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Generate multivariate normal data from an explicit factor model for factor analysis parameter recovery testing. The implied covariance matrix \(\Sigma = \Lambda \Phi \Lambda' + \Psi\) is fully specified and stored in the return value for direct comparison with estimated covariances.

Usage

simulate_fa(loadings, phi = NULL, psi = NULL, n, seed = NULL)

Arguments

loadings

Numeric matrix of dimension p x m (observed variables x factors). Must be a matrix (not a vector). Zero entries indicate no loading; use matrix(val, nrow = p, ncol = 1) for single-factor models.

phi

Numeric matrix of dimension m x m. Factor correlation matrix. Must be symmetric and positive-definite. Defaults to diag(m) (orthogonal factors).

psi

Numeric vector of length p. Unique variances. All values must be positive. Defaults to 1 - diag(loadings %*% phi %*% t(loadings)) (communality complement). An error is raised if any auto-computed value is \(\le 0\) (over-factored model).

n

Positive integer. Sample size.

seed

Integer or NULL. Random seed.

Value

A named list with elements:

data

data.frame with columns y1...yp.

params

list with loadings, phi, psi, and sigma_implied (the \(p x p\) model-implied covariance matrix).

Examples

# Two orthogonal factors, 6 indicators (3 per factor)
loadings <- matrix(c(0.8, 0.7, 0.6, 0,   0,   0,
                     0,   0,   0,   0.8, 0.7, 0.6),
                   nrow = 6, ncol = 2)  # byrow = FALSE (default)
r <- simulate_fa(loadings = loadings, n = 500, seed = 1)
r$data                  # data.frame: y1..y6
#>               y1            y2            y3           y4           y5
#> 1   -0.626453811 -0.2867690683  0.6872958302  0.850043472 -0.258144036
#> 2    0.183643324 -0.1431132137  0.9880917992 -0.925312995 -2.110749248
#> 3   -0.835628612 -1.4482594715 -1.3642366102  0.893581214  1.842315572
#> 4    1.595280802  0.9027131581  0.9486193298 -0.941009738 -0.096754176
#> 5    0.329507772  1.0060584798  0.3986777489  0.538952094  0.255541917
#> 6   -0.820468384  0.8611279564 -1.5296039570 -0.181974398  0.475071178
#> 7    0.487429052 -0.8643208703  0.6792079626  0.891767595  0.543727197
#> 8    0.738324705  0.2066610222 -1.3320954007  1.329208205 -0.341203596
#> 9    0.575781352  1.2830122059 -0.5818385116 -0.103466125 -1.816885564
#> 10  -0.305388387 -1.0941424746  0.5065598197  0.615064611  0.172044609
#> 11   1.511781168 -1.2482466734 -0.1999064133 -1.799772395 -1.267013910
#> 12   0.389843236 -0.5570761383 -0.1693443584 -0.262705142 -1.023855341
#> 13  -0.621240581 -1.1492454653 -1.8664615838 -1.210141877 -0.332012787
#> 14  -2.214699887 -1.2008879892 -2.2994260227  0.204477253 -0.146842003
#> 15   1.124930918  0.2954683655  0.7673918993 -0.013994105  0.676124656
#> 16  -0.044933609  0.1666300098 -0.1290945189 -0.235200840  0.938096867
#> 17  -0.016190263 -0.3589989647 -0.5923446707 -0.188318654 -0.623353299
#> 18   0.943836211  0.8385026022 -0.6233781868  0.951283069 -0.192334098
#> 19   0.821221195  0.1566507905 -0.6141749753 -0.154014786  0.032521887
#> 20   0.593901321  1.3185749900  2.2493970825  1.854244505  2.219135998
#> 21   0.918977372 -0.0962430756  0.0263940285 -1.904167354 -2.503560793
#> 22   0.782136301  0.6788114953  1.0926270956  0.359299702 -0.492575726
#> 23   0.074564983 -0.6913349350  0.5479008648  2.114534946  0.591143820
#> 24  -1.989351696 -0.9417051197 -0.2620047813 -1.135748987 -0.325483040
#> 25   0.619825748  0.3075583238  0.5417737951 -0.796255986  1.528666245
#> 26  -0.056128740 -1.4270449959 -1.4089830545 -0.397569450 -0.606987351
#> 27  -0.155795507 -0.2067361197 -0.9673337284  0.091724042 -0.301986967
#> 28  -1.470752384  0.1541769617  0.1541784284 -0.238694074 -1.544670476
#> 29  -0.478150055  0.2967707680 -1.2278226621 -0.461962364 -1.121571783
#> 30   0.417941560  0.3527268769  0.6794239351  1.926340607  1.715641973
#> 31   1.358679552 -0.2269648101 -0.0232489897  0.122054815 -0.549141726
#> 32  -0.102787727  0.9111361675 -0.1777904706  1.092050577  0.208510285
#> 33   0.387671612  0.2827141328 -0.4769735717 -2.972257475 -1.956954756
#> 34  -0.053805041 -0.4044220370 -0.3057536732  1.128489051  0.580338345
#> 35  -1.377059557  0.5892548831  0.3913726527  1.312000129  2.076559217
#> 36  -0.414994563 -0.8699985044  0.0496892797 -0.482607973  0.762216472
#> 37  -0.394289954  0.0305299392 -0.3333675752 -0.224858997  1.538180891
#> 38  -0.059313397  1.0286944755  0.9519773003  1.667765311 -0.602424283
#> 39   1.100025372  1.1149513419  2.0588942806  0.041218532 -0.360273067
#> 40   0.763175748  0.1730127428  0.3048277368  1.038174846  1.445581728
