0.038102281
185 9649.252 30 96 1 0.980029784 3941.531 18 72 0 0.223982281
189 10036.312 25 77 1 0.986759911 3364.974 22 85 0 0.278556361
192 9919.054 22 71 1 0.953787482 3118.172 19 78 0 0.124398661
194 9054.288 18 50 1 0.993372179 4521.036 21 80 0 0.371211147
196 8119.149 21 76 1 0.647891157 4302.487 21 90 0 0.033277126
198 9408.028 22 72 1 0.939516140 3424.183 27 107 0 0.097785543
205 9027.826 19 57 1 0.982308420 4744.342 18 72 0 0.223982281
213 9896.261 23 66 1 0.995699002 3832.287 18 69 0 0.403716516
215 9404.786 25 58 1 0.999939391 4772.660 19 67 0 0.764011430
216 9152.874 18 68 1 0.473574259 4088.401 23 99 0 0.019188698
217 9070.869 21 78 1 0.510343260 4726.676 20 88 0 0.021944768
219 9536.295 29 77 1 0.999750742 3688.849 21 75 0 0.709711664
220 9222.398 28 76 1 0.999492028 5083.920 24 87 0 0.616037075
221 9955.165 23 83 1 0.648663308 3763.615 21 90 0 0.033277126
222 8455.751 18 65 1 0.678481820 3566.131 18 79 0 0.037978361
223 8476.346 24 77 1 0.964932328 3843.996 21 84 0 0.159248355
227 8190.552 24 85 1 0.739074650 3439.161 16 71 0 0.049679585
230 8500.147 23 69 1 0.989968995 4076.849 19 74 0 0.306908446
231 8292.887 18 70 1 0.337555917 4496.564 20 89 0 0.016606109
236 8155.931 28 75 1 0.999617645 4943.073 21 76 0 0.647891157
237 8361.284 22 69 1 0.973288688 5060.458 20 80 0 0.178957916
238 8964.878 25 79 1 0.976859852 3195.795 26 101 0 0.180455509
241 8612.428 22 71 1 0.953787482 4816.215 19 78 0 0.124398661
242 8626.602 22 55 1 0.999486844 3285.766 22 80 0 0.615235752
246 9796.252 22 70 1 0.964817558 4764.508 17 70 0 0.158343642
247 10064.063 23 82 1 0.710408842 3148.260 17 75 0 0.043454549
249 9443.321 23 69 1 0.989968995 5042.336 19 74 0 0.306908446
250 8281.874 22 82 1 0.475263037 4821.783 18 81 0 0.021872202
255 9645.268 26 76 1 0.996285458 3637.976 20 76 0 0.404531992
256 8505.833 21 78 1 0.510343260 4724.054 20 88 0 0.021944768
269 9991.929 23 76 1 0.931027491 3119.447 21 86 0 0.096892912
271 10052.958 25 85 1 0.884684965 3170.933 21 87 0 0.074713924
278 9414.422 21 82 1 0.250597545 4779.018 17 79 0 0.014366017
284 8439.111 21 50 1 0.999664324 4615.027 25 90 0 0.649434682
286 10052.207 25 80 1 0.969485761 3913.853 18 73 0 0.178460883
289 8605.068 22 82 1 0.475263037 4384.436 18 81 0 0.021872202
290 8518.714 19 72 1 0.438756765 4939.092 21 92 0 0.019125067
291 9652.115 23 75 1 0.947189168 4466.576 20 82 0 0.109893723
293 8206.735 20 75 1 0.474418575 3260.781 16 74 0 0.021799870
297 9768.883 19 81 1 0.057107080 4177.373 22 98 0 0.009506231
304 9926.004 21 66 1 0.969284761 4076.939 16 66 0 0.177964931
305 8355.090 24 94 1 0.179955228 4746.976 18 83 0 0.012507663
306 10043.549 23 77 1 0.910387791 4634.916 22 90 0 0.085282779
309 9232.894 24 86 1 0.680693976 3604.583 20 86 0 0.038102281
310 8609.751 27 69 1 0.999811757 3529.923 23 82 0 0.710408842
311 9070.206 21 80 1 0.371211147 3385.246 17 78 0 0.018998427
313 9384.540 22 74 1 0.897943907 3312.147 20 83 0 0.085018977
315 10005.416 22 80 1 0.615235752 3812.498 20 87 0 0.028949215
318 8415.244 22 80 1 0.615235752 4267.990 20 87 0 0.028949215
321 9261.289 25 77 1 0.986759911 4880.289 22 85 0 0.278556361
324 8160.594 21 78 1 0.510343260 4185.908 18 81 0 0.021872202
343 9668.226 24 65 1 0.998801157 3473.282 17 63 0 0.579033680
347 9321.374 20 67 1 0.897633155 3237.670 18 76 0 0.084755914
348 8914.603 23 74 1 0.959727643 4706.045 20 81 0 0.140925361
351 8119.209 19 73 1 0.370421056 5001.261 20 89 0 0.016606109
354 9389.141 22 76 1 0.832880575 4780.139 21 88 0 0.057289698
357 9046.107 24 82 1 0.869184755 4194.928 17 73 0 0.074247052
359 9942.282 21 53 1 0.999212942 4242.838 20 73 0 0.614433803
362 8998.446 23 65 1 0.996759557 4572.975 19 72 0 0.438756765
364 8118.007 23 83 1 0.648663308 4546.985 21 90 0 0.033277126
367 9655.120 22 73 1 0.921201637 4618.401 17 72 0 0.096301872
369 8536.379 30 86 1 0.998813260 3324.102 21 77 0 0.580683696
373 8285.052 22 77 1 0.789510917 3660.493 20 85 0 0.050000319
378 9507.320 22 77 1 0.789510917 4662.885 18 78 0 0.049839708
379 8349.869 24 72 1 0.991300799 4337.673 20 77 0 0.338313577
382 9678.451 28 91 1 0.965160787 4949.419 16 66 0 0.177964931
387 8202.671 18 57 1 0.953488036 4369.485 22 89 0 0.110225411
392 9826.312 21 64 1 0.982367175 4693.392 24 93 0 0.225753057
394 9122.539 20 68 1 0.868412737 4712.556 20 84 0 0.065361248
395 8441.566 24 62 1 0.999488578 3427.332 24 87 0 0.616037075
399 9896.750 23 66 1 0.995699002 3653.354 18 69 0 0.403716516
402 9533.508 19 74 1 0.306908446 3917.424 16 75 0 0.016495867
403 8974.255 26 95 1 0.547839674 3589.605 19 84 0 0.025169522
405 8942.022 21 69 1 0.930809713 3190.460 19 79 0 0.096596988
406 8747.899 21 70 1 0.910111136 4826.418 22 90 0 0.085282779
409 9691.459 21 68 1 0.947019516 3622.643 20 82 0 0.109893723
411 8480.075 26 102 1 0.142159789 4958.331 14 69 0 0.012424285
413 8091.298 21 83 1 0.201068490 4627.313 20 90 0 0.012549558
414 8308.879 20 63 1 0.964702426 4394.633 22 88 0 0.141335839
421 9261.591 28 62 1 0.999990492 4546.530 23 75 0 0.947189168
422 8701.330 23 84 1 0.581508030 4500.648 16 73 0 0.028759428
427 9316.743 20 83 1 0.085018977 3830.132 17 80 0 0.010850639
428 8290.262 23 84 1 0.581508030 3559.140 16 73 0 0.028759428
429 8270.488 28 78 1 0.999103552 3195.390 18 66 0 0.613631233
430 9420.592 20 74 1 0.545321906 3710.020 17 77 0 0.025086566
435 9825.739 25 90 1 0.649434682 3340.577 16 72 0 0.037854828
436 9742.111 23 88 1 0.308351017 3751.969 20 89 0 0.016606109
437 8161.450 26 79 1 0.991329954 3786.049 20 77 0 0.338313577
438 8454.059 24 67 1 0.997885448 3087.984 19 71 0 0.509496988
441 8825.902 25 80 1 0.969485761 3645.211 18 73 0 0.178460883
444 8739.745 21 63 1 0.986671133 4885.968 20 78 0 0.277876327
446 9319.413 24 71 1 0.993438732 3263.481 21 80 0 0.371211147
447 8343.560 25 86 1 0.852376356 3513.789 20 84 0 0.065361248
450 9411.461 15 61 1 0.248694489 4780.506 22 97 0 0.012591592
455 9586.175 21 65 1 0.976706259 3791.226 22 87 0 0.179456031
461 9748.195 25 78 1 0.982484112 3795.292 19 75 0 0.249962118
464 9414.435 19 56 1 0.986626524 3663.815 20 78 0 0.277876327
