This function adds measured data columns that can be functions of unmeasured data columns.
Usage
declare_measurement(..., handler = measurement_handler, label = NULL)
measurement_handler(data, ...)Details
It is also possible to include measured variables in your declare_model call or to add variables using declare_step. However, putting latent variables in declare_model and variables-as-measured in declare_measurement helps communicate which parts of your research design are in M and which parts are in D.
Examples
# declare_measurement in use
## Two-arm randomized experiment
design <-
declare_model(
N = 500,
X = rep(c(0, 1), each = N / 2),
U = rnorm(N, sd = 0.25),
potential_outcomes(Y ~ 0.2 * Z + X + U)
) +
declare_inquiry(ATE = mean(Y_Z_1 - Y_Z_0)) +
declare_sampling(S = complete_rs(N = N, n = 200)) +
declare_assignment(Z = complete_ra(N = N, m = 100)) +
declare_measurement(Y = reveal_outcomes(Y ~ Z)) +
declare_estimator(Y ~ Z, inquiry = "ATE")
run_design(design)
#> inquiry estimand estimator term estimate std.error statistic p.value
#> 1 ATE 0.2 estimator Z 0.01267358 0.08170231 0.155119 0.8768855
#> conf.low conf.high df outcome
#> 1 -0.1484448 0.173792 198 Y
# Reveal potential outcomes according to treatment assignment
design <-
declare_model(N = 100,
potential_outcomes(Y ~ rbinom(
N, size = 1, prob = 0.1 * Z + 0.5
))) +
declare_assignment(Z = complete_ra(N, m = 50)) +
declare_measurement(Y = reveal_outcomes(Y ~ Z))
head(draw_data(design))
#> ID Y_Z_0 Y_Z_1 Z Y
#> 1 001 0 0 1 0
#> 2 002 0 1 0 0
#> 3 003 1 0 1 0
#> 4 004 0 0 1 0
#> 5 005 0 1 0 0
#> 6 006 0 0 0 0
# Generate observed measurement from a latent value
design <-
declare_model(N = 100, latent = runif(N)) +
declare_measurement(observed = rbinom(N, 1, prob = latent))
head(draw_data(design))
#> ID latent observed
#> 1 001 0.1830983 1
#> 2 002 0.1779913 0
#> 3 003 0.2305162 0
#> 4 004 0.6299517 0
#> 5 005 0.8878633 1
#> 6 006 0.7812405 1
# Index creation
library(psych)
design <-
declare_model(
N = 500,
X = rep(c(0, 1), each = N / 2),
Y_1 = 0.2 * X + rnorm(N, sd = 0.25),
Y_2 = 0.3 * X + 0.5 * rnorm(N, sd = 0.50),
Y_3 = 0.1 * X + 0.4 * rnorm(N, sd = 0.75)) +
declare_measurement(
index = fa(
r = cbind(Y_1, Y_2, Y_3),
nfactors = 1,
rotate = "varimax"
)$scores
)
draw_data(design)
#> ID X Y_1 Y_2 Y_3 MR1
#> 1 001 0 0.217380106 -0.075675091 -0.273417273 0.412030020
#> 2 002 0 0.222766155 0.040045057 0.068188240 0.433643954
#> 3 003 0 -0.133464455 -0.627876517 -0.167340895 -0.882196184
#> 4 004 0 0.220755097 -0.152654970 0.016001543 0.426431205
#> 5 005 0 -0.161018274 0.079815279 -0.877468855 -0.990166503
#> 6 006 0 -0.218831231 0.241356980 -0.259024577 -1.200553515
#> 7 007 0 -0.246598450 0.078295894 0.395429537 -1.298817916
#> 8 008 0 -0.275677935 0.328818248 0.362149026 -1.407150961
#> 9 009 0 0.225131916 -0.436397205 0.132020471 0.444070594
