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 0.1343672 0.08278017 1.623181 0.1061418
#> conf.low conf.high df outcome
#> 1 -0.02887678 0.2976111 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 1 0 0 1
#> 2 002 1 1 0 1
#> 3 003 0 0 0 0
#> 4 004 1 1 1 1
#> 5 005 1 1 0 1
#> 6 006 1 0 0 1
# 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 0.85799465 1
#> 2 002 0.65768689 1
#> 3 003 0.04111667 0
#> 4 004 0.08502660 0
#> 5 005 0.67294424 0
#> 6 006 0.37739894 0
# 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 -0.2432641846 0.022031261 0.3338628478 -0.426159570
#> 2 002 0 0.1489107558 0.017082577 -0.1876286329 -0.427686004
#> 3 003 0 0.2347926889 -0.183423370 0.3127436184 -1.138190355
#> 4 004 0 -0.0934134497 0.379648159 0.3717280497 0.783825034
#> 5 005 0 0.3949096222 -0.444719430 -0.0770785600 -2.011565075
#> 6 006 0 -0.0201315515 0.117211641 -0.1201636863 -0.085547075
#> 7 007 0 -0.5973338081 0.212894794 0.1899633847 0.241086878
#> 8 008 0 -0.0269761478 -0.696345090 0.2139565749 -2.869940085
#> 9 009 0 0.0353797438 0.329510636 0.2587229311 0.615292275
#> 10 010 0 -0.1048781306 0.102563417 0.2834044157 -0.153750907
#> 11 011 0 0.0846300701 0.207896370 0.1594165609 0.205299669
#> 12 012 0 -0.3154070644 -0.252194598 0.1420986094 -1.346839453
#> 13 013 0 -0.2177552048 0.210856786 0.2435492791 0.220041588
#> 14 014 0 -0.6315128641 -0.461433297 0.0109882529 -2.042323911
#> 15 015 0 0.1472454940 0.109873512 0.2358991370 -0.133954608
#> 16 016 0 0.0087485309 -0.107978151 0.0414175595 -0.860756981
#> 17 017 0 0.2935792319 -0.175911097 0.2718136272 -1.112272718
#> 18 018 0 0.1549847490 0.060897782 -0.2252405859 -0.276882720
#> 19 019 0 -0.1123285835 0.250603393 0.0371781464 0.362782021
#> 20 020 0 -0.0095894937 0.086326046 0.7062239648 -0.233734651
#> 21 021 0 -0.1683284051 0.148834427 0.0683696971 0.016674711
#> 22 022 0 0.5037635202 -0.867327398 -0.3030993504 -3.440592632
#> 23 023 0 -0.1024661726 -0.154567972 0.3265619601 -1.030682867
#> 24 024 0 0.5202312761 0.108766578 -0.3327058337 -0.119399321
#> 25 025 0 -0.0195100735 0.391454722 -0.0152032563 0.841824924
#> 26 026 0 -0.5945966907 0.016738913 -0.3520235515 -0.398131411
#> 27 027 0 0.2759267899 -0.249137440 0.0276357294 -1.348171243
#> 28 028 0 -0.2697786530 0.139347660 0.0459415162 -0.011402205
#> 29 029 0 0.0136957799 0.378076904 0.2049357836 0.783923237
#> 30 030 0 -0.1404540513 0.011149694 0.5677756536 -0.478362820
#> 31 031 0 0.1363860535 -0.169846845 -0.2094408925 -1.062016021
#> 32 032 0 -0.2685274187 0.219661655 -0.5179873106 0.290963814
#> 33 033 0 -0.2515770632 -0.085126810 -0.2760843019 -0.758803622
#> 34 034 0 0.4417453270 -0.208338061 -0.2079909242 -1.202137767
#> 35 035 0 -0.1913080888 -0.233411772 -0.0789359470 -1.275204568
#> 36 036 0 0.0708053726 0.769350651 0.4164150782 2.102165142
#> 37 037 0 -0.0317078241 -0.115268338 0.0700673459 -0.885830404
#> 38 038 0 0.0083360888 0.262782079 0.2526761353 0.389438302
#> 39 039 0 -0.2202999595 -0.010630455 -0.0523811539 -0.517931286
#> 40 040 0 -0.0796833786 0.303205095 -0.4387286919 0.565387417
#> 41 041 0 0.0738873065 -0.081507480 0.0960110202 -0.775491912
#> 42 042 0 -0.1984017761 0.392411810 -0.4403904041 0.872452897
#> 43 043 0 0.5170559792 -0.184617408 0.0678544250 -1.137993990
#> 44 044 0 -0.0311323812 -0.400396076 0.0678277977 -1.855584074
#> 45 045 0 -0.0132521365 0.265555088 -0.1085810783 0.418232650
#> 46 046 0 0.0606858607 -0.295939907 -0.0353787955 -1.497674893
#> 47 047 0 0.0698126733 0.132669764 0.0403500626 -0.043969567
#> 48 048 0 -0.0955417446 0.428606007 0.0760894958 0.965734571
#> 49 049 0 -0.0723655633 0.103399594 0.3172202074 -0.153629767
#> 50 050 0 0.1454499684 0.021187540 -0.1457777170 -0.415788107
#> 51 051 0 -0.0729511621 0.303833496 0.3474835171 0.526588985
#> 52 052 0 0.7710605845 0.199838046 0.0776134676 0.161626577
#> 53 053 0 0.0905161753 -0.116516419 -0.5276775939 -0.862756047
#> 54 054 0 -0.4725337905 -0.042623817 -0.3461426281 -0.604002059
#> 55 055 0 -0.2683945086 0.475666954 -0.1056303751 1.140388516
#> 56 056 0 -0.0811096778 0.222048158 -0.2085385685 0.277450896