465 9081.892 18 69 1 0.403716516 3801.045 17 78 0 0.018998427
466 9830.065 26 88 1 0.898562905 4231.355 20 83 0 0.085018977
468 9725.604 24 78 1 0.953936515 3342.331 19 78 0 0.124398661
470 9497.040 23 83 1 0.648663308 3861.137 21 90 0 0.033277126
471 10065.244 25 93 1 0.441260013 3367.179 21 92 0 0.019125067
472 8892.571 22 79 1 0.679957488 4289.723 20 86 0 0.038102281
473 8595.018 23 76 1 0.931027491 4905.844 21 86 0 0.096892912
477 9980.913 21 79 1 0.439590841 4531.763 21 92 0 0.019125067
480 9759.734 23 65 1 0.996759557 4270.356 22 83 0 0.405347997
483 9931.586 25 80 1 0.969485761 3535.805 18 73 0 0.178460883
484 8936.788 22 82 1 0.475263037 4580.260 18 81 0 0.021872202
485 8369.125 19 73 1 0.370421056 3623.627 20 89 0 0.016606109
487 9583.058 22 80 1 0.615235752 4353.505 20 87 0 0.028949215
491 9130.948 25 90 1 0.649434682 4789.753 16 72 0 0.037854828
494 8685.271 18 69 1 0.403716516 4918.379 17 78 0 0.018998427
504 9653.641 20 69 1 0.832408685 4808.642 17 74 0 0.056925008
506 9843.296 20 75 1 0.474418575 3722.363 16 74 0 0.021799870
508 8113.734 23 80 1 0.812414196 4093.411 15 67 0 0.056743482
509 9578.616 22 62 1 0.996260309 3754.009 20 76 0 0.404531992
516 9295.038 27 58 1 0.999991738 4341.911 20 63 0 0.964702426
517 9693.419 30 75 1 0.999947863 4536.841 22 77 0 0.789510917
521 9173.679 24 82 1 0.869184755 4213.439 22 91 0 0.065568426
523 8827.148 21 68 1 0.947019516 3801.285 20 82 0 0.109893723
525 9938.390 20 73 1 0.614433803 3193.754 18 80 0 0.028854170
527 8883.776 19 64 1 0.883644485 3762.962 19 80 0 0.074480152
537 8771.457 19 66 1 0.811379847 5025.034 20 85 0 0.050000319
538 9316.234 26 80 1 0.988512838 4950.287 19 74 0 0.306908446
540 9003.491 24 75 1 0.979829980 3750.268 25 97 0 0.202158682
543 8770.785 23 63 1 0.998161937 3370.383 19 71 0 0.509496988
544 9698.870 20 60 1 0.984641531 4759.155 21 82 0 0.250597545
548 8553.925 27 79 1 0.996781360 3708.935 19 72 0 0.438756765
550 8148.534 22 76 1 0.832880575 5064.087 19 81 0 0.057107080
553 9122.285 23 74 1 0.959727643 4656.117 20 81 0 0.140925361
558 9616.789 24 66 1 0.998407724 4323.322 20 74 0 0.545321906
559 9108.177 24 67 1 0.997885448 3617.278 19 71 0 0.509496988
560 9289.606 17 57 1 0.883295851 3862.948 17 73 0 0.074247052
561 8548.169 24 72 1 0.991300799 4157.915 20 77 0 0.338313577
569 8708.500 22 81 1 0.546161426 3725.990 19 84 0 0.025169522
570 8230.249 22 72 1 0.939516140 4514.903 23 93 0 0.097189644
577 9275.231 16 58 1 0.677742646 4481.920 18 79 0 0.037978361
578 9006.976 23 65 1 0.996759557 4082.801 22 83 0 0.405347997
582 8377.612 28 81 1 0.997899691 4441.679 19 71 0 0.509496988
584 8877.054 22 75 1 0.868799228 4944.180 22 91 0 0.065568426
588 9899.855 25 80 1 0.969485761 3637.471 16 66 0 0.177964931
594 8280.168 28 78 1 0.999103552 4266.283 21 77 0 0.580683696
597 9666.974 21 60 1 0.994274081 3517.968 23 87 0 0.372001927
598 9065.296 22 76 1 0.832880575 4909.346 19 81 0 0.057107080
600 9909.194 19 68 1 0.709013494 4953.035 22 93 0 0.038226589
601 9711.214 23 64 1 0.997559238 3457.374 18 68 0 0.473574259
605 9961.203 20 71 1 0.737766439 3108.033 19 82 0 0.043595528
606 10000.974 21 73 1 0.811897568 4917.363 22 92 0 0.050161420
609 9846.051 24 75 1 0.979829980 3467.874 23 90 0 0.201613035
610 9010.990 26 69 1 0.999490306 3392.080 24 87 0 0.616037075
611 9043.765 22 68 1 0.979762945 4959.721 23 90 0 0.201613035
615 9667.326 24 68 1 0.997192344 3782.931 21 79 0 0.439590841
619 8619.818 27 85 1 0.982542294 3223.524 19 75 0 0.249962118
620 8611.190 22 82 1 0.475263037 4768.974 18 81 0 0.021872202
628 9535.096 24 65 1 0.998801157 3336.727 17 63 0 0.579033680
631 8996.625 21 83 1 0.201068490 4978.838 20 90 0 0.012549558
635 8411.801 24 58 1 0.999835857 4517.031 22 78 0 0.738421072
636 9844.647 22 73 1 0.921201637 4600.600 15 65 0 0.096007562
638 9692.800 22 82 1 0.475263037 3718.050 16 74 0 0.021799870
640 9759.973 21 80 1 0.371211147 4288.910 15 71 0 0.018935415
643 9341.530 25 90 1 0.649434682 4056.878 14 65 0 0.037731681
644 9097.679 20 71 1 0.737766439 4281.972 17 75 0 0.043454549
645 8961.481 23 72 1 0.976783179 4591.927 22 87 0 0.179456031
647 9524.166 18 71 1 0.277197315 4249.309 19 86 0 0.014414046
652 8677.993 21 71 1 0.883992214 4673.457 19 80 0 0.074480152
654 8138.474 20 73 1 0.614433803 3686.546 18 80 0 0.028854170
655 9844.808 22 85 1 0.278556361 4744.370 19 86 0 0.014414046
657 8510.441 22 67 1 0.984692658 4696.832 21 82 0 0.250597545
658 9221.766 24 77 1 0.964932328 4203.980 19 77 0 0.158795476
660 9356.284 24 67 1 0.997885448 4531.060 22 82 0 0.475263037
662 9836.159 26 83 1 0.973464204 4645.562 20 80 0 0.178957916
663 9888.191 18 77 1 0.065154678 4989.183 13 66 0 0.010778187
664 9360.120 24 74 1 0.984743618 4654.608 18 71 0 0.277197315
665 8431.482 26 59 1 0.999970267 4567.696 22 76 0 0.832880575
666 9425.583 20 74 1 0.545321906 4586.345 22 95 0 0.022017569
668 9045.037 23 83 1 0.648663308 4432.423 21 90 0 0.033277126
669 9714.318 30 85 1 0.999106580 3918.885 18 66 0 0.613631233
671 9902.385 22 59 1 0.998402331 3597.790 20 74 0 0.545321906
674 8772.066 21 80 1 0.371211147 3899.471 15 71 0 0.018935415
675 9779.431 21 81 1 0.307629262 4320.953 18 82 0 0.016550898
676 9123.872 26 68 1 0.999616348 4636.373 21 76 0 0.647891157
680 9118.848 22 81 1 0.546161426 3928.217 19 84 0 0.025169522
682 9877.023 21 73 1 0.811897568 3732.042 20 85 0 0.050000319
683 9758.971 23 79 1 0.851949731 3672.480 20 84 0 0.065361248
685 8318.104 28 84 1 0.995087087 3637.931 25 94 0 0.372793394
686 8834.475 22 74 1 0.897943907 3683.068 18 76 0 0.084755914
689 9092.217 20 62 1 0.973200507 3379.247 18 73 0 0.178460883
692 8209.204 24 73 1 0.988474321 4783.862 17 67 0 0.306188572
693 8207.055 27 72 1 0.999558541 4705.610 17 62 0 0.646344537
694 9214.067 20 74 1 0.545321906 3115.949 20 88 0 0.021944768
700 8857.915 19 51 1 0.996737608 5082.830 22 83 0 0.405347997
715 9907.322 21 67 1 0.959596552 4060.123 16 67 0 0.140107396
716 9327.662 15 52 1 0.810341127 3703.936 20 85 0 0.050000319
717 10086.969 25 81 1 0.959858326 4167.778 20 81 0 0.140925361