#> 10 010 0 -0.256536159 -0.001023887 -0.039901078 -1.337906870
#> 11 011 0 0.110914583 0.087726041 0.008606862 0.019867905
#> 12 012 0 0.054162826 0.200558561 0.339314475 -0.188174078
#> 13 013 0 -0.496073414 0.073525768 0.015818842 -2.222869861
#> 14 014 0 0.200904045 -0.200135476 0.449023466 0.355784577
#> 15 015 0 0.104682414 0.451855916 -0.218988121 -0.005510272
#> 16 016 0 0.114106816 0.110146268 0.424594269 0.034073367
#> 17 017 0 -0.184295058 -0.041376035 0.113811745 -1.069952235
#> 18 018 0 0.392526576 0.016546420 0.190297611 1.061698328
#> 19 019 0 -0.219627064 0.039437366 0.411273110 -1.198958051
#> 20 020 0 -0.163798250 0.387829283 -0.086533612 -0.996583356
#> 21 021 0 -0.318549297 0.032387232 0.217773189 -1.565605891
#> 22 022 0 0.050107468 0.269951804 0.066571294 -0.204969342
#> 23 023 0 -0.154017736 -0.193478787 0.579486375 -0.954893846
#> 24 024 0 0.089035428 0.231729681 -0.010408261 -0.061483216
#> 25 025 0 0.022550626 0.006292297 0.206091924 -0.305240180
#> 26 026 0 -0.061213101 -0.228345385 0.302038848 -0.613533798
#> 27 027 0 -0.154837597 0.042941607 -0.069678647 -0.962428302
#> 28 028 0 0.113332665 -0.193294527 0.063290837 0.029897880
#> 29 029 0 0.619102099 -0.299293267 -0.197890834 1.897453717
#> 30 030 0 0.030779401 -0.453425077 -0.037799404 -0.275023915
#> 31 031 0 -0.036308492 0.629662060 0.040092629 -0.525419420
#> 32 032 0 0.062599698 -0.029765402 0.135857749 -0.157577401
#> 33 033 0 -0.357830314 -0.021351018 -0.094357015 -1.712456427
#> 34 034 0 0.110558219 -0.158027374 0.200699476 0.020366063
#> 35 035 0 -0.075878972 0.140828386 0.263367882 -0.668965807
#> 36 036 0 -0.279154508 0.392819373 -0.282952594 -1.424005232
#> 37 037 0 -0.211636340 0.314882464 0.377769705 -1.170386379
#> 38 038 0 0.248955856 -0.126190620 -0.485129499 0.527582915
#> 39 039 0 0.423391913 0.118834885 0.162078291 1.175297659
#> 40 040 0 0.327583665 -0.108834012 0.415644437 0.823416963
#> 41 041 0 0.058880723 -0.357692283 0.100707260 -0.170629034
#> 42 042 0 0.270850300 -0.455469525 -0.092393622 0.611718843
#> 43 043 0 -0.436239071 -0.338246923 0.186525048 -1.999639170
#> 44 044 0 -0.209821274 -0.117769769 0.478897072 -1.161892989
#> 45 045 0 0.067381024 -0.120215915 0.142841723 -0.139620998
#> 46 046 0 0.266371074 -0.315413743 0.148979316 0.596218362
#> 47 047 0 -0.235421529 0.189875519 0.649388469 -1.256316132
#> 48 048 0 0.395305310 0.360914973 -0.159108391 1.068945837
#> 49 049 0 0.063155320 0.324242468 -0.457313784 -0.160019060
#> 50 050 0 0.372018223 -0.004126818 -0.567700332 0.981472968
#> 51 051 0 -0.066546019 -0.241866450 -0.253920209 -0.636505127
#> 52 052 0 -0.472462616 0.454567372 0.327889920 -2.134818219
#> 53 053 0 0.289843541 -0.510039145 -0.334247945 0.680611413
#> 54 054 0 -0.291381415 0.322881968 0.261926629 -1.465754499
#> 55 055 0 0.028047709 -0.136286184 -0.281403929 -0.287434161
#> 56 056 0 0.022780494 0.175706977 -0.225286772 -0.307418236