#> 57 057 0 -0.1132267930 -0.130678565 -0.1472371565 -0.924554211
#> 58 058 0 -0.2871366947 0.200083763 0.4707912529 0.173695945
#> 59 059 0 -0.2240969970 -0.569352650 -0.1054157075 -2.415545041
#> 60 060 0 0.0212834894 0.199347355 0.3574364171 0.167852714
#> 61 061 0 0.4173543910 0.614421734 -0.0434261600 1.588654431
#> 62 062 0 0.0696536978 0.134068455 0.1262643304 -0.043658569
#> 63 063 0 0.5140058055 -0.165547162 -0.4510057450 -1.046153150
#> 64 064 0 0.2874584130 0.241336774 0.2433525065 0.308639457
#> 65 065 0 -0.6164292389 0.011791750 0.1054996743 -0.438011930
#> 66 066 0 -0.0474594339 -0.540941264 -0.6653118852 -2.295171144
#> 67 067 0 -0.0851273648 0.016414623 -0.5851532047 -0.402371766
#> 68 068 0 -0.0997664663 -0.157135308 -0.0844976968 -1.018198585
#> 69 069 0 -0.0983699426 -0.304792004 0.7131326498 -1.561816071
#> 70 070 0 -0.2942987228 -0.168517558 -0.0707559913 -1.051816899
#> 71 071 0 -0.2342953794 -0.045385099 0.1242561241 -0.644881901
#> 72 072 0 -0.5123561370 0.069302252 0.2964247804 -0.255392295
#> 73 073 0 -0.2426594185 0.453790120 -0.2066297880 1.070439506
#> 74 074 0 -0.0690292650 -0.177225841 0.0275570683 -1.093259605
#> 75 075 0 -0.6387459809 0.345692036 0.4345831137 0.681354999
#> 76 076 0 0.2763092782 0.028714059 -0.1068702001 -0.396111077
#> 77 077 0 0.0489900471 0.093693706 0.5239981823 -0.200981976
#> 78 078 0 -0.1192567524 -0.235080531 0.1854386242 -1.296730371
#> 79 079 0 0.2255709237 -0.183730652 -0.0615159649 -1.119569187
#> 80 080 0 -0.2884415655 -0.012879349 0.4095408200 -0.547478547
#> 81 081 0 -0.6453887094 0.247168315 0.3375409542 0.351456137
#> 82 082 0 0.2600110357 0.073200568 -0.1804908717 -0.240490526
#> 83 083 0 0.3949402890 -0.420532787 -0.1511829025 -1.925456471
#> 84 084 0 0.1286301468 -0.381277600 -0.2503943635 -1.778837197
#> 85 085 0 0.1353611952 0.023974553 0.0367585946 -0.415464341
#> 86 086 0 0.0897180621 -0.045632180 -0.7209797190 -0.611606553
#> 87 087 0 0.2287571752 -0.374234328 -0.6660429977 -1.736334804
#> 88 088 0 -0.1332201734 -0.045494798 0.0552149433 -0.644696678
#> 89 089 0 0.2224241195 -0.202808719 -0.5667552870 -1.158191399
#> 90 090 0 -0.1559644002 -0.196531754 -0.0514437638 -1.152238418
#> 91 091 0 0.1840198955 -0.426234333 -0.2369293494 -1.934107970
#> 92 092 0 0.2512064258 -0.043170352 -0.1568731358 -0.637283049
#> 93 093 0 -0.1641797320 0.037187748 0.1171273978 -0.365737873
#> 94 094 0 0.1907086883 0.302498320 0.1035237761 0.526812744
#> 95 095 0 -0.0670205117 -0.146414806 -0.0415227071 -0.984937760
#> 96 096 0 -0.1218226072 -0.417609555 -0.1977882719 -1.897664573
#> 97 097 0 -0.2680359686 0.031977751 0.2407701514 -0.386763794
#> 98 098 0 -0.1142622085 -0.045346195 0.4771787999 -0.666620008
#> 99 099 0 0.2951934220 -0.063142496 0.0820890862 -0.718912366
#> 100 100 0 -0.4823802482 -0.304824429 0.0227840180 -1.514689289
#> 101 101 0 0.2607981818 0.138236842 -0.2852521843 -0.013867472
#> 102 102 0 -0.3572808209 -0.111722109 0.0654732976 -0.863806256
#> 103 103 0 -0.0731736238 0.387690677 0.1419009314 0.822484588
#> 104 104 0 0.0836641757 -0.355477268 0.0629604086 -1.705970633
#> 105 105 0 0.2056274841 -0.092421816 -0.5811465577 -0.781466729
#> 106 106 0 -0.2317792220 -0.111207278 -0.0540676430 -0.859609778
#> 107 107 0 0.4236045535 -0.062396334 0.2141005548 -0.727049232
#> 108 108 0 0.0812596502 -0.144754781 -0.1834958583 -0.976364014
#> 109 109 0 -0.2755698120 0.039448330 0.1460251507 -0.356218977
#> 110 110 0 -0.0409975046 -0.463817583 -0.2294889317 -2.055611153
#> 111 111 0 -0.0220115249 0.377600807 0.1346015336 0.787014390
#> 112 112 0 0.1844273021 -0.083722843 -0.2669583961 -0.767522849
#> 113 113 0 -0.3781345036 0.002755259 0.2424905931 -0.482964005
#> 114 114 0 -0.0533830958 -0.304191991 0.2350916237 -1.536350720
#> 115 115 0 0.1087758491 0.207899344 -0.1897824368 0.222681163
#> 116 116 0 -0.0470473274 -0.345699811 0.2871595080 -1.680425130
#> 117 117 0 0.1202415211 0.278454646 0.5877737710 0.422043870
#> 118 118 0 -0.1441681760 -0.186076572 -0.2531701849 -1.106576026
#> 119 119 0 -0.0140115743 0.161866732 0.0753204366 0.056034622