723 9530.951 25 69 1 0.998620689 4116.149 22 81 0 0.546161426
730 9008.398 22 68 1 0.979762945 3132.943 19 76 0 0.200525046
733 9501.549 25 83 1 0.931244634 3905.312 21 86 0 0.096892912
734 10003.496 22 84 1 0.339072068 4982.467 20 89 0 0.016606109
739 9935.454 20 63 1 0.964702426 3102.088 22 88 0 0.141335839
741 9356.085 19 58 1 0.976629089 4460.763 20 80 0 0.178957916
745 8291.639 24 85 1 0.739074650 3696.189 16 71 0 0.049679585
746 9058.627 22 71 1 0.953787482 4275.412 17 71 0 0.124030268
747 8923.276 19 70 1 0.579858911 3199.457 19 84 0 0.025169522
748 9117.954 25 65 1 0.999557044 3778.927 17 62 0 0.646344537
753 10026.682 21 76 1 0.647891157 3331.939 19 83 0 0.033168357
758 8739.011 25 83 1 0.931244634 4310.834 21 86 0 0.096892912
759 8607.717 21 65 1 0.976706259 3173.547 20 80 0 0.178957916
761 8737.445 25 73 1 0.995713480 5015.905 20 76 0 0.404531992
769 8157.387 22 71 1 0.953787482 4613.179 15 64 0 0.123662813
771 9327.811 22 66 1 0.988435676 3935.257 17 67 0 0.306188572
777 9042.511 21 69 1 0.930809713 4566.430 19 79 0 0.096596988
778 9145.595 20 71 1 0.737766439 3614.355 17 75 0 0.043454549
781 9431.008 19 65 1 0.851093425 3950.395 16 70 0 0.064948716
783 9789.438 29 66 1 0.999989059 4480.375 22 73 0 0.921201637
787 10033.700 25 77 1 0.986759911 4798.640 20 78 0 0.277876327
792 9501.017 17 82 1 0.006175169 4769.599 17 82 0 0.006175169
796 8596.839 19 68 1 0.709013494 3473.114 20 86 0 0.038102281
799 8731.523 19 75 1 0.249962118 4935.013 17 79 0 0.014366017
803 9509.512 24 74 1 0.984743618 3989.823 23 89 0 0.251234047
807 9652.646 22 70 1 0.964817558 4174.019 24 95 0 0.141747314
811 8628.473 21 55 1 0.998611329 4758.149 22 81 0 0.546161426
814 9375.139 23 92 1 0.125138262 4336.254 17 80 0 0.010850639
817 9415.824 26 63 1 0.999907333 4913.931 24 85 0 0.739074650
819 9477.929 26 70 1 0.999322883 5026.756 22 80 0 0.615235752
821 8164.909 19 59 1 0.969183780 4573.342 16 66 0 0.177964931
824 9830.793 26 75 1 0.997201809 4911.846 21 79 0 0.439590841
827 9303.990 24 92 1 0.279237416 4224.286 14 68 0 0.016441016
832 9219.476 21 67 1 0.959596552 3863.213 14 60 0 0.139699906
834 9312.676 25 79 1 0.976859852 3446.375 24 94 0 0.179955228
836 9510.294 25 82 1 0.947358307 5012.410 22 89 0 0.110225411
837 9548.625 21 83 1 0.201068490 3735.015 18 83 0 0.012507663
838 9994.571 21 68 1 0.947019516 3259.661 18 75 0 0.109562910
842 8812.415 27 83 1 0.990036029 3769.511 23 88 0 0.308351017
849 10061.063 22 66 1 0.988435676 3489.379 24 92 0 0.279237416
851 10073.666 19 73 1 0.370421056 4461.740 20 89 0 0.016606109
852 8418.042 22 76 1 0.832880575 3588.470 17 74 0 0.056925008
853 9900.234 28 82 1 0.997211243 4699.492 21 79 0 0.439590841
854 8962.587 27 94 1 0.813444176 3077.864 17 74 0 0.056925008
855 8990.795 23 76 1 0.931027491 4233.272 19 79 0 0.096596988
858 8155.517 25 62 1 0.999811119 4844.151 21 75 0 0.709711664
859 9146.016 21 76 1 0.647891157 3695.342 17 76 0 0.033059932
860 8426.751 18 71 1 0.277197315 4597.203 17 79 0 0.014366017
864 10063.369 29 99 1 0.885374115 4211.637 25 101 0 0.075183493
865 9840.049 26 86 1 0.939899867 3842.442 16 68 0 0.109232971
866 8696.431 31 67 1 0.999998018 5050.338 26 78 0 0.993460769
868 9050.921 21 76 1 0.647891157 4883.102 15 69 0 0.032951850
870 10012.378 22 78 1 0.738421072 3890.864 21 89 0 0.043736943
872 9579.439 21 69 1 0.930809713 4893.802 19 79 0 0.096596988
873 8431.956 27 99 1 0.512881702 3302.124 20 88 0 0.021944768
885 8343.694 22 71 1 0.953787482 3588.777 26 103 0 0.110891418
887 9919.208 19 55 1 0.989901514 3921.689 19 74 0 0.306908446
892 8148.956 26 82 1 0.979896798 4559.346 18 72 0 0.223982281
894 8118.491 22 81 1 0.546161426 4394.837 17 77 0 0.025086566
897 9312.310 23 64 1 0.997559238 3572.118 23 86 0 0.440425259
899 9182.428 21 73 1 0.811897568 3406.904 20 85 0 0.050000319
900 8873.222 22 68 1 0.979762945 4103.937 19 76 0 0.200525046
902 8817.309 20 75 1 0.474418575 3482.710 14 67 0 0.021727773
903 8631.704 22 69 1 0.973288688 3505.314 18 73 0 0.178460883
911 9577.510 29 81 1 0.999223524 4807.917 20 73 0 0.614433803
920 8367.827 27 65 1 0.999939596 4087.288 25 88 0 0.765838210
922 9301.979 27 77 1 0.998174321 4619.310 25 92 0 0.512035622
928 8924.814 27 83 1 0.990036029 4625.083 23 88 0 0.308351017
929 9071.670 27 75 1 0.998965063 3356.189 21 77 0 0.580683696
930 9060.541 21 81 1 0.307629262 3247.475 18 82 0 0.016550898
931 8129.692 22 78 1 0.738421072 3950.700 21 89 0 0.043736943
932 8139.725 22 66 1 0.988435676 4783.892 24 92 0 0.279237416
938 9330.340 28 68 1 0.999947686 4752.035 27 95 0 0.766444950
941 9781.638 26 82 1 0.979896798 3299.474 25 97 0 0.202158682
943 9010.214 26 85 1 0.954085092 3901.443 21 85 0 0.124767992
944 9845.467 16 59 1 0.612828045 4249.283 18 80 0 0.028854170
945 9292.751 22 58 1 0.998797095 3784.042 24 88 0 0.547000683
946 9879.860 27 77 1 0.998174321 4174.790 21 78 0 0.510343260
948 9557.862 22 71 1 0.953787482 4056.185 24 96 0 0.110557975
950 8701.499 25 79 1 0.976859852 3580.496 22 87 0 0.179456031
951 8474.594 20 72 1 0.679220102 3248.846 18 79 0 0.037978361
961 10066.037 21 71 1 0.883992214 3216.871 19 80 0 0.074480152
963 8558.791 29 105 1 0.583978287 4183.886 18 80 0 0.028854170
969 9436.242 26 87 1 0.921691872 5074.048 19 79 0 0.096596988
973 8728.427 14 71 1 0.007075591 4130.988 14 71 0 0.007075591
975 8984.511 20 82 1 0.109893723 3254.130 17 80 0 0.010850639
976 9987.146 28 59 1 0.999995947 3414.553 25 78 0 0.982484112
977 9932.142 23 84 1 0.581508030 4543.395 23 98 0 0.025336236
984 8939.801 22 75 1 0.868799228 3125.927 22 91 0 0.065568426
989 9415.052 22 70 1 0.964817558 4864.085 24 95 0 0.141747314
992 10040.653 22 92 1 0.050161420 3115.820 20 91 0 0.009474397
996 9246.277 23 68 1 0.992431736 3094.405 22 84 0 0.339072068
1000 10042.248 28 65 1 0.999977698 5025.905 21 72 0 0.851522088Optimal matching solves the problem inherent to the NNM, that matches units one at a time, without taking into account any global (over the entire population) distance measure. This way, with NNM the last treated unit could could match an inappropriate unit.