#> 41  -0.164523596 -0.4387895193  0.2483828316  0.587642933  0.077352902
#> 42  -0.253361680  0.1523446203  0.1819312998 -0.158299577  0.174879745
#> 43   0.696963375  0.8157147976 -0.4108618512 -0.292085415 -0.701051590
#> 44   0.556663199  0.3271474849 -0.5244867561 -1.419898963 -2.343516851
#> 45  -0.688755695  0.7066220374  1.5573225210 -2.138318025 -2.197445836
#> 46  -0.707495157 -0.4507386131  0.4045909284 -0.022500105  1.559264216
#> 47   0.364581962 -0.3760242249  0.6839574728  0.269770954 -0.065649968
#> 48   0.768532925  0.8755491653  0.5935870218 -0.502969399  1.199666770
#> 49  -0.112346212 -1.8870742553 -0.0392516434  0.630807390  1.071804204
#> 50   0.881107726  0.8181676757  0.6247709236  0.474565208  0.847839630
#> 51   0.398105880  0.6346677681  0.3178243613 -0.340659062  1.154315383
#> 52  -0.612026393 -0.5290418195 -0.1430991007  0.049601560 -1.289657861
#> 53   0.341119691 -0.7345178263 -0.9071967274  1.295263191  0.219974175
#> 54  -1.129363096 -0.9596934425  1.4462492068  0.314624205 -0.083361548
#> 55   1.433023702  2.0865162537  1.6588394307  0.801572504 -0.315097094
#> 56   1.980399899  0.4930276934  0.5993450538  0.486058896  0.059700694
#> 57  -0.367221476 -2.1374502782  0.4389467047  1.725561057 -0.759315477
#> 58  -1.044134626  0.0882239533 -0.8911845781  0.102432861 -1.116739193
#> 59   0.569719627 -0.0962891820  1.6502795003 -0.989837075 -0.048281211
#> 60  -0.135054604 -0.4988963211 -0.4964653858 -0.460441209 -0.057748882
#> 61   2.401617761  0.3379858229 -1.0610421783  0.237661492  1.213415651
#> 62  -0.039240003 -0.0406640583  1.1475652203 -0.269397264 -0.428016922
#> 63   0.689739362  0.9672256192  1.4305893235 -0.169554070 -0.413538740
#> 64   0.028002159 -0.4710433061 -0.7581964310  0.664868973  0.023391875
#> 65  -0.743273209 -0.9189026110 -1.6777073835 -0.775550915 -1.228298738
#> 66   0.188792300  1.0142819985 -1.2834060492 -1.919261131 -0.868395214
#> 67  -1.804958629 -1.2158367698 -1.1423846360  2.019332540  0.154133380
#> 68   1.465554862  0.6882333351 -0.8993650816  0.435210515  0.654313260
#> 69   0.153253338 -0.4326307850 -0.7395181235  1.050168832  0.440867842
#> 70   2.172611670  1.9626659742  1.3475402749 -0.312114841  0.467077027
#> 71   0.475509529 -0.5573967357  0.7809042728  0.093617617  1.086340213
#> 72  -0.709946431  0.3060276650 -0.8893763279 -2.153187751 -1.550617647
#> 73   0.610726353  1.0095251479  0.3341289036  0.357993071 -0.155542013
#> 74  -0.934097632 -0.9104985923 -0.3149392337  0.467864811  0.223458490
#> 75  -1.253633400  0.0008752535  1.0280614967 -0.906688835 -1.053383970
#> 76   0.291446236  0.9807414288 -0.5025229850 -0.529349916  1.031293107
#> 77  -0.443291873  0.2286537045 -1.4843487909  1.343576717  0.699651140
#> 78   0.001105352  1.6781856621 -1.2136078962  0.469434057  0.982700343
#> 79   0.074341324 -1.5841639699  0.1544186525 -0.253105088  0.171742439
#> 80  -0.589520946 -1.2952601087 -0.5471550737  0.369103715  1.379585262
#> 81  -0.568668733 -1.4588904825  0.1383324927 -1.346707190 -0.927333149
#> 82  -0.135178615  0.0632215616 -0.1551349664  1.171935426 -1.562456308
#> 83   1.178086997  1.9725821951  1.1919810544 -1.908736345 -0.564190837
#> 84  -1.523566800  0.5369211848 -0.2327006456 -1.004390811 -1.418822099
#> 85   0.593946188  0.7371600698  0.3944091786  0.676687514  0.791030185
#> 86   0.332950371  0.9144265100 -0.2143748937  1.152321744 -0.161562424
#> 87   1.063099837  0.4753081468  1.5667476752 -1.732759918 -1.048614831
#> 88  -0.304183924  0.2181966389 -0.4086056793  0.601308857 -0.122232636
#> 89   0.370018810  0.5189188449  0.8184057604  0.341650314 -0.012285816
#> 90   0.267098791 -0.4809409187  0.1305903168 -0.035281009 -0.562242401
#> 91  -0.542520031 -0.5468039017  1.2147466771 -0.626165020 -1.165727781
#> 92   1.207867806  0.5646909807  1.1654433371 -0.855971210 -0.316621748
#> 93   1.160402616  1.8046164189  0.5216057484  0.151777842 -0.922887465
#> 94   0.700213650 -0.4670178193  0.1390014992  1.206372694  0.439412803
#> 95   1.586833455 -0.8630843043  0.2682888685 -1.488577883 -1.082438109
#> 96   0.558486426  0.9492652223 -1.3858196327 -1.050374123 -1.117301872
#> 97  -1.276592208 -1.3910746772  0.6947785850  1.637874117  2.361146103
#> 98  -0.573265414 -0.6823399937  0.5581334774 -1.207334181 -2.224891715
#> 99  -1.224612615  0.0637583657 -1.0805202957 -2.626155085 -1.444810726
#> 100 -0.473400636 -0.8973156852 -0.0387042811  0.017463266 -0.991962688
#> 101 -0.620366677 -0.6299768104 -0.1524558012  0.344194027 -0.918302141
#> 102  0.042115873  1.2683325083 -0.6775849156  0.012719837 -0.030744990
#> 103 -0.910921649 -0.0724170893  0.9376270022 -0.873450133  1.323602389