#> 120 120 0 0.1181808960 -0.032746717 0.0693756742 -0.609576679
#> 121 121 0 0.2043206229 0.401634765 0.5415188759 0.840922332
#> 122 122 0 -0.1774226090 0.571524634 0.2294509771 1.446367134
#> 123 123 0 -0.0904940733 -0.125807932 0.0121260527 -0.916922714
#> 124 124 0 0.2091946119 0.383946059 0.3058262488 0.792820808
#> 125 125 0 0.1037604494 0.249149256 0.1880949257 0.343562760
#> 126 126 0 0.2376159216 -0.426018073 0.1810748767 -1.956630534
#> 127 127 0 -0.3898660249 0.250191139 0.2626834781 0.357985067
#> 128 128 0 -0.0233386256 0.167798484 -0.3821198093 0.100190519
#> 129 129 0 -0.3691236231 -0.108322267 0.0673425697 -0.851984951
#> 130 130 0 0.2716136333 0.314981399 0.5252857084 0.545005044
#> 131 131 0 -0.1901646538 0.052567041 -0.0008245592 -0.306538370
#> 132 132 0 0.5093533894 0.427280977 0.0630824538 0.943835307
#> 133 133 0 0.1797906466 0.076680549 -0.1864558320 -0.225948526
#> 134 134 0 -0.0286613594 0.125003024 0.1146778371 -0.070957683
#> 135 135 0 0.0161415053 0.172566250 -0.4990294025 0.121286042
#> 136 136 0 -0.0200841842 -0.240679495 0.2272998849 -1.320905896
#> 137 137 0 -0.2413515702 -0.313661328 0.2154885301 -1.561930717
#> 138 138 0 -0.3318736259 -0.457855454 0.3560732682 -2.056982564
#> 139 139 0 -0.4739405084 0.213149997 -0.0532274436 0.250869695
#> 140 140 0 0.1480106082 -0.332057806 0.2318806105 -1.636983930
#> 141 141 0 0.2429479877 -0.044078496 -0.0675368388 -0.644754067
#> 142 142 0 -0.4760243389 0.107913985 -0.1890875327 -0.099985745
#> 143 143 0 -0.1278134026 -0.122933788 -0.3048457485 -0.889609021
#> 144 144 0 0.2613777644 0.228972505 -0.0823365645 0.284236193
#> 145 145 0 -0.5184815250 -0.292921090 0.2325449489 -1.483990288
#> 146 146 0 0.0607670058 -0.017567445 -0.2870004174 -0.537765750
#> 147 147 0 -0.3142871302 0.061471980 -0.2528280492 -0.259484720
#> 148 148 0 -0.3784020578 -0.094234634 -0.0390891155 -0.798274834
#> 149 149 0 0.5259169721 0.281405852 -0.1807915290 0.459786704
#> 150 150 0 -0.0541422351 -0.083099876 0.0050217808 -0.772370305
#> 151 151 0 -0.0466024832 -0.109702459 0.1921678898 -0.872779613
#> 152 152 0 -0.0963853294 0.237731550 -0.4579318412 0.344175104
#> 153 153 0 -0.2718316041 -0.146723336 -0.1888939683 -0.972234687
#> 154 154 0 0.2379167542 0.054758764 -0.1090647400 -0.306260525
#> 155 155 0 -0.0617328124 0.200979072 -0.1166123589 0.200443543
#> 156 156 0 -0.0413231673 -0.014589069 -0.4977584557 -0.513666128
#> 157 157 0 -0.0563923906 -0.317197986 -0.0644815745 -1.564978960
#> 158 158 0 -0.3185076449 -0.170623388 -0.0296824265 -1.060384857
#> 159 159 0 -0.1082837103 -0.416218160 -0.0773302895 -1.899577260
#> 160 160 0 -0.3358075756 0.527442148 -0.0474801269 1.315500659
#> 161 161 0 0.0835596907 0.153317829 -0.3926599625 0.048288466
#> 162 162 0 -0.2102432394 -0.014573333 0.1393730537 -0.541578289
#> 163 163 0 -0.4010660809 -0.587136300 -0.1699604193 -2.467405921
#> 164 164 0 -0.0539029905 0.187902267 -0.2670973636 0.163526233
#> 165 165 0 -0.2553365922 0.309373565 -0.3065501887 0.584767050
#> 166 166 0 0.4228436633 0.280195984 0.6358522900 0.416438267
#> 167 167 0 -0.0326226631 -0.167671531 0.0378559497 -1.062381879
#> 168 168 0 -0.3095759618 0.187638637 -0.2230462598 0.167983220
#> 169 169 0 0.4013729592 -0.099002987 0.2448520212 -0.852494843
#> 170 170 0 0.3461798111 0.082135945 0.3651116432 -0.240939197
#> 171 171 0 0.1168837322 0.176969583 -0.3613905204 0.126123730
#> 172 172 0 0.0248471635 -0.124311299 0.4983247974 -0.940467505
#> 173 173 0 0.0716114127 -0.089219502 -0.1757609742 -0.787575209
#> 174 174 0 -0.1875101601 0.013692036 0.2378760715 -0.451217126
#> 175 175 0 -0.0630743470 -0.491682717 0.3021436791 -2.177278812
#> 176 176 0 -0.3100002065 0.055661165 0.1469937224 -0.300093424
#> 177 177 0 0.0317536188 -0.185455400 -0.2232815498 -1.111265884
#> 178 178 0 -0.5431924308 -0.285405515 -0.0272845020 -1.444226123
#> 179 179 0 -0.5595913602 0.202391762 0.1562062325 0.205982935
#> 180 180 0 -0.0636263437 -0.146589107 0.3816170322 -1.007555522
#> 181 181 0 0.0185278985 -0.120917914 0.3912404906 -0.923188084
#> 182 182 0 -0.1696928832 -0.114192250 -0.3290685947 -0.857369149