#Optimal matchingm5.ps <- matchit(z ~ x1 + x2, method = "optimal", data = Data)summary(m5.ps, covariates = T)
Call:
matchit(formula = z ~ x1 + x2, data = Data, method = "optimal")
Summary of Balance for All Data:
Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
distance 0.7919 0.1135 2.6166 1.6655 0.4027
x1 22.7875 17.9969 1.5648 0.8264 0.1993
x2 74.2040 83.4436 -0.9872 1.0623 0.1589
eCDF Max
distance 0.7901
x1 0.5562
x2 0.3919
Summary of Balance for Matched Data:
Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
distance 0.7919 0.2063 2.2586 1.2210 0.2663
x1 22.7875 19.7422 0.9947 1.3479 0.1269
x2 74.2040 80.7394 -0.6983 1.2004 0.1127
eCDF Max Std. Pair Dist.
distance 0.6969 2.2586
x1 0.4193 1.2057
x2 0.2890 1.1892
Sample Sizes:
Control Treated
All 647 353
Matched 353 353
Unmatched 294 0
Discarded 0 0plot(m5.ps)
plot(m5.ps, type="jitter")
To identify the units, use first mouse button; to stop, use second.plot(m5.ps, type="hist")
m5.data <- match.data(m5.ps)# m5.data[(m5.data$subclass == 1),]Full matching forms subgroups in an optimal way.
#Full matchingm4.ps <- matchit(z ~ x1 + x2, method = "full", data = Data)summary(m4.ps, covariates = T)
Call:
matchit(formula = z ~ x1 + x2, data = Data, method = "full")
Summary of Balance for All Data:
Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
distance 0.7919 0.1135 2.6166 1.6655 0.4027
x1 22.7875 17.9969 1.5648 0.8264 0.1993
x2 74.2040 83.4436 -0.9872 1.0623 0.1589
eCDF Max
distance 0.7901
x1 0.5562
x2 0.3919
Summary of Balance for Matched Data:
Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
distance 0.7919 0.7904 0.0056 0.9107 0.0181
x1 22.7875 23.1741 -0.1263 1.1357 0.0359
x2 74.2040 77.3825 -0.3396 1.6409 0.0692
eCDF Max Std. Pair Dist.
distance 0.2153 0.0203
x1 0.1642 0.8179
x2 0.2849 0.9079
Sample Sizes:
Control Treated
All 647. 353
Matched (ESS) 10.07 353
Matched 647. 353
Unmatched 0. 0
Discarded 0. 0plot(m4.ps)
plot(m4.ps, type="jitter")
To identify the units, use first mouse button; to stop, use second.plot(m4.ps, type="hist")
m4.data <- match.data(m4.ps)Caliper matching is a refinement of the NNM. It defines a constraint over the individual distant measure. So, it minimises the probability of bad matching.
# Caliper matchingsd.ps <- sd(Data$ps)
m8.ps <- matchit(z ~ x1 + x2, method = "nearest", caliper = 0.25 * sd.ps, data = Data)summary(m8.ps, covariates = T)
Call:
matchit(formula = z ~ x1 + x2, data = Data, method = "nearest",
caliper = 0.25 * sd.ps)
Summary of Balance for All Data:
Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
distance 0.7919 0.1135 2.6166 1.6655 0.4027
x1 22.7875 17.9969 1.5648 0.8264 0.1993
x2 74.2040 83.4436 -0.9872 1.0623 0.1589
eCDF Max
distance 0.7901
x1 0.5562
x2 0.3919
Summary of Balance for Matched Data:
Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
distance 0.4976 0.4769 0.0797 1.0914 0.0117
x1 21.8246 21.0965 0.2378 1.3718 0.0318
x2 80.3246 78.9123 0.1509 1.0908 0.0313
eCDF Max Std. Pair Dist.
distance 0.114 0.0802
x1 0.114 0.5186
x2 0.114 0.5539
Sample Sizes:
Control Treated
All 647 353
Matched 114 114
Unmatched 533 239
Discarded 0 0plot(m8.ps)
plot(m8.ps, type="jitter")
To identify the units, use first mouse button; to stop, use second.plot(m8.ps, type="hist")
m8.data <- match.data(m8.ps)m8.data.control <- match.data(m8.ps,"control")m8.data.treat <- match.data(m8.ps,"treat")m8.ps$match.matrix [,1]
3 NA
5 NA
10 "274"
11 "111"
16 NA
17 NA
18 "401"
21 NA
23 "443"
25 NA
29 NA
31 "133"
33 NA
35 NA
47 NA
51 "845"
55 "905"
60 NA
61 NA
63 NA
64 NA
66 "159"
67 NA
73 "797"
74 "50"
75 "105"
77 NA
79 NA
81 "939"
84 NA
85 NA
88 "718"
89 "262"
90 "802"
92 "377"
96 NA
97 NA
99 NA
100 "529"
109 NA
112 "150"
113 "927"
114 "169"
115 "193"
116 NA
117 NA
118 "59"
119 NA
120 NA
123 "907"
126 NA
130 NA
139 NA
140 NA
142 NA
154 NA
155 NA
156 NA
163 NA
164 NA
166 NA
167 NA
168 "355"
174 "978"
177 NA
184 "415"
185 NA
189 NA
192 NA
194 NA
196 "883"
198 NA
205 NA
213 NA
215 NA
216 NA
217 "72"
219 NA
220 NA
221 "490"
222 NA
223 NA
227 "979"
230 NA
231 "46"
236 NA
237 NA
238 NA
241 NA
242 NA
246 NA
247 NA
249 NA
250 "264"
255 NA
256 "815"
269 NA
271 "460"
278 "27"
284 NA
286 NA
289 "847"
290 "248"
291 NA
293 NA
297 "684"
304 NA
305 "138"
306 NA
309 "545"
310 NA
311 "572"
313 NA
315 "754"
318 "554"
321 NA
324 NA
343 NA
347 NA
348 NA
351 "12"
354 NA
357 NA
359 NA
362 NA
364 "618"
367 NA
369 NA
373 "344"
378 "268"
379 NA
382 NA
387 NA
392 NA
394 NA
395 NA
399 NA
402 "127"
403 "579"
405 NA
406 NA
409 NA
411 "891"
413 "801"
414 NA
421 NA
422 "602"
427 "423"
428 "260"
429 NA
430 "197"
435 "731"
436 "2"
437 NA
438 NA
441 NA
444 NA
446 NA
447 NA
450 "568"
455 NA
461 NA
464 NA
465 "982"
466 NA
468 NA
470 "316"
471 "990"
472 "272"
473 NA
477 "69"
480 NA
483 NA
484 "203"
485 "994"
487 "245"
491 "856"
494 "141"
504 NA
506 NA
508 "857"
509 NA
516 "719"
517 NA
521 NA
523 NA
525 "641"
527 NA
537 NA
538 NA
540 NA
543 NA
544 NA
548 NA
550 NA
553 NA
558 NA
559 NA
560 NA
561 NA
569 "353"
570 NA
577 NA
578 NA
582 NA
584 NA
588 NA
594 NA
597 NA
598 NA
600 NA
601 NA
605 NA
606 NA
609 NA
610 NA
611 NA
615 NA
619 NA
620 "121"
628 NA
631 "265"
635 NA
636 NA
638 "968"
640 "955"
643 "535"
644 NA
645 NA
647 "182"
652 NA
654 "70"
655 "986"
657 NA
658 NA
660 NA
662 NA
663 "630"
664 NA
665 NA
666 "146"
668 "78"
669 NA
671 NA
674 "336"
675 "252"
676 NA
680 "536"
682 NA
683 NA
685 NA
686 NA
689 NA
692 NA
693 NA
694 "39"
700 NA
715 NA
716 NA
717 "161"
723 NA
730 NA
733 NA
734 "456"
739 NA
741 NA
745 "621"