#> 104  0.158028772  0.5376976422 -0.0382109813  0.342800284  1.370164012
#> 105 -0.654584644 -0.4798002654 -0.1816148356 -0.177387754  0.052481660
#> 106  1.767287269  0.0479052772  0.9882537525  0.921433255 -0.024947407
#> 107  0.716707476 -0.8385883464 -0.7821489801  0.300944402  1.860774158
#> 108  0.910174229  0.3246242143 -0.5352646814  0.693386753  0.194022360
#> 109  0.384185358  1.8735533821  0.5080697897  0.325471906 -0.556274561
#> 110  1.682176081  1.1256985778  1.3422304792  0.408051023 -0.896145540
#> 111 -0.635736454 -0.2198306741 -0.2118032456  0.759842256 -0.058351207
#> 112 -0.461644730  0.0170551519  0.4448690356 -2.287153520  0.101198501
#> 113  1.432282239  0.4829360741  0.9046332161  0.517838262  1.189519770
#> 114 -0.650696353 -1.5232473280 -0.0996230673 -1.347236258 -0.292544206
#> 115 -0.207380744  2.1006982514 -0.8150190445  0.363159859 -1.152734368
#> 116 -0.392807929 -0.5709932327  0.3150928442  1.314752565  0.511294186
#> 117 -0.319992869 -0.4265851515 -0.8857998669 -0.448305911  0.653495720
#> 118 -0.279113303 -1.6412453197 -0.8607075536 -0.808164468 -0.712514359
#> 119  0.494188331  0.0712724845  0.1019778712 -0.086268499 -0.613362116
#> 120 -0.177330482 -0.3041945381 -1.5442324088  1.585424273  0.930986056
#> 121 -0.505957462 -0.4950246384 -0.3749004846  0.101057448 -0.531054709
#> 122  1.343038825 -0.7283632632 -0.0588888794  0.148762212 -0.210566378
#> 123 -0.214579409  1.3584154804 -0.3938340716 -0.546434668  1.678264003
#> 124 -0.179556530  1.3605665942 -0.2402190706 -0.527675587  0.161009330
#> 125 -0.100190741  0.5152218706  1.1464844189 -0.139871559  0.956281809
#> 126  0.712666307 -0.5128623543 -0.9390551443 -1.589411414 -0.849084737
#> 127 -0.073564404  0.5507696536 -0.0897290353  1.234104166  0.313679507
#> 128 -0.037634171 -0.2252739715 -2.1841752504 -0.335454848  0.357201791
#> 129 -0.681660479 -0.6466703424 -0.9640462758 -2.001002507 -2.351260173
#> 130 -0.324270272  0.9473493703 -0.3371178587 -0.017458403  1.207431832
#> 131  0.060160440 -0.9836018015  1.1282203915 -0.240966896 -0.318668948
#> 132 -0.588894486 -0.7533222672 -1.2014511369 -1.791989399 -3.507469932
#> 133  0.531496193 -0.3081517832 -0.6267209667  2.049691511  0.427788017
#> 134 -1.518394082 -0.8339362941 -1.9244962650 -1.117217612 -0.968547956
#> 135  0.306557861 -1.1314337233  0.0143863438 -1.353549545  0.890064881
#> 136 -1.536449824 -1.4431183156  0.1244438341  0.451302311  0.187286856
#> 137 -0.300976127  0.4245978118 -1.0422432753  1.033227425 -0.650733955
#> 138 -0.528279904  0.0895903642 -0.5339762920 -0.195885695 -0.347366534
#> 139 -0.652094781 -1.1720439381  0.6816532740  0.227310387 -0.619197715
#> 140 -0.056896778  0.4314455599 -0.5124320365 -1.102199750 -1.921293401
#> 141 -1.914359426 -3.0874653232 -0.7746282812  0.955277369 -0.018738654
#> 142  1.176583312  0.3767974101  0.8368449295  0.312830446 -1.362633528
#> 143 -1.664972436 -0.3416418337 -1.7891864944  0.101005713  2.280173495
#> 144 -0.463530401 -0.8055846273  0.7014128950  0.748115414  0.649469995
#> 145 -1.115920105 -0.6550745625  0.1400342760  0.998960895  1.077283657
#> 146 -0.750819001 -1.7404845625 -1.0700827143 -0.732515309 -1.364161889
#> 147  2.087166546  1.8712033304  0.3808675182  0.480895240  1.342752120
#> 148  0.017395620 -1.5232919343 -0.6643548007 -0.989450308 -0.121512592
#> 149 -1.286300530 -0.9884704527  0.0220374060  2.229559048  0.470907951
#> 150 -1.640605534 -1.1302102735 -1.3182419977  0.456736600  0.166512473
#> 151  0.450187101  0.3025775632 -1.3810018818 -0.035815444 -0.351148399
#> 152 -0.018559833 -0.6926502330 -0.2818190838 -0.490442706  0.791374651
#> 153 -0.318068375  1.3377998899  0.8436051960 -0.220566611 -0.259099371
#> 154 -0.929362147 -1.7051178161 -1.7016645052 -1.101209361  0.282427655
#> 155 -1.487460310 -0.6224270295 -0.8717503950  0.063470471  0.640203835
#> 156 -1.075192297 -3.0376884592 -2.1013356047  0.583525933  0.078909755
#> 157  1.000028804  0.5620176099  0.5806832705 -0.513358846 -0.328838156
#> 158 -0.621266695  0.0743448088 -0.3188886813 -0.812552122 -1.169529751
#> 159 -1.384426847 -1.6739615362 -0.8913905007 -1.629319906 -1.325006890
#> 160  1.869290622  1.6307516591  0.4918884973  0.568905707 -0.837920727
#> 161  0.425100377  0.5122676704 -0.3442360612  0.333783307 -0.164674729
#> 162 -0.238647101  0.6752377169  0.8113953044 -0.211322559 -0.420647089
#> 163  1.058483049 -0.1059503489  0.4443786012 -0.551097930 -0.489293087
#> 164  0.886422651 -0.3077215910  0.0879473351  0.258361129  2.215376711
#> 165 -0.619243048 -1.8144767326 -3.3776999699 -1.375210446 -0.649842356
#> 166  2.206102465  0.9682530861 -0.0944989555 -1.472754149 -2.049091551