#> 183 183 0 0.0832050300 0.129764596 -0.1642270131 -0.043651935
#> 184 184 0 0.1546306927 0.279416462 -0.0400549943 0.456817129
#> 185 185 0 0.1029862366 0.390808427 -0.1265559880 0.841737383
#> 186 186 0 -0.0821388772 -0.401375183 0.3729959031 -1.873202307
#> 187 187 0 0.0445414149 -0.003285305 -0.3733273364 -0.484228195
#> 188 188 0 0.0603081560 -0.340085039 -0.2989459765 -1.634165996
#> 189 189 0 0.1857185107 -0.101877820 0.3534083961 -0.861457110
#> 190 190 0 0.2910911086 0.002579157 0.1332933359 -0.497892796
#> 191 191 0 0.2136166741 0.114040863 -0.2215556755 -0.098060352
#> 192 192 0 0.0575021742 -0.071602702 -0.0619650122 -0.733126796
#> 193 193 0 -0.0543361452 -0.058561466 0.1270959793 -0.695222777
#> 194 194 0 -0.2661579486 0.176601464 -0.0068203284 0.117940903
#> 195 195 0 0.1779116866 -0.114013636 0.8954267688 -0.930586315
#> 196 196 0 -0.2538252029 0.084005901 -0.5233933832 -0.170623728
#> 197 197 0 0.1422292940 -0.519543040 -0.3178724231 -2.246052511
#> 198 198 0 0.4591911270 0.520897966 -0.2344292550 1.279183086
#> 199 199 0 0.2038105628 -0.110650255 -0.1117148939 -0.867737859
#> 200 200 0 0.0219724039 0.142213669 -0.1340709228 -0.001040454
#> 201 201 0 0.2726744950 -0.383882452 -0.4902696970 -1.779571317
#> 202 202 0 -0.0974905084 0.038404953 0.6333590430 -0.390336111
#> 203 203 0 -0.0355597159 0.048883963 -0.1270976692 -0.317141351
#> 204 204 0 0.3225628545 -0.204216893 0.7415683668 -1.233758287
#> 205 205 0 0.2949746842 -0.258727337 -0.1205413989 -1.373682571
#> 206 206 0 -0.3271238540 -0.254794621 -0.1738809548 -1.338962024
#> 207 207 0 0.3136961986 0.162641789 0.3405360995 0.035142223
#> 208 208 0 -0.0354329910 -0.075181136 0.6116029876 -0.777421644
#> 209 209 0 0.4180261846 0.006968354 -0.0709555654 -0.476171758
#> 210 210 0 -0.2831444641 0.096774614 -0.2519445066 -0.140379889
#> 211 211 0 -0.4138448975 0.185700013 -0.5848785507 0.183250288
#> 212 212 0 -0.2152984839 -0.186693783 -0.0390143130 -1.117646772
#> 213 213 0 -0.3685816100 0.285010395 0.1257759217 0.482879304
#> 214 214 0 0.0623505553 -0.402785710 -0.0168621766 -1.862116431
#> 215 215 0 -0.0882554143 0.313268163 0.1075779870 0.571567649
#> 216 216 0 0.2669185908 -0.115698536 -0.0002343905 -0.892570211
#> 217 217 0 -0.1456739816 -0.388566674 -0.1696310703 -1.799622689
#> 218 218 0 0.5216697290 0.311713435 0.1164035729 0.547605663
#> 219 219 0 0.0994954072 0.009722920 0.4994346505 -0.486841557
#> 220 220 0 -0.6886046772 -0.405339164 -0.1794730577 -1.839948357
#> 221 221 0 0.1543226964 0.257739696 -0.6584671717 0.415134401
#> 222 222 0 0.0609892148 0.114604572 0.1017218857 -0.108333957
#> 223 223 0 0.1029010253 0.109160220 -0.0067478224 -0.122484524
#> 224 224 0 0.0357271852 0.229890228 0.7034329324 0.253385292
#> 225 225 0 -0.1939283996 -0.052977087 -0.1699763380 -0.656666789
#> 226 226 0 0.0016104320 -0.095257841 -0.3164796194 -0.798732881
#> 227 227 0 -0.0346081293 0.090877026 -0.4498953850 -0.157607128
#> 228 228 0 -0.2797764064 0.345342832 -0.1916749124 0.701893385
#> 229 229 0 -0.2287553633 -0.405187428 0.4618547939 -1.886394517
#> 230 230 0 0.4448788100 0.363815441 -0.2278413841 0.744958236
#> 231 231 0 -0.7275336202 -0.106429877 0.2890671390 -0.846331465
#> 232 232 0 0.0413238623 -0.098324624 0.3868529004 -0.846791269
#> 233 233 0 -0.3722740619 0.117650625 -0.4215426794 -0.057921698
#> 234 234 0 -0.3085991657 -0.503622169 0.4610580821 -2.218791075
#> 235 235 0 0.0894068353 0.313009582 -0.1486247503 0.578656187
#> 236 236 0 -0.0234636258 -0.055697163 -0.5479247177 -0.651428153
#> 237 237 0 0.1923076109 -0.256029470 -0.2549892659 -1.354473606
#> 238 238 0 -0.5166391076 -0.255216279 0.0172086426 -1.344636754
#> 239 239 0 0.5352492092 0.113003812 0.3848102899 -0.142610643
#> 240 240 0 0.2435816158 0.417943396 0.1215197578 0.916983798
#> 241 241 0 0.1331844526 -0.074915946 -0.0618418389 -0.746663436
#> 242 242 0 0.0130989674 0.009400854 -0.1008362061 -0.454255746
#> 243 243 0 -0.0021818839 0.317690232 -0.0915512285 0.594355636
#> 244 244 0 -0.0296685680 -0.078462079 0.5563983784 -0.785893594