#> 57 057 0 0.117396704 -0.038323685 0.046340949 0.044389022
#> 58 058 0 -0.044210198 -0.158327922 -0.018043402 -0.552801806
#> 59 059 0 -0.126188280 -0.198373080 -0.263779267 -0.857060964
#> 60 060 0 0.054221451 -0.097421553 -0.248201566 -0.190631485
#> 61 061 0 -0.182729973 -0.164122239 0.171251340 -1.063491530
#> 62 062 0 0.222471683 -0.070173225 -0.007422617 0.432408735
#> 63 063 0 0.072681423 -0.004118845 0.165861075 -0.120217474
#> 64 064 0 -0.012157550 -0.373496131 0.249608298 -0.432187298
#> 65 065 0 -0.218733880 0.534232367 0.172797301 -1.198430855
#> 66 066 0 -0.334055527 -0.084160784 0.118843226 -1.623169729
#> 67 067 0 0.370619362 0.238017230 -0.104770088 0.978391013
#> 68 068 0 -0.064956835 -0.058389923 -0.513624215 -0.632679041
#> 69 069 0 0.450020393 -0.412014845 -0.243087954 1.272737541
#> 70 070 0 -0.583504557 0.096180053 0.455508464 -2.543377421
#> 71 071 0 0.008763528 0.114373700 0.290409778 -0.355978744
#> 72 072 0 -0.220392336 0.378892630 0.084446114 -1.204658017
#> 73 073 0 -0.233414644 -0.134648320 0.770466753 -1.247291802
#> 74 074 0 -0.127586736 -0.022839337 0.135902667 -0.860334646
#> 75 075 0 -0.312795146 -0.017953238 -0.368280700 -1.547688411
#> 76 076 0 -0.045720226 -0.123568928 -0.018432035 -0.558478936
#> 77 077 0 -0.289342791 0.580239495 0.273018165 -1.458861285
#> 78 078 0 -0.026091030 -0.088914997 -0.310959315 -0.487782149
#> 79 079 0 0.061437202 0.462992707 0.366904148 -0.161850660
#> 80 080 0 0.385898651 -0.115483439 0.648583835 1.040292981
#> 81 081 0 0.188556714 -0.346126570 0.123659654 0.308628188
#> 82 082 0 -0.072572403 -0.041372528 0.083160542 -0.657319356
#> 83 083 0 0.136102535 -0.124483077 -0.446590827 0.110814402
#> 84 084 0 0.185967916 -0.478476347 0.237854245 0.300103840
#> 85 085 0 -0.211913045 -0.560607086 0.296735233 -1.169490621
#> 86 086 0 -0.258879193 0.095538542 0.056883024 -1.346253997
#> 87 087 0 0.313823441 0.031941636 0.107389940 0.770355589
#> 88 088 0 0.289086899 -0.428939183 0.077300218 0.680038572
#> 89 089 0 0.063311964 0.482700361 0.180355624 -0.156085826
#> 90 090 0 -0.274764656 0.205957999 0.147599110 -1.404714410
#> 91 091 0 -0.416247157 -0.161005047 -0.302496790 -1.929160448
#> 92 092 0 -0.199126699 0.436575023 -0.208655482 -1.127981113
#> 93 093 0 -0.061053640 -0.111389088 -0.304112948 -0.616866651
#> 94 094 0 0.156597952 0.559966215 0.242896829 0.188765542
#> 95 095 0 0.365168602 -0.329116167 -0.258595643 0.958890972
#> 96 096 0 -0.312437239 0.195257182 -0.171581578 -1.545781638
#> 97 097 0 -0.054028338 -0.279291703 -0.071253686 -0.589064413
#> 98 098 0 0.623101278 0.137941337 0.550332034 1.915477866
#> 99 099 0 0.375032830 0.085614596 -0.127495020 0.994981470
#> 100 100 0 0.143184036 0.365911755 0.209168229 0.139532636
#> 101 101 0 -0.277796872 0.221153853 0.125965332 -1.416088633
#> 102 102 0 -0.012250570 0.307711734 0.103212513 -0.435267970