#> 167 -0.255027030 -1.2520016543  0.2878870133 -1.445209673 -0.039446058
#> 168 -1.424494650 -0.2275848223 -0.9072470160 -0.361288425 -0.440944501
#> 169 -0.144399602 -0.0218082837 -1.0931310683  0.790709965  1.610452241
#> 170  0.207538339  1.9304151110  0.1222764256  0.714657846  0.444754785
#> 171  2.307978399  0.3333157163  0.5742711885 -0.565153517  1.014709256
#> 172  0.105802368  1.0382691510 -0.1638321258  1.418014303  0.779815465
#> 173  0.456998805 -0.1810014578  0.5492457630 -1.145756781 -1.091196239
#> 174 -0.077152935 -1.2500111824  1.0021626024 -0.492817823  1.363354259
#> 175 -0.334000842  0.2876587588  0.7921036807 -0.733052274 -1.542323500
#> 176 -0.034726028 -1.2069894073  0.7910072236  0.159232080  0.441193459
#> 177  0.787639606 -0.4331348078 -0.0975554809 -1.751192959 -1.789532864
#> 178  2.075245009  0.5547594342  1.5868361815  1.184830867  1.651873506
#> 179  1.027392439  0.7500748749 -0.3101981792  1.207031601  1.041269490
#> 180  1.207908398 -0.1511697343  0.2780303905  0.977649327  0.191979467
#> 181 -1.231323422  0.2034499083  1.4809434766 -0.081991744 -0.358807429
#> 182  0.983895570 -0.4423598928  0.2424495032  1.156263423  1.383788944
#> 183  0.219924804  0.3026400721 -0.1168779441  0.486796337 -0.609743741
#> 184 -1.467250029 -0.7031134699 -1.1794659198  0.958848663 -0.107008190
#> 185  0.521022743 -0.5911933356  0.7173980667  0.177792371  0.437474905
#> 186 -0.158754605 -0.4440139056  1.6528436306  0.292250881  0.785255028
#> 187  1.464587312  0.2765290493  0.9369109664 -2.113340685 -2.604338233
#> 188 -0.766082000  0.3658451873 -0.4168147929 -0.538047911 -0.142025243
#> 189 -0.430211754  1.0482595231  1.8569412618  1.014025585 -0.394633072
#> 190 -0.926109497 -1.3809134694 -1.3027732306  0.101269641 -0.475039304
#> 191 -0.177103961  0.6717941424  1.0557600956 -1.218707372  0.404870036
#> 192  0.402011779  0.1626202004 -0.1823492038 -0.958376793  0.293077560
#> 193 -0.731748173 -2.0395857803 -1.5869889802 -0.555797485 -0.471582976
#> 194  0.830373168 -0.1612516055  1.3060247136  2.121875912  0.415120414
#> 195 -1.208082786 -0.2944676901 -2.0400506509 -0.179589988  0.156535258
#> 196 -1.047984413 -0.4666515001 -0.7410522862 -0.644735408  0.950718506
#> 197  1.441157707 -1.2163885579  0.2593468422 -2.092583772 -0.421109020
#> 198 -1.015847465 -0.0880848399 -0.7612405881 -1.901870838 -0.732703799
#> 199  0.411974712  0.7734115769 -1.0882395104  1.222250276  0.747174925
#> 200 -0.381076051 -0.4656859091 -0.7888600749 -0.851220441  0.401095496
#> 201  0.409401840 -0.3569500195 -1.2686727585  1.621202883  1.667550000
#> 202  1.688873286  2.5792018786  2.8206910790 -0.329102802  0.486179192
#> 203  1.586588433  0.8139262812 -0.8481624880 -2.326409527 -1.892363132
#> 204 -0.330907801 -0.1969215580 -1.9686026992  2.192998000 -1.000222557
#> 205 -2.285235535 -2.2105076665 -0.7033089159 -1.082479976 -1.075983055
#> 206  2.497661590  0.2850886201  1.7322295439 -0.506360967  0.792814486
#> 207  0.667066167 -0.8883662424 -0.1259570386  0.095918957 -0.103940522
#> 208  0.541327336 -0.0464542346  0.0053602615 -0.120165258 -0.595910872
#> 209 -0.013399523  1.1200121243  0.8640789478 -1.518667630 -2.536754371
#> 210  0.510108423  1.7386667806  1.7651263956 -1.510585063 -1.346645664
#> 211 -0.164375832  1.2073281218 -1.1574901847  1.395604928  0.111982609
#> 212  0.420694643  1.3099414031  1.5579485652 -0.708421944 -0.899428352
#> 213 -0.400246744 -0.4209849144 -0.0672868988  0.827938353  0.535648793
#> 214 -1.370207878 -1.7815157488 -1.1722896524  1.707755837  0.762229912
#> 215  0.987838267  0.2815990478  1.4999258107 -0.779166557  0.609660927
#> 216  1.519745025 -1.1476400046  1.0956020007 -0.706899069 -1.691458636
#> 217 -0.308740569 -0.4328697946  0.8911171143 -1.992902511 -2.353355521
#> 218 -1.253289756  0.6733549723 -0.5484884304  1.899876533  0.154962769
#> 219  0.642241306  0.4681488069  0.9981894106 -0.756206936 -0.447590610
#> 220 -0.044709137  0.8828985551  0.4322943753 -0.377955780  1.589226649
#> 221 -1.733218407 -0.5651869426 -1.1864363616 -1.363954801  0.371043754
#> 222  0.002131860 -0.6441275799  1.3667108224  0.741958159  0.102010989
#> 223 -0.630300334  1.0915578469  0.1544294648  1.610975996  0.256962185
#> 224 -0.340968580 -0.2558856911 -0.2248939350  0.227387447  1.174622320
#> 225 -1.156572363 -1.4559196280 -0.2792958033 -0.400515674  0.030897813
#> 226  1.803141908  1.0683006108  1.2128252189 -1.669580400 -1.281690580
#> 227 -0.331132036 -1.4435824231 -1.0416931916  1.490701097  0.803605726
#> 228 -1.605513412 -0.1834529680 -0.6586378120  0.691487433  1.370901047
#> 229  0.197193439  0.5259740249  2.4227155155 -0.040977477 -0.110484005