#> 245 245 0 0.0106386042 0.578209714 -0.1924819266 1.485350456
#> 246 246 0 0.1096071781 -0.314863601 0.2326459069 -1.577391085
#> 247 247 0 -0.0444065053 -0.085133521 -0.0777473374 -0.775290058
#> 248 248 0 -0.1974911023 0.262673304 -0.1986924585 0.418601748
#> 249 249 0 -0.0996352647 -0.324126044 0.1829995484 -1.600075375
#> 250 250 0 -0.0165747043 -0.082968035 -0.5350340787 -0.745062749
#> 251 251 1 0.4201774907 0.242278373 0.0306896264 0.318896802
#> 252 252 1 0.3343056543 0.570017547 0.5475292150 1.409477153
#> 253 253 1 -0.1985105110 0.165349091 -0.2682642035 0.091191738
#> 254 254 1 0.2389177794 -0.060729445 -0.2975623719 -0.689353377
#> 255 255 1 0.0372200717 0.599885747 0.0724151132 1.544562148
#> 256 256 1 0.7359494612 0.082074378 0.2235004486 -0.245452600
#> 257 257 1 -0.0145494605 -0.330673651 0.6474606469 -1.648952494
#> 258 258 1 0.1882297186 0.421415280 0.4184715386 0.915060944
#> 259 259 1 -0.2432286330 0.416909902 0.3262437458 0.917400688
#> 260 260 1 0.1247823357 0.469559604 -0.2492091338 1.115310764
#> 261 261 1 -0.0139885114 0.236660127 -0.1095342165 0.320018779
#> 262 262 1 0.2621205850 -0.244360952 -0.2560570980 -1.316813277
#> 263 263 1 0.1255820513 0.959444701 0.4414202406 2.745832184
#> 264 264 1 0.3288863037 0.424776313 0.2063982066 0.933280297
#> 265 265 1 0.3789390714 0.489296580 -0.2640233242 1.175622190
#> 266 266 1 -0.0392076895 0.224700103 0.0237520403 0.273184601
#> 267 267 1 0.6312483020 0.348409946 -0.5797705464 0.705224724
#> 268 268 1 0.0660616345 0.542392563 0.1956799914 1.341753054
#> 269 269 1 0.4241095144 -0.100005963 0.3280897526 -0.860898170
#> 270 270 1 0.3990294554 0.228193407 -0.4626923056 0.297181742
#> 271 271 1 0.7726749484 0.336523528 0.1412480070 0.623212479
#> 272 272 1 -0.4023128488 0.453599713 0.1289250496 1.057174536
#> 273 273 1 0.3589985600 0.630769934 -0.3783849123 1.663359900
#> 274 274 1 0.9087049395 0.035368783 -0.0576954431 -0.394910555
#> 275 275 1 -0.2654573333 0.562849223 0.2205457730 1.419948701
#> 276 276 1 -0.0003217162 0.070000423 0.2268898384 -0.264707484
#> 277 277 1 -0.1016828234 -0.002065021 -0.0351279017 -0.493232850
#> 278 278 1 -0.0177666483 0.250130255 0.1042082842 0.354875487
#> 279 279 1 0.3813421023 0.530807467 -0.2482997789 1.315933661
#> 280 280 1 0.2753524703 -0.278595058 0.2181986407 -1.458226549
#> 281 281 1 0.7710111142 0.640319403 0.0557213595 1.661045000
#> 282 282 1 0.3109186663 0.518991623 0.2447360419 1.252300831
#> 283 283 1 0.6041032240 0.104599009 0.3088082963 -0.169317952
#> 284 284 1 0.0090904675 -0.063303213 -0.0578337814 -0.703664515
#> 285 285 1 -0.2232560664 0.475745841 0.0262292919 1.132476868
#> 286 286 1 0.3460211433 0.312279939 -0.2613471701 0.574350463
#> 287 287 1 -0.0630659419 0.509890286 -0.3267772855 1.262123540
#> 288 288 1 0.2798693603 0.583101536 -0.2537170231 1.497121514
#> 289 289 1 -0.1415327043 0.360590109 0.5729190405 0.710012855
#> 290 290 1 -0.0974734079 0.185295748 0.0082087026 0.141697517
#> 291 291 1 0.3650202852 0.353219758 -0.0926970685 0.704300441
#> 292 292 1 -0.0339300414 0.086266474 0.1624167167 -0.205034835
#> 293 293 1 -0.2940944272 0.469208789 0.4662961011 1.089556471
#> 294 294 1 0.2061629611 0.287099577 0.3882817042 0.459219124
#> 295 295 1 0.3366545823 -0.372237665 0.2060753546 -1.777951519
#> 296 296 1 0.2083673305 0.133933680 -0.3206191663 -0.025106186
#> 297 297 1 -0.0027241830 0.684089825 0.3386765880 1.818377103
#> 298 298 1 0.1727873756 0.458257116 0.4637772173 1.038491078
#> 299 299 1 -0.2409965704 0.600465653 0.3470468898 1.540614962
#> 300 300 1 -0.0976269650 0.027064135 -0.1932949397 -0.386077254
#> 301 301 1 0.0390114096 0.236320893 -0.2830607261 0.326272631
#> 302 302 1 0.4432234342 0.196766755 0.3451192624 0.147111166
#> 303 303 1 0.4111708887 0.801599022 -0.0286227109 2.224749442
#> 304 304 1 0.0279832805 0.207528839 0.1195961954 0.207804524
#> 305 305 1 0.3615268692 0.094267730 -0.0623271973 -0.177985442
#> 306 306 1 0.0783273786 0.281530988 0.1353693210 0.457199536
#> 307 307 1 0.4026038233 0.572296593 -0.0622696292 1.446784023
#> 308 308 1 -0.1118072509 0.267127116 0.4392224274 0.398140820