746 NA
747 NA
748 NA
753 "844"
758 NA
759 NA
761 NA
769 NA
771 NA
777 NA
778 NA
781 NA
783 NA
787 NA
792 "410"
796 NA
799 "573"
803 NA
807 NA
811 NA
814 "749"
817 NA
819 NA
821 NA
824 NA
827 "622"
832 NA
834 NA
836 NA
837 "32"
838 NA
842 NA
849 NA
851 "751"
852 NA
853 NA
854 "276"
855 NA
858 NA
859 "183"
860 "691"
864 "187"
865 NA
866 "724"
868 NA
870 "370"
872 NA
873 "58"
885 NA
887 NA
892 NA
894 "329"
897 NA
899 NA
900 NA
902 NA
903 NA
911 NA
920 NA
922 NA
928 NA
929 NA
930 "95"
931 "358"
932 NA
938 NA
941 NA
943 NA
944 NA
945 NA
946 NA
948 NA
950 NA
951 "40"
961 NA
963 "698"
969 NA
973 "772"
975 "576"
976 "228"
977 "738"
984 NA
989 NA
992 "397"
996 NA
1000 NA Pairs <- cbind(Data[row.names(m8.ps$match.matrix),], Data[m8.ps$match.matrix,])Pairs y x1 x2 z ps y x1 x2 z ps
3 10063.205 23 76 1 0.931027491 NA NA NA NA NA
5 9705.856 26 70 1 0.999322883 NA NA NA NA NA
10 8759.264 20 73 1 0.614433803 3735.166 19 70 0 0.579858911
11 8789.761 20 78 1 0.277876327 3663.815 20 78 0 0.277876327
16 8433.025 23 69 1 0.989968995 NA NA NA NA NA
17 8823.235 26 72 1 0.998805205 NA NA NA NA NA
18 9172.051 19 76 1 0.200525046 3914.979 23 90 0 0.201613035
21 8189.328 28 74 1 0.999712207 NA NA NA NA NA
23 8248.042 23 85 1 0.511189473 4347.073 20 75 0 0.474418575
25 8988.314 24 80 1 0.921447105 NA NA NA NA NA
29 8276.923 22 76 1 0.832880575 NA NA NA NA NA
31 9489.524 20 78 1 0.277876327 4885.968 20 78 0 0.277876327
33 8236.849 27 68 1 0.999858319 NA NA NA NA NA
35 9715.245 23 58 1 0.999555543 NA NA NA NA NA
47 8581.192 20 69 1 0.832408685 NA NA NA NA NA
51 8121.518 23 82 1 0.710408842 3459.289 20 72 0 0.679220102
55 9021.084 20 72 1 0.679220102 4705.610 17 62 0 0.646344537
60 8619.468 20 70 1 0.788947598 NA NA NA NA NA
61 8516.199 26 88 1 0.898562905 NA NA NA NA NA
63 9327.283 19 65 1 0.851093425 NA NA NA NA NA
64 8694.914 22 74 1 0.897943907 NA NA NA NA NA
66 9850.745 22 85 1 0.278556361 4880.289 22 85 0 0.278556361
67 9595.795 19 57 1 0.982308420 NA NA NA NA NA
73 9816.380 24 74 1 0.984743618 4546.530 23 75 0 0.947189168
74 8472.126 19 78 1 0.124398661 4816.215 19 78 0 0.124398661
75 9324.843 22 78 1 0.738421072 3529.923 23 82 0 0.710408842
77 8703.039 24 75 1 0.979829980 NA NA NA NA NA
79 8760.662 26 63 1 0.999907333 NA NA NA NA NA
81 9699.242 19 73 1 0.370421056 3637.931 25 94 0 0.372793394
84 9117.942 31 91 1 0.998186622 NA NA NA NA NA
85 9459.019 22 70 1 0.964817558 NA NA NA NA NA
88 9524.842 20 75 1 0.474418575 4572.975 19 72 0 0.438756765
89 8576.767 30 105 1 0.791753158 4752.035 27 95 0 0.766444950
90 9108.723 19 70 1 0.579858911 4561.407 18 67 0 0.544482128
92 8301.088 24 85 1 0.739074650 4913.931 24 85 0 0.739074650
96 8781.966 22 65 1 0.991271548 NA NA NA NA NA
97 8190.420 25 83 1 0.931244634 NA NA NA NA NA
99 8350.664 31 92 1 0.997591998 NA NA NA NA NA
100 8893.035 21 74 1 0.764621449 4076.043 24 85 0 0.739074650
109 8710.371 23 76 1 0.931027491 NA NA NA NA NA
112 9323.273 21 77 1 0.580683696 3597.790 20 74 0 0.545321906
113 8983.719 24 82 1 0.869184755 4567.696 22 76 0 0.832880575
114 9217.271 20 81 1 0.140925361 4656.117 20 81 0 0.140925361
115 8134.586 21 79 1 0.439590841 4082.801 22 83 0 0.405347997
116 8270.879 24 83 1 0.833351401 NA NA NA NA NA
117 9256.702 19 71 1 0.509496988 NA NA NA NA NA
118 10052.430 20 76 1 0.404531992 5015.905 20 76 0 0.404531992
119 8729.021 20 70 1 0.788947598 NA NA NA NA NA
120 8856.850 22 76 1 0.832880575 NA NA NA NA NA
123 9688.339 21 76 1 0.647891157 4807.917 20 73 0 0.614433803
126 9861.592 17 58 1 0.850663742 NA NA NA NA NA
130 8684.901 30 74 1 0.999960760 NA NA NA NA NA
139 9704.264 21 71 1 0.883992214 NA NA NA NA NA
140 8536.793 25 84 1 0.910663678 NA NA NA NA NA
142 8156.267 21 67 1 0.959596552 NA NA NA NA NA
154 9310.721 19 65 1 0.851093425 NA NA NA NA NA
155 8139.426 29 85 1 0.997583850 NA NA NA NA NA
156 8773.188 21 71 1 0.883992214 NA NA NA NA NA
163 9368.322 29 68 1 0.999980685 NA NA NA NA NA
164 9036.764 26 84 1 0.965046737 NA NA NA NA NA
166 8996.454 22 68 1 0.979762945 NA NA NA NA NA
167 9553.791 23 69 1 0.989968995 NA NA NA NA NA
168 8230.864 22 84 1 0.339072068 4157.915 20 77 0 0.338313577
174 9799.736 18 69 1 0.403716516 3653.354 18 69 0 0.403716516
177 8315.752 27 77 1 0.998174321 NA NA NA NA NA
184 8937.535 26 93 1 0.681429563 4615.027 25 90 0 0.649434682
185 9649.252 30 96 1 0.980029784 NA NA NA NA NA
189 10036.312 25 77 1 0.986759911 NA NA NA NA NA
192 9919.054 22 71 1 0.953787482 NA NA NA NA NA
194 9054.288 18 50 1 0.993372179 NA NA NA NA NA
196 8119.149 21 76 1 0.647891157 4242.838 20 73 0 0.614433803
198 9408.028 22 72 1 0.939516140 NA NA NA NA NA
205 9027.826 19 57 1 0.982308420 NA NA NA NA NA
213 9896.261 23 66 1 0.995699002 NA NA NA NA NA
215 9404.786 25 58 1 0.999939391 NA NA NA NA NA
216 9152.874 18 68 1 0.473574259 NA NA NA NA NA
217 9070.869 21 78 1 0.510343260 4531.086 20 75 0 0.474418575
219 9536.295 29 77 1 0.999750742 NA NA NA NA NA
220 9222.398 28 76 1 0.999492028 NA NA NA NA NA
221 9955.165 23 83 1 0.648663308 3427.332 24 87 0 0.616037075
222 8455.751 18 65 1 0.678481820 NA NA NA NA NA
223 8476.346 24 77 1 0.964932328 NA NA NA NA NA
227 8190.552 24 85 1 0.739074650 3452.033 22 78 0 0.738421072
230 8500.147 23 69 1 0.989968995 NA NA NA NA NA
231 8292.887 18 70 1 0.337555917 3769.511 23 88 0 0.308351017
236 8155.931 28 75 1 0.999617645 NA NA NA NA NA
237 8361.284 22 69 1 0.973288688 NA NA NA NA NA
238 8964.878 25 79 1 0.976859852 NA NA NA NA NA
241 8612.428 22 71 1 0.953787482 NA NA NA NA NA