#> 230  0.263175646 -0.1465553468 -0.0007136956  1.204344853  0.842154530
#> 231 -0.985826700 -0.9567226747 -0.8165588227  1.298514964  1.373731031
#> 232 -2.888920672 -0.8420829627 -0.5856972336 -0.462217021 -0.708002485
#> 233 -0.640481703 -1.2388672473 -0.1568200494 -1.225773748 -2.365400200
#> 234  0.570507636 -0.4956040428 -0.3676067714  0.963266754  0.521474296
#> 235 -0.059723276  0.3180411951 -0.8802998914  0.693211228  1.400850390
#> 236 -0.098178744 -0.4288899788  0.5979871257 -0.501393166 -0.424674121
#> 237  0.560820729  1.0804855230  0.5400000415  3.153971417  2.316354014
#> 238 -1.186458639 -0.8289727101 -0.1919439012 -2.549106895 -1.881379758
#> 239  1.096777044  1.6041203789  0.4945347332 -0.008138085 -0.764651246
#> 240 -0.005344028  0.4075624689 -1.3297636501  1.138780641  0.999856044
#> 241  0.707310667 -1.4639983357 -0.0109431056  1.482346468  0.511170415
#> 242  1.034107735 -0.5272449684  2.3039617752  0.975845009  1.244374917
#> 243  0.223480415  1.1879188072 -0.9129333642  0.148350293  0.872643127
#> 244 -0.878707613  0.0802430364 -1.1407475528  0.788908757  0.101583481
#> 245  1.162964556 -0.1499441196 -0.7647011617  0.557581220  0.395764395
#> 246 -2.000164945 -2.2350724878 -1.5189972028 -0.027394393  0.747498425
#> 247 -0.544790740  0.5513013189  1.1125366615 -0.877074959  0.718101868
#> 248 -0.255670709 -0.8157263926 -0.4024290351  1.216243471  0.352315238
#> 249 -0.166121037  1.3996884584  0.0297772389 -0.351249812 -0.596931276
#> 250  1.020463909  2.0391692062 -0.2926101572 -0.294393117 -0.426845359
#> 251  0.136221893 -1.1289167853 -0.1440913217  0.253137809  1.144236499
#> 252  0.407167603 -0.4726044882  0.9294967591  0.011497986 -0.617400028
#> 253 -0.069654813 -1.0750198484  1.6777889857 -1.975783962 -1.644352130
#> 254 -0.247664342  0.4141511998  1.1310100413 -0.426326724 -0.449382615
#> 255  0.695550807 -0.6798846920 -0.6482470250  0.612302560 -0.731143161
#> 256  1.146228357 -1.0440975070 -0.2529223765  1.230814109  0.337430641
#> 257 -2.403096215  0.3289371610 -0.2633473348 -1.270807808 -1.042349943
#> 258  0.572739555  1.1541757484  0.4498889744 -0.650555664 -0.314705252
#> 259  0.374724407  0.8868265305  0.5652470777 -2.443166237 -0.804236514
#> 260 -0.425267722 -0.7882593082 -1.4513579913  0.996548595  1.858321539
#> 261  0.951012808  0.5232207556  0.0884324570  0.005113528  0.675027103
#> 262 -0.389237182  0.2954252038 -0.8686675388  0.791024764 -0.610262210
#> 263 -0.284330662 -1.2207219962 -1.1670778241 -0.563191537  0.931225586
#> 264  0.857409778  0.3771998855 -0.2279920669  0.213826203  0.788325521
#> 265  1.719627299  1.1085919490  0.5015723168  0.977082664  0.600667843
#> 266  0.270054901  1.5536813187  0.4336942919 -0.234161103  0.982408345
#> 267 -0.422184010  0.2955791635  0.4580880240  0.848660554  0.924208208
#> 268 -1.189113295  0.3964171427 -0.7736822888  0.653970891  0.238581951
#> 269 -0.331032979 -0.0689363396 -0.8686241611 -1.590570026 -1.373176683
#> 270 -0.939829327 -1.4480046712  0.7326439862  0.309423133  0.907809083
#> 271 -0.258932583 -0.4264221066  0.6665337686 -2.485982190 -3.224077227
#> 272  0.394379168 -1.1583928620  0.4834286719 -0.278439107 -0.284249696
#> 273 -0.851857092  0.2925068461  1.2193274800 -0.552433759 -1.243168065
#> 274  2.649166881  2.6573640115  0.6911946801  0.876042073 -1.183068469
#> 275  0.156011676  0.0354028378  1.8214793962  0.293483694  0.348795695
#> 276  1.130207267 -0.1797542640  1.4158709135 -0.597222047 -0.440411137
#> 277 -2.289123980 -0.3812134828 -0.6369255093 -0.157203603 -1.764940452
#> 278  0.741001157  0.5303920595  0.9168326437  0.184185060 -0.128568250
#> 279 -1.316245160 -1.0571208671 -0.6496567871 -1.013032014 -0.218808536
#> 280  0.919803678  1.4459722760  0.5514633339 -0.679843405  0.151913111
#> 281  0.398130155 -0.4065736226 -1.3000969800 -1.242693614 -0.452015625
#> 282 -0.407528579  0.7236881185  0.6512696708 -1.535018736 -0.263806884
#> 283  1.324258630  0.0435994807  2.3201675233 -0.524540013 -0.134253687
#> 284 -0.701231669 -0.0684066759  1.5280249286 -0.018527385  0.294045686
#> 285 -0.580614304  0.4133554450  0.0296779537 -1.568147171 -0.972112584
#> 286 -1.001072181 -1.6668523933 -0.8167668185  0.467851674 -0.596813209
#> 287 -0.668178607 -0.0443376617 -0.0919031168 -0.667828864 -0.164714252
#> 288  0.945184953  0.4368547326  1.4166171625  0.311082360  0.938528184
#> 289  0.433702150  0.8027220430  1.5991344261  0.142551004  1.964596175
#> 290  1.005159218 -0.0904583975  0.6886041234 -0.374034721 -0.575188117
#> 291 -0.390118664 -0.2905339866  0.7530034003 -1.944926376 -1.079422298
#> 292  0.376370292  1.3559794447  0.4096916164 -1.597681314 -2.656899577