#> 309 309 1 0.1387051348 0.580560418 0.4915772349 1.454079247
#> 310 310 1 0.3965315057 0.152383920 0.3256355047 -0.001451559
#> 311 311 1 0.0603442416 0.362299414 0.0155043584 0.738678130
#> 312 312 1 -0.0460863716 0.414734813 0.1789907737 0.911743634
#> 313 313 1 0.4118550747 0.572326714 -0.2117142107 1.454353126
#> 314 314 1 0.2374834506 0.182190239 -0.3215935511 0.138217780
#> 315 315 1 0.2805748345 0.518644754 0.0403783369 1.262615315
#> 316 316 1 0.5508471595 0.087419409 0.1646390148 -0.218693588
#> 317 317 1 -0.0891805832 0.193059953 0.0426195287 0.166076648
#> 318 318 1 0.6048424813 0.377850528 -0.1431917124 0.783534725
#> 319 319 1 0.1912411693 0.363225207 0.4715147388 0.714291156
#> 320 320 1 0.4622344464 0.053305003 0.2236980579 -0.335145988
#> 321 321 1 0.3727242531 0.604174510 -0.3054482222 1.568707547
#> 322 322 1 -0.0992718913 0.817239229 0.1319326884 2.284875636
#> 323 323 1 0.3433037026 0.074644857 0.4852894563 -0.272560580
#> 324 324 1 -0.0972831528 0.206181510 0.2225026495 0.201631165
#> 325 325 1 0.4478772560 0.143237819 0.1922167795 -0.027182613
#> 326 326 1 0.1235976523 0.445468021 0.0378053526 1.018528772
#> 327 327 1 0.0003496112 0.585177642 0.4232494186 1.477456952
#> 328 328 1 -0.0080449824 0.179945159 -0.1399563152 0.128503403
#> 329 329 1 0.0626727321 0.388722629 0.7741996191 0.789177122
#> 330 330 1 0.1003763144 0.195727964 0.4750736428 0.147084282
#> 331 331 1 0.3266331109 0.531699162 -0.1737474130 1.316738027
#> 332 332 1 0.3817990712 0.506917611 0.0719248497 1.218068137
#> 333 333 1 0.1860540013 0.155282378 0.1331587123 0.024666202
#> 334 334 1 0.6086558536 0.330832814 -0.0694392532 0.619670415
#> 335 335 1 0.6919354175 0.048982862 -0.4397968746 -0.322331304
#> 336 336 1 -0.4769046654 -0.146526720 0.2132373138 -0.986276109
#> 337 337 1 0.6731658800 -0.032811039 -0.0836898296 -0.618440402
#> 338 338 1 0.0703343795 0.300079548 -0.0951232604 0.532472741
#> 339 339 1 0.0967898079 0.259124648 0.1771159645 0.378270752
#> 340 340 1 0.0375614845 0.633682643 -0.5514187028 1.691832742
#> 341 341 1 0.6599826797 0.316878435 -0.3173988846 0.583519268
#> 342 342 1 0.2103504295 0.531899545 0.3258826122 1.295005999
#> 343 343 1 -0.2686018991 0.362807802 -0.2488391325 0.763927921
#> 344 344 1 -0.3012662703 0.381031778 0.5460429640 0.785707695
#> 345 345 1 -0.1142656977 0.349609859 0.4403225407 0.678719555
#> 346 346 1 0.4281144828 0.106569938 0.1453920256 -0.148890881
#> 347 347 1 0.4901700052 0.534872060 -0.1993996984 1.323975335
#> 348 348 1 0.3104715105 0.389977397 -0.2235719868 0.837740336
#> 349 349 1 -0.1760194576 0.624224771 0.4671396385 1.613267981
#> 350 350 1 0.2041638817 0.294495360 -0.2312831379 0.516535933
#> 351 351 1 0.0514881994 -0.173449547 0.1922582277 -1.092547524
#> 352 352 1 0.2502525492 0.451444833 0.3928257204 1.016681808
#> 353 353 1 0.1422380295 0.099393801 0.5525144701 -0.185855761
#> 354 354 1 0.1473963537 0.465451134 -0.0475010684 1.090209734
#> 355 355 1 -0.1977522075 0.039393753 0.2042799503 -0.361747031
#> 356 356 1 0.3803168801 0.417552774 -0.1894386459 0.927682523
#> 357 357 1 0.7868657599 0.103969618 0.0266922174 -0.162300434
#> 358 358 1 0.1906957108 -0.046949029 -0.0372848877 -0.654524893
#> 359 359 1 -0.0205748134 0.339498224 -0.1151739211 0.670308056
#> 360 360 1 0.4223998465 0.257569657 0.3421828523 0.354704283
#> 361 361 1 0.0955086388 0.075757217 0.5077930079 -0.262542081
#> 362 362 1 0.3505240336 0.175152491 0.2497918798 0.081298635
#> 363 363 1 0.1491318094 0.562197651 0.1662815431 1.408161560
#> 364 364 1 0.6387360644 -0.166008540 -0.1645705402 -1.066288418
#> 365 365 1 0.2189349747 0.466940971 0.1828196416 1.081207490
#> 366 366 1 0.1575158960 0.282612221 0.0652252395 0.462146499
#> 367 367 1 0.1243366872 0.791638440 -0.0139910422 2.198677512
#> 368 368 1 -0.3282974430 0.600612350 -0.0127526122 1.562363082
#> 369 369 1 0.6281564638 -0.074542581 0.2002497383 -0.773755916
#> 370 370 1 0.2004401036 -0.368462267 -0.0774005370 -1.746354057
#> 371 371 1 -0.1012565896 0.368730828 0.3401512237 0.748560385
#> 372 372 1 0.3217257813 0.453256608 0.3257819959 1.024183480