#> 103 103 0 -0.074942017 0.313930571 0.046593716 -0.667266200
#> 104 104 0 -0.154497708 0.346919996 -0.308395784 -0.963423949
#> 105 105 0 -0.182455870 -0.119108972 -0.143312252 -1.064471099
#> 106 106 0 0.019148115 -0.325266858 -0.248436537 -0.319604283
#> 107 107 0 -0.217049372 0.167763011 0.094498007 -1.191667355
#> 108 108 0 0.219938245 0.005370203 0.454146621 0.425583071
#> 109 109 0 -0.118934998 0.073630856 0.085630710 -0.828929599
#> 110 110 0 0.239403437 -0.009721258 -0.480894909 0.491992670
#> 111 111 0 0.424566607 0.105745669 -0.115188678 1.178026629
#> 112 112 0 -0.031267056 0.392360006 0.081865257 -0.505892702
#> 113 113 0 0.333221796 0.063069060 0.573216711 0.844714902
#> 114 114 0 0.123319804 0.006169494 0.049860387 0.066173825
#> 115 115 0 -0.197948327 -0.122449027 0.043390390 -1.120597240
#> 116 116 0 0.002978290 -0.071108673 -0.713185005 -0.382809722
#> 117 117 0 0.038259722 -0.004177953 0.562301776 -0.245049955
#> 118 118 0 0.100735019 -0.094159654 0.622700729 -0.013598348
#> 119 119 0 -0.007396155 0.272948932 -0.359077180 -0.419982357
#> 120 120 0 -0.178393372 0.013068190 0.071749916 -1.048544658
#> 121 121 0 -0.101941087 -0.286197252 0.302524108 -0.763862180
#> 122 122 0 0.002098044 -0.290139601 0.173966047 -0.380190813
#> 123 123 0 0.289798277 -0.207721672 0.435321613 0.684187981
#> 124 124 0 -0.193862806 -0.473091748 0.492186857 -1.101873603
#> 125 125 0 -0.134627008 -0.179599653 0.312289084 -0.884870755
#> 126 126 0 -0.235485966 0.709076862 0.289813887 -1.260113755
#> 127 127 0 0.222196606 0.218973670 0.741717360 0.435050862
#> 128 128 0 0.375316554 0.002702836 0.049271316 0.997307357
#> 129 129 0 -0.009774418 0.076507846 -0.080864737 -0.426578585
#> 130 130 0 -0.046150934 0.055415413 -0.143512253 -0.561304159
#> 131 131 0 -0.430347472 0.426212670 0.162615527 -1.980107111
#> 132 132 0 0.384524967 0.216397040 0.304077310 1.032260652
#> 133 133 0 -0.109007421 -0.426312699 -0.135563106 -0.792191148
#> 134 134 0 0.039720643 0.009951222 -0.177262919 -0.244084756
#> 135 135 0 0.095989642 0.309193474 -0.298016943 -0.037708579
#> 136 136 0 0.115310584 -0.036676954 0.153835298 0.037314985
#> 137 137 0 0.111065292 -0.273437738 -0.057669193 0.021020915
#> 138 138 0 -0.258580573 -0.263876460 0.309688130 -1.342663407
#> 139 139 0 -0.099251132 -0.697564560 -0.021753932 -0.754721994
#> 140 140 0 0.060235214 -0.002955713 -0.217186086 -0.168485284
#> 141 141 0 0.102423148 -0.014350383 0.103307035 -0.010665481
#> 142 142 0 0.119665595 0.017233278 0.353906403 0.054447713
#> 143 143 0 0.064398874 0.047659297 -0.094866437 -0.152512528
#> 144 144 0 -0.288559429 0.003547435 0.373596360 -1.453788498
#> 145 145 0 -0.074648992 0.210268690 -0.043037073 -0.666431894
#> 146 146 0 -0.355366942 -0.258630634 -0.150619847 -1.703038195
#> 147 147 0 0.302815728 0.145414486 0.577898469 0.732166648
#> 148 148 0 -0.031031253 -0.294031162 -0.161066137 -0.504583455