#> 293  0.244164924  0.2763252128  0.5750319087 -2.540657861 -2.079029464
#> 294 -1.426257342 -0.1166964969  0.4829976683  1.362047250  1.830522714
#> 295  1.778429287  0.8129108599  3.9363620294 -0.360666003 -0.412688895
#> 296  0.134447661 -0.7775526856 -0.1696675317  1.936397311  1.555700120
#> 297  0.765598999  0.4196835854 -0.2078273188 -1.455883798 -0.262317262
#> 298  0.955136677 -0.4800195770  0.6174414954  1.481905708  0.043110491
#> 299 -0.050565701 -2.1791758853 -0.8462909109  1.076119636  0.615475817
#> 300 -0.305815420  0.7973527892  0.6116945662 -0.757488401 -0.231542127
#> 301  0.893673702 -0.4000386461  0.5234193070  0.714085544  0.141655740
#> 302 -1.047298149 -2.0993832394  0.2934074258  0.581384629  0.496036966
#> 303  1.971337386  1.9285325556  0.3043202285 -0.146723902 -0.623988718
#> 304 -0.383632106 -0.2246613777 -1.2207828400  1.506981777 -0.111555689
#> 305  1.654145302  0.4295336772  2.0296536572 -0.279532643  0.280484046
#> 306  1.512212694  0.6994105173  0.8866988083  2.027738733  2.290385368
#> 307  0.082965734 -0.3064615816 -0.8294161565 -1.195740196 -0.519134937
#> 308  0.567220915  1.1433681404 -0.4672215020  1.312317892  0.677482219
#> 309 -1.024548480  0.0291143689 -0.8329502617 -0.524007513 -0.537406603
#> 310  0.323006503 -1.2496170422  0.3465933420  0.354249509  1.369893404
#> 311  1.043612458  0.8772110177  0.1129870923 -0.071674488  0.871202274
#> 312  0.099078487  0.6576437016  1.3316066842 -0.133144306  1.088983520
#> 313 -0.454136909  0.2993326091  0.1132091135 -0.088077384  0.466937150
#> 314 -0.655781852 -2.3757668054 -0.5891329658  0.917788931  0.740921466
#> 315 -0.035922423 -0.2151084433 -0.0735126213  0.031439264  0.431558834
#> 316  1.069161461  2.2388419891  0.6191369799  1.358930582  0.979177598
#> 317 -0.483974930  0.3891124237 -0.2307742497  0.113494845 -0.930732007
#> 318 -0.121010111 -1.4838883415  0.6223180707  0.174306546  1.880347097
#> 319 -1.294140004 -2.1030556306 -2.0735676488 -0.053480405 -0.978962123
#> 320  0.494312836  0.6836958215  1.2594274639 -0.424758034  0.551113728
#> 321  1.307901520  0.5882211682  0.2951140361  0.207911552 -0.907523454
#> 322  1.497041009  1.6347650907  1.5244634040  0.992922918 -0.184508264
#> 323  0.814702731  0.6996667463  0.3945566695  0.813857888 -0.131567091
#> 324 -1.869788790 -0.9799743487 -2.0375254183  0.996005584 -0.434486899
#> 325  0.482029504  0.4220990013  0.5625634115  1.732744271  0.912267461
#> 326  0.456135603  0.3931770056 -0.2985127863  0.357042034 -0.503636765
#> 327 -0.353400286 -1.2497576004  0.5634795064  0.155726335  0.217166880
#> 328  0.170489471  2.0420119503 -0.1996397447  1.552788656  2.540975151
#> 329 -0.864035954 -1.6536961755 -2.2064788978 -0.064069618  0.575211047
#> 330  0.679230774  0.3663167621 -0.4098698339 -1.008218758 -1.966071671
#> 331 -0.327101015 -0.6341411277 -0.7471855651 -0.892895524 -0.104236828
#> 332 -1.569082185  0.6126937364 -1.1333496812 -0.654514621 -0.304654278
#> 333 -0.367450756  0.6321982850 -0.1956535197 -1.433782829  0.806371621
#> 334  1.364434929  0.2970485612  0.0412152967  1.418184353  1.212694110
#> 335 -0.334281365 -0.0170079539 -0.4754135836 -0.593885665 -0.546709478
#> 336  0.732750042  1.3759166332  0.8458584105  1.118971798 -0.419324134
#> 337  0.946585640  2.3828648981 -0.1360064515  2.384081563  1.373850545
#> 338  0.004398704  0.2528876554  0.7095646838 -0.403286494  0.760041545
#> 339 -0.352322306 -1.0610095039 -0.3615653869  0.370108558 -0.533437418
#> 340 -0.529695509 -1.1114870206 -0.4665527512 -0.575293014 -0.956202277
#> 341  0.739589226  2.0758929821 -1.0261989021  2.919228807  2.450439843
#> 342 -1.063457415 -2.3109893195 -1.1468164212 -1.078914790  0.155346413
#> 343  0.246210844  2.6695380342  0.1990681981  1.178491329  0.420069538
#> 344 -0.289499367 -0.3786466803  0.5403872972  0.869602773  0.083078535
#> 345 -2.264889356 -1.6447994955  0.0233554057  0.931166310  0.296241810
#> 346 -1.408850456 -0.6584185000  0.4090089154  1.024681228  1.490314541
#> 347  0.916019329  1.2862764847 -0.3452948596  0.612975056  0.391834960
#> 348 -0.191278951  0.1437747754 -0.7196221078  0.608190081  0.554881207
#> 349  0.803283216 -1.1708173966 -0.0482365269 -0.892891710  0.851588107
#> 350  1.887474463  1.3498882496  0.0612425323  0.452035606  0.973405395
#> 351  1.473881181  1.1985468411 -0.5869556267 -0.374712307  0.798473410
#> 352  0.677268492  0.9257033759  1.1244956733  2.840185145  3.015840127
#> 353  0.379962687 -0.6417453431  0.0526311358  0.732393453  0.151006548
#> 354 -0.192798426 -2.0723420473  0.0019430013  0.840518928  0.386031329
#> 355  1.577891795  0.6147103337 -0.3341702170 -2.219652117 -1.104477517