#> 373 373 1 0.1837079572 0.508504741 0.1502508178 1.225324821
#> 374 374 1 -0.4223512102 0.100070148 -0.0945398544 -0.133167985
#> 375 375 1 -0.1137105388 0.274889966 -0.0110503942 0.447932059
#> 376 376 1 0.0413736159 0.343226884 -0.4038852896 0.696099357
#> 377 377 1 0.1482958744 0.346670592 -0.1980571382 0.693955346
#> 378 378 1 0.3518909718 0.595235957 0.0545953373 1.520271174
#> 379 379 1 -0.2994535334 0.149731908 0.3965630278 0.006639523
#> 380 380 1 0.1962777886 0.268518331 0.2586191881 0.403028881
#> 381 381 1 0.1001780876 0.542195559 -0.2257938976 1.361901211
#> 382 382 1 -0.0310673514 -0.036334059 0.6185636561 -0.645775633
#> 383 383 1 0.2775479520 0.130810305 0.4800833622 -0.079282042
#> 384 384 1 0.2615816068 0.294797508 0.1723659035 0.494935142
#> 385 385 1 -0.1287841927 0.466299593 0.7341689393 1.060844795
#> 386 386 1 0.5646390663 0.372785291 -0.3172207885 0.776522937
#> 387 387 1 -0.3333586912 0.398953828 -0.3272282536 0.892872949
#> 388 388 1 -0.1186823752 -0.066043597 0.3608129240 -0.730860423
#> 389 389 1 0.3246531168 0.504502924 0.6322063588 1.182532380
#> 390 390 1 0.0298898133 -0.143262335 -0.0606279580 -0.976119242
#> 391 391 1 -0.1960609602 0.323418797 0.0726712321 0.611123042
#> 392 392 1 -0.0314770779 0.091469643 0.2265001311 -0.190729951
#> 393 393 1 0.2280969404 0.344225670 -0.1017006521 0.678263267
#> 394 394 1 0.1487889617 0.151439911 -0.0054834760 0.019892417
#> 395 395 1 0.6762736518 0.134104147 -0.2517278356 -0.042070463
#> 396 396 1 0.2063878807 -0.047136634 -0.3065433103 -0.641681008
#> 397 397 1 0.3325303798 0.548997067 0.1993696322 1.356068386
#> 398 398 1 -0.0234015714 0.049897129 0.4264722430 -0.342739520
#> 399 399 1 0.2968671962 0.237446944 0.1524553697 0.299836842
#> 400 400 1 -0.2166274973 0.322411957 0.0699198760 0.608455115
#> 401 401 1 0.2491490254 0.136772313 -0.1154005150 -0.027301368
#> 402 402 1 -0.2349305296 0.420376573 0.4248382480 0.923836286
#> 403 403 1 0.6454583796 0.031917337 -0.3215968677 -0.385115132
#> 404 404 1 0.2607196341 0.265642750 -0.3824956631 0.424540165
#> 405 405 1 0.4293251358 0.571329491 0.3534255366 1.421158587
#> 406 406 1 0.3909866944 0.388715784 0.0725303098 0.815702782
#> 407 407 1 -0.1912289438 0.346350415 -0.1863051689 0.702397824
#> 408 408 1 0.2052609533 0.265240303 0.3280141856 0.388015022
#> 409 409 1 0.1267292495 0.833230046 0.2242133261 2.327736791
#> 410 410 1 0.5577430810 0.363326047 0.2685400292 0.714204436
#> 411 411 1 0.5294065014 0.179803848 0.4562467464 0.081080729
#> 412 412 1 -0.0410532353 0.602972844 -0.2026822047 1.571653769
#> 413 413 1 0.2343103539 0.435976045 0.3028554535 0.969202875
#> 414 414 1 0.2231317330 0.269721836 0.4998460938 0.393822199
#> 415 415 1 0.2119122973 0.619117235 -0.2080666022 1.619292140
#> 416 416 1 0.2676529479 -0.151151421 0.2058661648 -1.023862334
#> 417 417 1 0.1250750273 0.589582707 0.2250506406 1.498984495
#> 418 418 1 0.0061314729 -0.081150178 0.0237981213 -0.768511471
#> 419 419 1 -0.2799802731 0.316580136 0.1650665086 0.585580808
#> 420 420 1 -0.0134770500 0.436672266 0.3233289261 0.977910845
#> 421 421 1 0.4888972006 0.396998651 -0.2598097911 0.858171475
#> 422 422 1 0.1301173457 0.343278808 0.0455504370 0.670339558
#> 423 423 1 0.4477274636 0.176044867 0.0107872134 0.093814083
#> 424 424 1 0.0344819841 0.297322038 0.7663977384 0.479527240
#> 425 425 1 -0.1076721478 0.051418573 0.0838782701 -0.317297192
#> 426 426 1 0.2161145425 0.287793828 -0.2670999862 0.495239696
#> 427 427 1 -0.0803189813 0.040296584 0.3571191968 -0.370102241
#> 428 428 1 0.4969035399 0.480235949 0.2036910266 1.117046573
#> 429 429 1 0.1525429690 -0.013843070 0.4623474305 -0.566663292
#> 430 430 1 -0.0776768124 -0.097744141 0.3097232770 -0.837266431
#> 431 431 1 0.2125311136 0.080371739 0.1093513615 -0.229697130
#> 432 432 1 0.1468083721 0.520260507 0.2590508689 1.260776633
#> 433 433 1 0.1622768538 0.631328838 -0.0676076477 1.655034550
#> 434 434 1 0.1215887815 0.312204501 -0.0072584988 0.567632167
#> 435 435 1 0.3330823425 -0.045402590 -0.3433114361 -0.637661630
#> 436 436 1 0.1416324821 0.198440923 -0.1223503565 0.186033585