242 8626.602 22 55 1 0.999486844 NA NA NA NA NA
246 9796.252 22 70 1 0.964817558 NA NA NA NA NA
247 10064.063 23 82 1 0.710408842 NA NA NA NA NA
249 9443.321 23 69 1 0.989968995 NA NA NA NA NA
250 8281.874 22 82 1 0.475263037 3572.118 23 86 0 0.440425259
255 9645.268 26 76 1 0.996285458 NA NA NA NA NA
256 8505.833 21 78 1 0.510343260 3457.374 18 68 0 0.473574259
269 9991.929 23 76 1 0.931027491 NA NA NA NA NA
271 10052.958 25 85 1 0.884684965 5025.905 21 72 0 0.851522088
278 9414.422 21 82 1 0.250597545 4759.155 21 82 0 0.250597545
284 8439.111 21 50 1 0.999664324 NA NA NA NA NA
286 10052.207 25 80 1 0.969485761 NA NA NA NA NA
289 8605.068 22 82 1 0.475263037 4699.492 21 79 0 0.439590841
290 8518.714 19 72 1 0.438756765 3637.976 20 76 0 0.404531992
291 9652.115 23 75 1 0.947189168 NA NA NA NA NA
293 8206.735 20 75 1 0.474418575 NA NA NA NA NA
297 9768.883 19 81 1 0.057107080 4909.346 19 81 0 0.057107080
304 9926.004 21 66 1 0.969284761 NA NA NA NA NA
305 8355.090 24 94 1 0.179955228 3446.375 24 94 0 0.179955228
306 10043.549 23 77 1 0.910387791 NA NA NA NA NA
309 9232.894 24 86 1 0.680693976 4943.073 21 76 0 0.647891157
310 8609.751 27 69 1 0.999811757 NA NA NA NA NA
311 9070.206 21 80 1 0.371211147 4521.036 21 80 0 0.371211147
313 9384.540 22 74 1 0.897943907 NA NA NA NA NA
315 10005.416 22 80 1 0.615235752 4266.283 21 77 0 0.580683696
318 8415.244 22 80 1 0.615235752 3356.189 21 77 0 0.580683696
321 9261.289 25 77 1 0.986759911 NA NA NA NA NA
324 8160.594 21 78 1 0.510343260 NA NA NA NA NA
343 9668.226 24 65 1 0.998801157 NA NA NA NA NA
347 9321.374 20 67 1 0.897633155 NA NA NA NA NA
348 8914.603 23 74 1 0.959727643 NA NA NA NA NA
351 8119.209 19 73 1 0.370421056 3094.405 22 84 0 0.339072068
354 9389.141 22 76 1 0.832880575 NA NA NA NA NA
357 9046.107 24 82 1 0.869184755 NA NA NA NA NA
359 9942.282 21 53 1 0.999212942 NA NA NA NA NA
362 8998.446 23 65 1 0.996759557 NA NA NA NA NA
364 8118.007 23 83 1 0.648663308 3285.766 22 80 0 0.615235752
367 9655.120 22 73 1 0.921201637 NA NA NA NA NA
369 8536.379 30 86 1 0.998813260 NA NA NA NA NA
373 8285.052 22 77 1 0.789510917 4087.288 25 88 0 0.765838210
378 9507.320 22 77 1 0.789510917 4772.660 19 67 0 0.764011430
379 8349.869 24 72 1 0.991300799 NA NA NA NA NA
382 9678.451 28 91 1 0.965160787 NA NA NA NA NA
387 8202.671 18 57 1 0.953488036 NA NA NA NA NA
392 9826.312 21 64 1 0.982367175 NA NA NA NA NA
394 9122.539 20 68 1 0.868412737 NA NA NA NA NA
395 8441.566 24 62 1 0.999488578 NA NA NA NA NA
399 9896.750 23 66 1 0.995699002 NA NA NA NA NA
402 9533.508 19 74 1 0.306908446 4950.287 19 74 0 0.306908446
403 8974.255 26 95 1 0.547839674 3474.498 25 92 0 0.512035622
405 8942.022 21 69 1 0.930809713 NA NA NA NA NA
406 8747.899 21 70 1 0.910111136 NA NA NA NA NA
409 9691.459 21 68 1 0.947019516 NA NA NA NA NA
411 8480.075 26 102 1 0.142159789 4174.019 24 95 0 0.141747314
413 8091.298 21 83 1 0.201068490 3132.943 19 76 0 0.200525046
414 8308.879 20 63 1 0.964702426 NA NA NA NA NA
421 9261.591 28 62 1 0.999990492 NA NA NA NA NA
422 8701.330 23 84 1 0.581508030 4116.149 22 81 0 0.546161426
427 9316.743 20 83 1 0.085018977 3795.357 20 83 0 0.085018977
428 8290.262 23 84 1 0.581508030 4758.149 22 81 0 0.546161426
429 8270.488 28 78 1 0.999103552 NA NA NA NA NA
430 9420.592 20 74 1 0.545321906 4441.679 19 71 0 0.509496988
435 9825.739 25 90 1 0.649434682 5082.799 28 101 0 0.617637828
436 9742.111 23 88 1 0.308351017 4625.083 23 88 0 0.308351017
437 8161.450 26 79 1 0.991329954 NA NA NA NA NA
438 8454.059 24 67 1 0.997885448 NA NA NA NA NA
441 8825.902 25 80 1 0.969485761 NA NA NA NA NA
444 8739.745 21 63 1 0.986671133 NA NA NA NA NA
446 9319.413 24 71 1 0.993438732 NA NA NA NA NA
447 8343.560 25 86 1 0.852376356 NA NA NA NA NA
450 9411.461 15 61 1 0.248694489 3795.292 19 75 0 0.249962118
455 9586.175 21 65 1 0.976706259 NA NA NA NA NA
461 9748.195 25 78 1 0.982484112 NA NA NA NA NA
464 9414.435 19 56 1 0.986626524 NA NA NA NA NA
465 9081.892 18 69 1 0.403716516 3832.287 18 69 0 0.403716516
466 9830.065 26 88 1 0.898562905 NA NA NA NA NA
468 9725.604 24 78 1 0.953936515 NA NA NA NA NA
470 9497.040 23 83 1 0.648663308 4548.612 22 80 0 0.615235752
471 10065.244 25 93 1 0.441260013 4270.356 22 83 0 0.405347997
472 8892.571 22 79 1 0.679957488 4636.373 21 76 0 0.647891157
473 8595.018 23 76 1 0.931027491 NA NA NA NA NA
477 9980.913 21 79 1 0.439590841 5082.830 22 83 0 0.405347997
480 9759.734 23 65 1 0.996759557 NA NA NA NA NA
483 9931.586 25 80 1 0.969485761 NA NA NA NA NA
484 8936.788 22 82 1 0.475263037 4911.846 21 79 0 0.439590841
485 8369.125 19 73 1 0.370421056 3786.049 20 77 0 0.338313577
487 9583.058 22 80 1 0.615235752 3324.102 21 77 0 0.580683696
491 9130.948 25 90 1 0.649434682 5083.920 24 87 0 0.616037075
494 8685.271 18 69 1 0.403716516 3754.009 20 76 0 0.404531992
504 9653.641 20 69 1 0.832408685 NA NA NA NA NA
506 9843.296 20 75 1 0.474418575 NA NA NA NA NA
508 8113.734 23 80 1 0.812414196 4536.841 22 77 0 0.789510917
509 9578.616 22 62 1 0.996260309 NA NA NA NA NA
516 9295.038 27 58 1 0.999991738 4341.911 20 63 0 0.964702426
517 9693.419 30 75 1 0.999947863 NA NA NA NA NA
521 9173.679 24 82 1 0.869184755 NA NA NA NA NA
523 8827.148 21 68 1 0.947019516 NA NA NA NA NA
525 9938.390 20 73 1 0.614433803 3473.282 17 63 0 0.579033680
527 8883.776 19 64 1 0.883644485 NA NA NA NA NA
537 8771.457 19 66 1 0.811379847 NA NA NA NA NA
538 9316.234 26 80 1 0.988512838 NA NA NA NA NA
540 9003.491 24 75 1 0.979829980 NA NA NA NA NA
543 8770.785 23 63 1 0.998161937 NA NA NA NA NA