#> 356  0.596234109 -0.4484534328 -0.1782782440 -1.327463782 -0.365083835
#> 357 -1.173576941 -1.2917372884 -1.7081118030 -0.976660698 -0.962480965
#> 358 -0.155642535 -0.8773588908 -0.9604738075 -0.587075872 -0.140744398
#> 359 -1.918909820 -1.4043332436 -0.7970313171 -0.568012815 -0.905184479
#> 360 -0.195258846 -0.3671859897 -0.8498469210  0.643640957  0.653300630
#> 361 -2.592327670 -0.7921465677 -1.9514816053 -0.237307108 -0.917638137
#> 362  1.314002167  1.5530898040 -0.3100469309 -0.298578026 -0.359706441
#> 363 -0.635543001 -1.0141676890 -1.6807334469  1.189562559  1.819048627
#> 364 -0.429978839 -0.4966415560 -1.0031379028 -2.108941204 -1.466193517
#> 365 -0.169318332  0.2046360504  1.4466794089 -0.073282004 -0.618846881
#> 366  0.612218174  1.5017302667 -0.0134380549  0.863402869  0.968516315
#> 367  0.678340177  0.3334165711 -0.6398123907  1.074707461 -1.879584507
#> 368  0.567951972 -1.0894510235 -1.2434575743 -0.205852630 -0.030783039
#> 369 -0.572542604 -0.1285357386 -0.3617710020 -0.433613832 -0.071525277
#> 370 -1.363291256 -0.8621088440 -1.0142015758 -0.182223784  1.840294479
#> 371 -0.388722244  1.2508127684  0.3531880092 -0.431078673 -0.706088231
#> 372  0.277914132  0.4401546394 -0.0465101215 -0.424609610 -0.902415859
#> 373 -0.823081122 -0.9771175666  0.2357387943 -1.353819676  1.135325183
#> 374 -0.068840934 -0.4026918944  0.5046360890 -0.196594949  0.194165231
#> 375 -1.167662326 -1.0725255572  0.2534928979  0.234116137  0.126245134
#> 376 -0.008309014  0.1494756878  0.2389062804 -0.557206294  0.112216659
#> 377  0.128855402  0.2183198660  1.0502542530 -1.113325275 -0.994116677
#> 378 -0.145875628  0.6770831166  0.0314340913 -1.630635426 -1.916487264
#> 379 -0.163910957  0.1734739148  0.7802752413 -0.387823881  0.421548167
#> 380  1.763552003  0.6837914068  0.6440242132  1.722632017  1.038417120
#> 381  0.762586512 -0.3522410572 -0.3904068223 -0.558500300 -0.394712663
#> 382  1.111431081  1.1482480916 -0.3976186757 -0.636660846 -1.446598311
#> 383 -0.923206953 -0.5687671392 -1.0628444215  2.781387134  0.898414330
#> 384  0.164341838  0.2435112512 -0.5301716673 -1.957255876 -0.696414399
#> 385  1.154825187  1.5610605294  1.2500487670  0.142527896 -0.708602973
#> 386 -0.056521425  1.4198965597  0.2479111485  0.664498799  0.785981703
#> 387 -2.129360648 -1.9826718488 -1.7370416671 -0.478627492  0.761083572
#> 388  0.344845762  1.5552221307 -0.3052693972  1.183689583  1.447680501
#> 389 -1.904955446 -1.7848573710  0.2254412279  0.805437291 -0.649813676
#> 390 -0.811170153 -0.2335844636 -0.5439011540  0.053317758  0.135040704
#> 391  1.324004321  0.9256747310 -0.3954630080 -1.167346415 -0.645499171
#> 392  0.615636849  0.1153399823 -0.1240106606  0.323350156  0.930830346
#> 393  1.091668956  1.7664629520  0.8585104139 -0.320783022  0.137853534
#> 394  0.306604862 -0.3742049981  0.7417310326 -0.885950264 -1.580156765
#> 395 -0.110158762  0.4855563757 -0.0052076539  0.151278172 -0.195612470
#> 396 -0.924312773 -0.5285974025 -0.3501109363  0.579363472  1.258310857
#> 397  1.592913754  0.1203071609 -0.2973112670 -0.079166826  0.730083409
#> 398  0.045010598  1.0315669102  0.9266769713  0.848767635  1.991945053
#> 399 -0.715128401 -2.1306464583 -0.6386593513 -2.511033487 -2.218708511
#> 400  0.865223100  0.0486115047  0.9516513691  0.738477114 -0.142160106
#> 401  1.074440958 -0.6753536946  1.5617666099 -0.570994285 -0.629885545
#> 402  1.895654774  1.2225602434  1.0989056274  0.286539016  0.985105137
#> 403 -0.602997304 -0.1186063627 -0.4836278902  1.147619856  0.727292261
#> 404 -0.390867821 -1.1457497962 -1.0501862030  0.139558702  1.306760788
#> 405 -0.416222032  0.3062253741 -0.5755859872  0.088926609  0.513795094
#> 406 -0.375657423 -1.0661183683 -1.1538354385 -2.630159317 -1.354869651
#> 407 -0.366630946  0.3408302393  0.2617330624 -1.217220832  0.834225838
#> 408 -0.295677453  0.0314605258 -1.3579053992  0.749152579  0.849014189
#> 409  1.441820410  1.4000202639 -0.6750407544 -1.415932924 -0.219709726
#> 410 -0.697538292 -1.1681477033 -1.0787556777 -0.112382662 -0.039728183
#> 411 -0.388167506 -0.1383737112  0.7614750561  0.304032006  0.033519236
#> 412  0.652536452 -0.0180220546  0.3341517298 -0.354012805 -0.795619380
#> 413  1.124772447 -0.5870854369 -0.1522837326 -0.851242490 -1.538682657
#> 414 -0.772110803 -0.3058824087  0.2318093914 -1.461173075 -1.002885523
#> 415 -0.508086216  1.1850209292 -0.2217649168  0.264251846  0.170614441
#> 416  0.523620590 -0.2436944466  0.0344029859 -1.907357944  0.446055700
#> 417  1.017754227  0.4043950655  0.5146836281 -0.925231266  0.458176050
#> 418 -0.251164588  0.4303811679  0.9394789720 -0.111571293 -0.357681073