#> 149 149 0 -0.426457179 0.079440064 0.128723824 -1.964983378
#> 150 150 0 -0.239140276 -0.217930249 0.406085414 -1.270384729
#> 151 151 0 0.412233878 0.223266065 0.181482874 1.133897797
#> 152 152 0 0.092371549 0.115066909 -0.081145853 -0.049256782
#> 153 153 0 0.400409729 -0.261279856 0.117208335 1.091153801
#> 154 154 0 -0.413909494 0.209471284 -0.392505474 -1.922073031
#> 155 155 0 0.007513882 0.031649294 -0.218254046 -0.363391703
#> 156 156 0 -0.218844938 -0.036859763 0.204999702 -1.197084558
#> 157 157 0 0.212350547 -0.416802720 -0.022561765 0.395871291
#> 158 158 0 0.137964131 0.013234240 0.236802674 0.121375952
#> 159 159 0 0.385413901 -0.116181707 0.041637543 1.034897533
#> 160 160 0 0.196430905 0.032043259 -0.130034244 0.335179435
#> 161 161 0 0.080466449 -0.004299488 -0.133103811 -0.093227643
#> 162 162 0 0.038898268 0.267051803 -0.204283867 -0.247988670
#> 163 163 0 0.004361478 -0.086406703 -0.403032541 -0.375814121
#> 164 164 0 0.162189077 0.211539631 -0.039229172 0.208703481
#> 165 165 0 -0.253070268 -0.380936986 0.221109301 -1.322508284
#> 166 166 0 0.143678624 -0.130585288 -0.280176953 0.139813523
#> 167 167 0 0.151350945 -0.195943406 0.141638448 0.170848121
#> 168 168 0 -0.666993453 0.207201325 -0.007805150 -2.854925848
#> 169 169 0 -0.316296167 0.060175064 0.444405227 -1.556010194
#> 170 170 0 0.266709068 -0.161686120 0.367438204 0.598343881
#> 171 171 0 0.242327912 -0.744259697 0.035690310 0.507881247
#> 172 172 0 -0.296297338 0.080623571 -0.189270292 -1.485935631
#> 173 173 0 -0.059964552 0.106023804 -0.099234812 -0.612221087
#> 174 174 0 -0.226739406 0.260652260 -0.415341711 -1.230755865
#> 175 175 0 0.039493785 0.009074836 -0.157197518 -0.244801375
#> 176 176 0 -0.183175602 0.100715549 -0.223781807 -1.068211146
#> 177 177 0 -0.277992325 0.161529719 -0.040577304 -1.417636929
#> 178 178 0 0.365503952 0.533543355 -0.025539264 0.959150323
#> 179 179 0 -0.395397535 -0.422020270 0.263439248 -1.848043161
#> 180 180 0 0.285521986 -0.288727774 -0.396675339 0.663665760
#> 181 181 0 0.098967699 -0.219579407 -0.315379897 -0.025358497
#> 182 182 0 -0.127216197 0.427853265 -0.686092801 -0.865084762
#> 183 183 0 -0.142636615 0.676111451 -0.241918037 -0.920104541
#> 184 184 0 -0.464345195 0.668235510 0.020420578 -2.107236864
#> 185 185 0 0.056583017 -0.097588461 0.418133586 -0.177945966
#> 186 186 0 -0.087640943 -0.232886794 -0.208675654 -0.714206625
#> 187 187 0 0.046331830 -0.261034255 0.188811002 -0.216738627
#> 188 188 0 -0.165286968 -0.028430497 -0.192350372 -1.001571945
#> 189 189 0 0.104825989 0.075526765 0.142413253 -0.001800984
#> 190 190 0 -0.189312623 -0.321138902 0.100488587 -1.087804481
#> 191 191 0 0.086418103 0.378180498 -0.206532517 -0.072720925
#> 192 192 0 0.143941045 0.335795937 -0.124178091 0.140431729
#> 193 193 0 0.258173947 0.526913316 -0.676614503 0.558715913