544 9698.870 20 60 1 0.984641531 NA NA NA NA NA
548 8553.925 27 79 1 0.996781360 NA NA NA NA NA
550 8148.534 22 76 1 0.832880575 NA NA NA NA NA
553 9122.285 23 74 1 0.959727643 NA NA NA NA NA
558 9616.789 24 66 1 0.998407724 NA NA NA NA NA
559 9108.177 24 67 1 0.997885448 NA NA NA NA NA
560 9289.606 17 57 1 0.883295851 NA NA NA NA NA
561 8548.169 24 72 1 0.991300799 NA NA NA NA NA
569 8708.500 22 81 1 0.546161426 4619.310 25 92 0 0.512035622
570 8230.249 22 72 1 0.939516140 NA NA NA NA NA
577 9275.231 16 58 1 0.677742646 NA NA NA NA NA
578 9006.976 23 65 1 0.996759557 NA NA NA NA NA
582 8377.612 28 81 1 0.997899691 NA NA NA NA NA
584 8877.054 22 75 1 0.868799228 NA NA NA NA NA
588 9899.855 25 80 1 0.969485761 NA NA NA NA NA
594 8280.168 28 78 1 0.999103552 NA NA NA NA NA
597 9666.974 21 60 1 0.994274081 NA NA NA NA NA
598 9065.296 22 76 1 0.832880575 NA NA NA NA NA
600 9909.194 19 68 1 0.709013494 NA NA NA NA NA
601 9711.214 23 64 1 0.997559238 NA NA NA NA NA
605 9961.203 20 71 1 0.737766439 NA NA NA NA NA
606 10000.974 21 73 1 0.811897568 NA NA NA NA NA
609 9846.051 24 75 1 0.979829980 NA NA NA NA NA
610 9010.990 26 69 1 0.999490306 NA NA NA NA NA
611 9043.765 22 68 1 0.979762945 NA NA NA NA NA
615 9667.326 24 68 1 0.997192344 NA NA NA NA NA
619 8619.818 27 85 1 0.982542294 NA NA NA NA NA
620 8611.190 22 82 1 0.475263037 3782.931 21 79 0 0.439590841
628 9535.096 24 65 1 0.998801157 NA NA NA NA NA
631 8996.625 21 83 1 0.201068490 4103.937 19 76 0 0.200525046
635 8411.801 24 58 1 0.999835857 NA NA NA NA NA
636 9844.647 22 73 1 0.921201637 NA NA NA NA NA
638 9692.800 22 82 1 0.475263037 3708.935 19 72 0 0.438756765
640 9759.973 21 80 1 0.371211147 3263.481 21 80 0 0.371211147
643 9341.530 25 90 1 0.649434682 3392.080 24 87 0 0.616037075
644 9097.679 20 71 1 0.737766439 NA NA NA NA NA
645 8961.481 23 72 1 0.976783179 NA NA NA NA NA
647 9524.166 18 71 1 0.277197315 4654.608 18 71 0 0.277197315
652 8677.993 21 71 1 0.883992214 NA NA NA NA NA
654 8138.474 20 73 1 0.614433803 3336.727 17 63 0 0.579033680
655 9844.808 22 85 1 0.278556361 3364.974 22 85 0 0.278556361
657 8510.441 22 67 1 0.984692658 NA NA NA NA NA
658 9221.766 24 77 1 0.964932328 NA NA NA NA NA
660 9356.284 24 67 1 0.997885448 NA NA NA NA NA
662 9836.159 26 83 1 0.973464204 NA NA NA NA NA
663 9888.191 18 77 1 0.065154678 4115.816 18 77 0 0.065154678
664 9360.120 24 74 1 0.984743618 NA NA NA NA NA
665 8431.482 26 59 1 0.999970267 NA NA NA NA NA
666 9425.583 20 74 1 0.545321906 3087.984 19 71 0 0.509496988
668 9045.037 23 83 1 0.648663308 5026.756 22 80 0 0.615235752
669 9714.318 30 85 1 0.999106580 NA NA NA NA NA
671 9902.385 22 59 1 0.998402331 NA NA NA NA NA
674 8772.066 21 80 1 0.371211147 3517.968 23 87 0 0.372001927
675 9779.431 21 81 1 0.307629262 3257.432 21 81 0 0.307629262
676 9123.872 26 68 1 0.999616348 NA NA NA NA NA
680 9118.848 22 81 1 0.546161426 4174.790 21 78 0 0.510343260
682 9877.023 21 73 1 0.811897568 NA NA NA NA NA
683 9758.971 23 79 1 0.851949731 NA NA NA NA NA
685 8318.104 28 84 1 0.995087087 NA NA NA NA NA
686 8834.475 22 74 1 0.897943907 NA NA NA NA NA
689 9092.217 20 62 1 0.973200507 NA NA NA NA NA
692 8209.204 24 73 1 0.988474321 NA NA NA NA NA
693 8207.055 27 72 1 0.999558541 NA NA NA NA NA
694 9214.067 20 74 1 0.545321906 3617.278 19 71 0 0.509496988
700 8857.915 19 51 1 0.996737608 NA NA NA NA NA
715 9907.322 21 67 1 0.959596552 NA NA NA NA NA
716 9327.662 15 52 1 0.810341127 NA NA NA NA NA
717 10086.969 25 81 1 0.959858326 4480.375 22 73 0 0.921201637
723 9530.951 25 69 1 0.998620689 NA NA NA NA NA
730 9008.398 22 68 1 0.979762945 NA NA NA NA NA
733 9501.549 25 83 1 0.931244634 NA NA NA NA NA
734 10003.496 22 84 1 0.339072068 3382.339 23 88 0 0.308351017
739 9935.454 20 63 1 0.964702426 NA NA NA NA NA
741 9356.085 19 58 1 0.976629089 NA NA NA NA NA
745 8291.639 24 85 1 0.739074650 4517.031 22 78 0 0.738421072
746 9058.627 22 71 1 0.953787482 NA NA NA NA NA
747 8923.276 19 70 1 0.579858911 NA NA NA NA NA
748 9117.954 25 65 1 0.999557044 NA NA NA NA NA
753 10026.682 21 76 1 0.647891157 3918.885 18 66 0 0.613631233
758 8739.011 25 83 1 0.931244634 NA NA NA NA NA
759 8607.717 21 65 1 0.976706259 NA NA NA NA NA
761 8737.445 25 73 1 0.995713480 NA NA NA NA NA
769 8157.387 22 71 1 0.953787482 NA NA NA NA NA
771 9327.811 22 66 1 0.988435676 NA NA NA NA NA
777 9042.511 21 69 1 0.930809713 NA NA NA NA NA
778 9145.595 20 71 1 0.737766439 NA NA NA NA NA
781 9431.008 19 65 1 0.851093425 NA NA NA NA NA
783 9789.438 29 66 1 0.999989059 NA NA NA NA NA
787 10033.700 25 77 1 0.986759911 NA NA NA NA NA
792 9501.017 17 82 1 0.006175169 4769.599 17 82 0 0.006175169
796 8596.839 19 68 1 0.709013494 NA NA NA NA NA
799 8731.523 19 75 1 0.249962118 3223.524 19 75 0 0.249962118
803 9509.512 24 74 1 0.984743618 NA NA NA NA NA
807 9652.646 22 70 1 0.964817558 NA NA NA NA NA
811 8628.473 21 55 1 0.998611329 NA NA NA NA NA
814 9375.139 23 92 1 0.125138262 3901.443 21 85 0 0.124767992
817 9415.824 26 63 1 0.999907333 NA NA NA NA NA
819 9477.929 26 70 1 0.999322883 NA NA NA NA NA
821 8164.909 19 59 1 0.969183780 NA NA NA NA NA
824 9830.793 26 75 1 0.997201809 NA NA NA NA NA
827 9303.990 24 92 1 0.279237416 3489.379 24 92 0 0.279237416
832 9219.476 21 67 1 0.959596552 NA NA NA NA NA
834 9312.676 25 79 1 0.976859852 NA NA NA NA NA
836 9510.294 25 82 1 0.947358307 NA NA NA NA NA
837 9548.625 21 83 1 0.201068490 4959.721 23 90 0 0.201613035
838 9994.571 21 68 1 0.947019516 NA NA NA NA NA