#> 437 437 1 -0.1695852991 -0.300612539 -0.1240708395 -1.502096019
#> 438 438 1 0.4466413670 0.487371917 -0.1790392666 1.162650326
#> 439 439 1 0.4373319525 0.347237943 0.3116587877 0.660843504
#> 440 440 1 0.5648241546 0.602983195 -0.4415175541 1.565967925
#> 441 441 1 -0.0331606505 0.504240721 0.4010526320 1.204303592
#> 442 442 1 0.1246065682 0.209910208 -0.0916081905 0.223961684
#> 443 443 1 0.3175277787 0.071021366 0.1333256189 -0.265880146
#> 444 444 1 0.0673250707 0.459309535 -0.1853278252 1.078851756
#> 445 445 1 -0.0025885577 0.488968620 0.3277546829 1.155240645
#> 446 446 1 0.4407298100 0.407097778 -0.5599304930 0.909511620
#> 447 447 1 0.0664786681 0.215601241 0.4954406895 0.214639733
#> 448 448 1 -0.3636494463 0.353649884 0.0461956460 0.720330112
#> 449 449 1 0.0397021747 0.164235026 0.5408253324 0.038367534
#> 450 450 1 -0.1080914522 0.382757733 0.2943629070 0.798848931
#> 451 451 1 0.2144645820 0.490143086 0.5098567209 1.143317940
#> 452 452 1 0.4510173893 0.556200330 0.0443327224 1.385063944
#> 453 453 1 0.2894250368 0.452563802 0.6188420672 1.007607750
#> 454 454 1 0.3523487783 0.052422781 0.2735535794 -0.337448018
#> 455 455 1 -0.0257008348 0.764237723 0.7282028078 2.071501802
#> 456 456 1 -0.0547466390 0.875822632 0.1195018313 2.483459376
#> 457 457 1 0.0429866389 0.302616392 0.0219687051 0.535851803
#> 458 458 1 0.3557597099 0.318559578 0.3900215374 0.561671189
#> 459 459 1 -0.0200445810 0.295579054 -0.2747348791 0.529169718
#> 460 460 1 0.4238651781 0.335311550 0.5685769075 0.607367163
#> 461 461 1 0.2925209049 0.355987728 0.2256102273 0.699388921
#> 462 462 1 -0.2290040176 0.332509642 -0.0863990650 0.651270818
#> 463 463 1 0.4109159996 0.199816150 0.2589381000 0.162913672
#> 464 464 1 0.0832235551 0.530836923 0.3067680247 1.296178724
#> 465 465 1 0.1360449267 0.176458592 -0.0153849077 0.105886260
#> 466 466 1 -0.0337444225 -0.238540263 0.3149229135 -1.317761267
#> 467 467 1 -0.2299227832 0.182363274 0.2867358246 0.121247697
#> 468 468 1 0.1087016534 0.076013108 0.5113031467 -0.262247571
#> 469 469 1 -0.0503419853 0.397113327 0.2383024360 0.848858809
#> 470 470 1 0.3373625540 0.514819859 -0.0212931262 1.251104303
#> 471 471 1 0.0837868777 0.817744799 0.3184427238 2.271464612
#> 472 472 1 0.1021840284 -0.279174883 0.6731290641 -1.478597495
#> 473 473 1 0.3448079729 0.134851808 0.2932444851 -0.057863425
#> 474 474 1 -0.0485449516 0.300206546 0.2829754789 0.516865369
#> 475 475 1 0.1298449072 0.445379101 0.0889426862 1.015390225
#> 476 476 1 0.2853609138 0.071288052 -0.3182992485 -0.240612938
#> 477 477 1 0.0876669301 0.403586763 0.2370091924 0.866823139
#> 478 478 1 0.0499438202 0.304133853 0.5338345796 0.514285062
#> 479 479 1 0.0216252407 0.103374614 -0.1077563535 -0.134503236
#> 480 480 1 0.3025331304 0.527459256 -0.0347833864 1.295835975
#> 481 481 1 0.0074845123 0.446439578 0.5560300403 0.998451382
#> 482 482 1 0.0927795067 0.076395728 -0.2910026588 -0.218901884
#> 483 483 1 0.4909810727 0.392907555 -0.2271685452 0.842502316
#> 484 484 1 -0.2378756899 0.171018724 0.3730965545 0.078422634
#> 485 485 1 0.7555187226 0.324538468 -0.1848242969 0.599852393
#> 486 486 1 0.3240247770 0.354547735 -0.0954172735 0.710182843
#> 487 487 1 0.1098398176 0.327731848 0.3156905852 0.604066341
#> 488 488 1 0.0660641826 0.349617778 -0.1525237537 0.704076923
#> 489 489 1 0.0347062807 -0.037198399 -0.8495396436 -0.574615432
#> 490 490 1 0.7486671376 0.195557458 -0.0959580629 0.156728117
#> 491 491 1 0.5892582283 0.550019134 0.1881355228 1.352459393
#> 492 492 1 0.3903510001 0.394928342 -0.3037078947 0.856347051
#> 493 493 1 -0.2501269669 0.413744014 -0.2490886358 0.936646897
#> 494 494 1 0.3297015855 0.177710738 0.3994417719 0.082868733
#> 495 495 1 0.1355836963 0.170377407 0.1575036441 0.076257468
#> 496 496 1 0.5992158146 0.666538911 -0.1660310013 1.766850045
#> 497 497 1 0.2932911317 0.412117811 -0.2571940622 0.915305349
#> 498 498 1 0.3633587945 -0.021891595 -0.0275181186 -0.574955748
#> 499 499 1 0.1518543343 0.331943433 0.1077452390 0.627911042
#> 500 500 1 0.1309996830 0.191635339 0.0546244899 0.154032850