#> 194 194 0 0.619636242 0.053945499 -0.158380695 1.898693924
#> 195 195 0 0.089295357 0.057231547 0.046090097 -0.059708805
#> 196 196 0 0.304366304 -0.252649045 -0.154232413 0.734637083
#> 197 197 0 0.080188432 -0.038635845 -0.427319179 -0.095908904
#> 198 198 0 -0.039494795 -0.527334171 0.183222705 -0.533171145
#> 199 199 0 0.002717621 0.119382569 0.086926275 -0.379541101
#> 200 200 0 -0.024244494 -0.102678543 0.214172433 -0.477801371
#> 201 201 0 0.284748470 0.327291867 -0.156190552 0.660548010
#> 202 202 0 0.010076871 -0.113186874 -0.080454977 -0.352705736
#> 203 203 0 -0.103109328 -0.437533614 -0.198268465 -0.770739519
#> 204 204 0 -0.235469220 0.223499345 -0.048628363 -1.260731826
#> 205 205 0 -0.496045370 0.205822952 0.400633324 -2.220842452
#> 206 206 0 -0.141926976 0.171214029 -0.312784714 -0.916519596
#> 207 207 0 -0.307935887 -0.350313950 0.043341582 -1.526376800
#> 208 208 0 -0.353530017 0.247539396 -0.285913270 -1.698441990
#> 209 209 0 -0.388232317 -0.596369725 0.269526809 -1.821053645
#> 210 210 0 -0.053105724 0.008888002 -0.196202730 -0.587187629
#> 211 211 0 -0.556081683 0.421569064 0.273043772 -2.444025946
#> 212 212 0 -0.221068993 -0.551540446 -0.138214495 -1.205930965
#> 213 213 0 -0.001027118 -0.074549775 -0.070056394 -0.393779072
#> 214 214 0 -0.300169224 0.267650838 0.198747554 -1.498449437
#> 215 215 0 0.023184051 -0.173218735 0.510288151 -0.300600246
#> 216 216 0 0.043882319 -0.184581730 -0.189900933 -0.228249262
#> 217 217 0 0.187691751 -0.204301790 -0.323239341 0.302388138
#> 218 218 0 -0.157127969 -0.307679866 0.148951782 -0.968631185
#> 219 219 0 -0.109036021 0.355757527 -0.495134834 -0.796576846
#> 220 220 0 0.458170249 -0.175110212 0.033031850 1.303842493
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#> 390 390 1 0.355820035 -0.013995264 0.180092563 0.926090807
#> 391 391 1 0.512833875 0.106754209 0.110902267 1.505514591
#> 392 392 1 0.277631499 0.364813656 0.089742848 0.635609203
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#> 394 394 1 -0.093532500 0.531568164 0.512283735 -0.733787599
#> 395 395 1 0.401359891 0.360425275 0.034890414 1.092471501
#> 396 396 1 0.411592670 0.231579824 -0.301318072 1.128637152
#> 397 397 1 -0.345055111 0.442713861 0.688672907 -1.661871617
#> 398 398 1 0.406604851 0.269065574 0.033174366 1.112091832
#> 399 399 1 0.009684093 0.168060062 0.008859430 -0.354397259
#> 400 400 1 0.274099402 0.245197339 0.188911135 0.623475185
#> 401 401 1 0.394597488 0.252582467 -0.319648844 1.065673503
#> 402 402 1 -0.032039515 0.355972338 0.539112969 -0.505930430
#> 403 403 1 0.418134409 0.519733628 -0.062413961 1.153438522
#> 404 404 1 -0.123388921 0.567887205 -0.237058785 -0.848658839
#> 405 405 1 0.719243494 0.097950308 0.474436152 2.270381847
#> 406 406 1 0.211027293 0.441919321 -0.731166871 0.384417948
#> 407 407 1 0.186079713 0.107542680 -0.073007827 0.297063687