842 8812.415 27 83 1 0.990036029 NA NA NA NA NA
849 10061.063 22 66 1 0.988435676 NA NA NA NA NA
851 10073.666 19 73 1 0.370421056 4337.673 20 77 0 0.338313577
852 8418.042 22 76 1 0.832880575 NA NA NA NA NA
853 9900.234 28 82 1 0.997211243 NA NA NA NA NA
854 8962.587 27 94 1 0.813444176 3766.032 24 84 0 0.790073132
855 8990.795 23 76 1 0.931027491 NA NA NA NA NA
858 8155.517 25 62 1 0.999811119 NA NA NA NA NA
859 9146.016 21 76 1 0.647891157 3195.390 18 66 0 0.613631233
860 8426.751 18 71 1 0.277197315 4447.631 18 71 0 0.277197315
864 10063.369 29 99 1 0.885374115 3831.602 27 93 0 0.852801965
865 9840.049 26 86 1 0.939899867 NA NA NA NA NA
866 8696.431 31 67 1 0.999998018 5050.338 26 78 0 0.993460769
868 9050.921 21 76 1 0.647891157 NA NA NA NA NA
870 10012.378 22 78 1 0.738421072 4844.151 21 75 0 0.709711664
872 9579.439 21 69 1 0.930809713 NA NA NA NA NA
873 8431.956 27 99 1 0.512881702 4531.060 22 82 0 0.475263037
885 8343.694 22 71 1 0.953787482 NA NA NA NA NA
887 9919.208 19 55 1 0.989901514 NA NA NA NA NA
892 8148.956 26 82 1 0.979896798 NA NA NA NA NA
894 8118.491 22 81 1 0.546161426 3370.383 19 71 0 0.509496988
897 9312.310 23 64 1 0.997559238 NA NA NA NA NA
899 9182.428 21 73 1 0.811897568 NA NA NA NA NA
900 8873.222 22 68 1 0.979762945 NA NA NA NA NA
902 8817.309 20 75 1 0.474418575 NA NA NA NA NA
903 8631.704 22 69 1 0.973288688 NA NA NA NA NA
911 9577.510 29 81 1 0.999223524 NA NA NA NA NA
920 8367.827 27 65 1 0.999939596 NA NA NA NA NA
922 9301.979 27 77 1 0.998174321 NA NA NA NA NA
928 8924.814 27 83 1 0.990036029 NA NA NA NA NA
929 9071.670 27 75 1 0.998965063 NA NA NA NA NA
930 9060.541 21 81 1 0.307629262 3743.188 21 81 0 0.307629262
931 8129.692 22 78 1 0.738421072 3688.849 21 75 0 0.709711664
932 8139.725 22 66 1 0.988435676 NA NA NA NA NA
938 9330.340 28 68 1 0.999947686 NA NA NA NA NA
941 9781.638 26 82 1 0.979896798 NA NA NA NA NA
943 9010.214 26 85 1 0.954085092 NA NA NA NA NA
944 9845.467 16 59 1 0.612828045 NA NA NA NA NA
945 9292.751 22 58 1 0.998797095 NA NA NA NA NA
946 9879.860 27 77 1 0.998174321 NA NA NA NA NA
948 9557.862 22 71 1 0.953787482 NA NA NA NA NA
950 8701.499 25 79 1 0.976859852 NA NA NA NA NA
951 8474.594 20 72 1 0.679220102 3778.927 17 62 0 0.646344537
961 10066.037 21 71 1 0.883992214 NA NA NA NA NA
963 8558.791 29 105 1 0.583978287 3784.042 24 88 0 0.547000683
969 9436.242 26 87 1 0.921691872 NA NA NA NA NA
973 8728.427 14 71 1 0.007075591 4130.988 14 71 0 0.007075591
975 8984.511 20 82 1 0.109893723 4466.576 20 82 0 0.109893723
976 9987.146 28 59 1 0.999995947 3414.553 25 78 0 0.982484112
977 9932.142 23 84 1 0.581508030 4323.322 20 74 0 0.545321906
984 8939.801 22 75 1 0.868799228 NA NA NA NA NA
989 9415.052 22 70 1 0.964817558 NA NA NA NA NA
992 10040.653 22 92 1 0.050161420 4917.363 22 92 0 0.050161420
996 9246.277 23 68 1 0.992431736 NA NA NA NA NA
1000 10042.248 28 65 1 0.999977698 NA NA NA NA NAFinally, with the matched data, we estimate the average treatment effects, via automatic simulation, with the Zelig package.
# Treatment Effectsz1.ps <- lm(y ~ z + x1 + x2, data = m8.data)summary(z1.ps)
Call:
lm(formula = y ~ z + x1 + x2, data = m8.data)
Residuals:
Min 1Q Median 3Q Max
-1034.52 -560.36 14.86 513.64 988.72
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4055.641 404.620 10.023 <2e-16 ***
z 4966.688 81.953 60.604 <2e-16 ***
x1 8.954 21.329 0.420 0.675
x2 -1.473 6.959 -0.212 0.833
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 612.9 on 224 degrees of freedom
Multiple R-squared: 0.9436, Adjusted R-squared: 0.9429
F-statistic: 1250 on 3 and 224 DF, p-value: < 2.2e-16x <- transform(m8.data, z = 0)
x1 <- transform(m8.data, z = 1)s.out <- mean(predict(z1.ps, newdata = x1) - predict(z1.ps, newdata = x))s.out[1] 4966.688barplot(s.out, main = "Estimated average treatment effect")
Zelig package also allows to estimate the effect on the treated, and the effect on the controls.
# Average Treatment Effect on the Controlsz1c.ps <- lm(y ~ x1 + x2, data = m8.data.control)summary(z1c.ps)
Call:
lm(formula = y ~ x1 + x2, data = m8.data.control)
Residuals:
Min 1Q Median 3Q Max
-1054.58 -497.42 27.01 505.60 934.99
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3691.38 558.52 6.609 1.4e-09 ***
x1 16.45 40.63 0.405 0.686
x2 1.14 12.45 0.092 0.927
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 594.8 on 111 degrees of freedom
Multiple R-squared: 0.006571, Adjusted R-squared: -0.01133
F-statistic: 0.3671 on 2 and 111 DF, p-value: 0.6936x.out1 <- predict(z1c.ps, newdata = m8.data.treat)s.out1 <- mean(m8.data.treat$y - x.out1)
s.out1[1] 4957.543barplot(s.out1, main = "Estimated effect on the treated")
# Average Treatment Effect on the Treatedz1t.ps <- lm(y ~ x1 + x2, data = m8.data.treat)summary(z1t.ps)
Call:
lm(formula = y ~ x1 + x2, data = m8.data.treat)
Residuals:
Min 1Q Median 3Q Max
-1003.19 -526.38 -27.49 549.61 1022.52
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9383.959 595.461 15.759 <2e-16 ***
x1 3.593 25.826 0.139 0.890
x2 -4.518 8.871 -0.509 0.612
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 633.7 on 111 degrees of freedom
Multiple R-squared: 0.002691, Adjusted R-squared: -0.01528
F-statistic: 0.1498 on 2 and 111 DF, p-value: 0.8611x.out2 <- predict(z1t.ps, newdata = m8.data.control)s.out2 <- mean(x.out2 - m8.data.control$y)s.out2[1] 4974.892barplot(s.out2, main = "Estimated effect on the controls")
I hope that you found this post valuable. Feel free to reproduce the code wherever you want.