#> 408 408 1 0.211821026 0.496254695 0.202438070 0.392748940
#> 409 409 1 0.153258566 0.453767065 0.123546806 0.176008474
#> 410 410 1 0.041910919 0.284771189 -0.293953659 -0.237438279
#> 411 411 1 0.076873770 0.408328170 0.071745326 -0.106416445
#> 412 412 1 -0.215094478 0.115452667 0.578790512 -1.181423188
#> 413 413 1 0.538258400 0.708540309 0.093396973 1.597704702
#> 414 414 1 0.144371436 0.272651133 -0.060317907 0.142574526
#> 415 415 1 0.438064776 -0.159395383 -0.068232617 1.228908063
#> 416 416 1 0.288709322 0.349647959 -0.101777101 0.675445377
#> 417 417 1 0.529714727 -0.025879698 -0.078850369 1.567125419
#> 418 418 1 0.209059898 0.033342483 -0.177398669 0.381558560
#> 419 419 1 0.371337287 0.042577348 0.304112636 0.984008836
#> 420 420 1 0.475510491 0.123457337 0.524328124 1.370015373
#> 421 421 1 0.363725147 0.325695281 -0.269345197 0.951698746
#> 422 422 1 -0.006648481 0.366241246 -0.039158555 -0.415574593
#> 423 423 1 0.473796470 0.456345321 -0.309852352 1.357813305
#> 424 424 1 -0.154030209 0.544280689 -0.157605702 -0.961341564
#> 425 425 1 0.155598151 0.018718225 0.208599936 0.186351024
#> 426 426 1 0.429148034 -0.161064471 0.360589447 1.198513166
#> 427 427 1 0.263932757 0.245679699 0.007963092 0.584833011
#> 428 428 1 0.304720070 0.044483394 0.114920092 0.736729014
#> 429 429 1 -0.133495153 0.737723560 0.262553620 -0.883498377
#> 430 430 1 0.350627584 -0.113090107 0.237602970 0.907518021
#> 431 431 1 0.293564708 0.361661842 -0.251522969 0.692463365
#> 432 432 1 0.390496602 0.342244703 -0.583695459 1.048706130
#> 433 433 1 0.469335968 0.462003784 -0.230239220 1.341789276
#> 434 434 1 -0.075999218 0.020105004 -0.334579901 -0.672631970
#> 435 435 1 -0.304599754 0.281046667 0.381301013 -1.513772301
#> 436 436 1 0.024201436 0.256567702 0.794543267 -0.296330101
#> 437 437 1 0.062940884 0.190792990 0.126114928 -0.156979144
#> 438 438 1 0.479578829 0.802273473 -0.475856343 1.377244624
#> 439 439 1 0.206193084 0.442025800 0.468547458 0.373683449
#> 440 440 1 0.553544706 0.632412747 -0.342551275 1.651806022
#> 441 441 1 0.280829473 0.385806524 0.126967822 0.647589342
#> 442 442 1 0.014790294 0.319638024 0.756838296 -0.331501153
#> 443 443 1 0.352518250 0.308389902 -0.101664856 0.911333000
#> 444 444 1 0.335581614 0.404324249 0.031923781 0.849282939
#> 445 445 1 0.278463223 0.424008984 0.293579391 0.639731280
#> 446 446 1 0.242438434 0.274235388 0.183607110 0.506376861
#> 447 447 1 -0.393847639 0.493552407 -0.191142886 -1.847526750
#> 448 448 1 0.115927644 0.560279300 -0.273465042 0.035419970
#> 449 449 1 0.176406430 0.328173809 -0.240804710 0.259719214
#> 450 450 1 0.062892285 -0.433501078 -0.011059390 -0.156262602
#> 451 451 1 0.403778700 0.037065128 0.265922846 1.103667997
#> 452 452 1 0.235249553 0.152192773 -0.406647175 0.476641431
#> 453 453 1 0.264838604 0.621256737 -0.192074378 0.585962150
#> 454 454 1 0.165624459 0.282731321 0.368935904 0.223627222
#> 455 455 1 0.592530840 0.105088986 0.339010267 1.801354614
#> 456 456 1 0.632295763 0.130563338 -0.297423977 1.944434691
#> 457 457 1 0.132566962 0.331665713 -0.195066459 0.097994647
#> 458 458 1 0.214809485 0.110957139 0.359148863 0.405778470
#> 459 459 1 0.508636953 0.134884822 -0.352036495 1.487179285
#> 460 460 1 0.672536574 0.352983296 0.319787218 2.096181981
#> 461 461 1 0.246096890 -0.213272654 0.297578662 0.521908242
#> 462 462 1 0.361513686 0.544187799 0.345384752 0.946580990
#> 463 463 1 0.724906724 0.438527224 0.012495512 2.287629323
#> 464 464 1 0.042222992 0.164276891 0.058077311 -0.233863286
#> 465 465 1 0.171005672 0.052406722 0.046969756 0.242229111
#> 466 466 1 0.242710566 0.341620079 -0.566924919 0.502738352
#> 467 467 1 0.550641780 0.338488122 0.384299151 1.646203974
#> 468 468 1 0.279122275 -0.007100794 -0.051802692 0.641296004
#> 469 469 1 0.572513612 0.103068453 -0.618714537 1.721706146
#> 470 470 1 0.113508330 0.690465654 -0.074957680 0.027303226
#> 471 471 1 -0.504212686 0.447001093 0.535641863 -2.250879558
#> 472 472 1 0.136867983 0.804204459 -0.026297229 0.113594468
#> 473 473 1 0.525701500 0.183512612 0.089431491 1.552722484
#> 474 474 1 0.016314914 0.338455635 -0.018235546 -0.330524416
#> 475 475 1 0.636733530 0.200440373 -0.150352194 1.961514542
#> 476 476 1 0.621667071 0.389034737 0.143602031 1.907073630
#> 477 477 1 0.124420041 0.523859128 -0.249419857 0.067042054
#> 478 478 1 0.127689472 0.546244808 -0.368568814 0.078353305
#> 479 479 1 0.227806761 0.159170529 0.231137107 0.452910642
#> 480 480 1 0.188323618 0.409877049 0.169920945 0.305969611
#> 481 481 1 -0.070744137 0.523724581 0.867571404 -0.647452176
#> 482 482 1 0.213946965 0.307527951 0.380822182 0.402181448
#> 483 483 1 0.111696129 0.455776310 0.709214566 0.025909626
#> 484 484 1 0.559785873 0.455480783 0.144728186 1.678247283
#> 485 485 1 0.431526468 0.383201108 -0.283958320 1.201980061
#> 486 486 1 -0.011772904 1.013954007 0.152849289 -0.435143833
#> 487 487 1 0.232782383 0.128294791 0.572672333 0.473409439
#> 488 488 1 0.725883954 0.205667410 -0.266652563 2.290219862
#> 489 489 1 0.091094547 0.333029917 0.231458382 -0.052715364
#> 490 490 1 -0.119800858 0.767453538 -0.012440133 -0.834613363
#> 491 491 1 -0.091042006 0.224075848 0.214458832 -0.725511963
#> 492 492 1 0.153442378 0.313998606 0.010343507 0.176398150
#> 493 493 1 0.058433986 0.066710933 0.124644771 -0.173300758
#> 494 494 1 0.618834530 -0.034485961 0.162034667 1.897877753
#> 495 495 1 0.087529520 0.465641239 0.431231089 -0.065064649
#> 496 496 1 0.193460308 -0.100862776 0.111113904 0.326000170
#> 497 497 1 0.267725429 0.540655402 0.325004548 0.599922144
#> 498 498 1 0.432941533 0.215426945 0.166717790 1.210346303
#> 499 499 1 0.245263332 0.544315810 0.020264479 0.515104070
#> 500 500 1 -0.162453328 0.284172938 -0.053952611 -0.991136176