#> 419 -1.429993447 -0.7708500429  0.4293213791 -0.965234425  0.233110669
#> 420  1.709121032  2.5673132443  2.2755653316 -0.162898924 -0.990418911
#> 421  1.435069572  1.4144150888  1.6634791390  0.860184055  0.580961818
#> 422 -0.710371146  1.5254001604  0.3653755473  0.018098775  0.400985400
#> 423 -0.065067574  0.2526309727  1.6453130766  0.137262456 -1.329406734
#> 424 -1.759468735 -1.9247440627  0.7014768578  1.598886071  1.883524122
#> 425  0.569722972  0.6681180188  1.4903797089 -0.111300849 -0.632165792
#> 426  1.612346798  0.1369261834  0.4167025360  0.285455874 -1.340094513
#> 427 -1.637280647 -1.7512208876 -1.8621230193 -1.983909896 -2.140556104
#> 428 -0.779568513 -0.5935364491 -0.2432064770  0.030740218 -1.615541597
#> 429 -0.641176934  0.4146839988 -0.6137596892 -0.760004886 -0.766972067
#> 430 -0.681131394 -0.0965066882 -0.0282164847 -1.224013218 -0.001274842
#> 431 -2.033285596 -0.4642301525 -1.2998003990  1.002366653  0.096078032
#> 432  0.500963559  1.0388928465  1.1980229709 -0.021541423 -1.028472247
#> 433 -1.531798140 -1.0001851779  1.1120925857  0.945321339  0.253008101
#> 434 -0.024997639 -2.0042293961  0.3767740589 -0.908491216 -0.503639541
#> 435  0.592984721  0.9914743864  1.0664220834 -2.402202227 -1.140960540
#> 436 -0.198195421  1.6861070257  0.3327848598  0.162938048  0.462052014
#> 437  0.892008392  0.5478949975  2.3101391610  0.943208931  0.325201451
#> 438 -0.025715071 -1.1369370444 -0.3279054032  2.544604860  1.361654219
#> 439 -0.647660451 -0.6672029443  0.8030100844  0.887190933  1.427265138
#> 440  0.646359415 -0.4122796331  1.4914437251  1.060436766  1.903484576
#> 441 -0.433832740 -0.2774441204 -0.0782233086 -0.615747889 -1.030695807
#> 442  1.772611185  1.5528160618 -1.8172648202  0.352854881  0.604563956
#> 443 -0.018259711  0.7076105039 -0.1337452561 -0.475328128 -0.250792864
#> 444  0.852814994  0.6724171658  0.8444882858  0.422056370  1.330747373
#> 445  0.205162903 -0.6588961248 -1.1909910597 -1.183559154  0.107896162
#> 446 -3.008048599 -1.0107338071 -2.4033691110 -0.383749583  0.676737353
#> 447 -1.366111931  0.3520492734  0.3680768875 -1.459665806 -1.066184835
#> 448 -0.424102260  1.6281709662 -2.1917464989  0.045773224  0.891192890
#> 449  0.236803664 -0.2763773407  0.2239867536  0.452456114  0.840893591
#> 450 -2.342723120 -0.9191427339 -1.2688383116  0.057565870 -1.019457811
#> 451  0.961696633  1.5275148352  0.1143818240 -0.638693853 -1.129894698
#> 452 -0.604425734 -0.4349111986 -0.2570110614 -0.238681318  1.004361868
#> 453 -0.752877279  0.0132301568 -0.2188490994 -1.642902622 -1.302004342
#> 454 -1.555611593 -0.6934958798 -0.4956089492 -0.222574571  0.965402750
#> 455 -1.453893738 -0.9255709387 -0.6159741753 -1.775568451 -0.448395795
#> 456  0.056331836  0.1711543741 -0.4014984919 -0.015465903 -0.895968913
#> 457  0.509369407  1.0845208351  0.6423587615  1.751046874  0.534039979
#> 458 -2.097882960 -0.8361441493  0.2583774761  0.704206506 -0.680520845
#> 459 -1.004361979 -0.9488833214  0.0052638895  1.481019324  0.986977858
#> 460  0.535771722 -1.5556114725  1.1329913469  1.352887912 -2.174903570
#> 461 -0.453037085 -0.9124047384 -0.5984250896 -0.329957836  0.818857569
#> 462  2.165368502  1.1960736938  1.5360582139  0.363498741  0.444554389
#> 463  1.245746673 -1.3855644879  0.5709951780 -1.827662733 -0.348459482
#> 464  0.595498034  2.1652363120  0.0515753788  0.893777744  0.316307983
#> 465  0.004884450 -1.2306932095 -0.9702974599 -0.719124934  0.786036783
#> 466  0.279360782 -0.8052323097  1.5271005793  0.940509520  0.683775089
#> 467 -0.705906125  0.8124179123 -0.7826431777 -1.871157591 -1.861086188
#> 468  0.628017153 -1.4626064283  0.7175789595  1.147002717  0.577449578
#> 469  1.480213960  1.4412277851  0.6169857333 -0.502991095  0.464582876
#> 470  1.083429910  0.3217120281 -0.4858308685  1.425898368 -0.399584038
#> 471 -0.813244257 -0.0777262736 -1.6236342961 -0.019339956 -0.070048620
#> 472 -1.618876849 -0.1790631748 -1.6519106958 -0.638073726 -1.016920381
#> 473 -0.109655699 -0.8554874660 -1.9008235895  0.498271000 -1.001353426
#> 474  0.440889371 -0.3378891887 -0.6757630347 -0.058246735  1.704068226
#> 475  1.350993980 -1.7263937128  0.9367894119 -0.626216778 -0.212036390
#> 476 -1.318609485 -1.5346460568 -1.3068420174 -0.894620761 -0.075060691
#> 477  0.364384593  0.5190385295  1.7345666899  2.410060215  1.453522320
#> 478  0.233499835  0.5492046717  0.0560863421 -0.949647251 -1.841854565
#> 479  1.193955261  2.3480158596  0.1381680002  0.559151501  0.373638570
#> 480 -0.027909972  0.0379134311 -0.2458052167 -0.211414690  0.998164722
#> 481 -0.357298855  0.1840504039 -0.5923077423 -1.017854802  0.569509678
#> 482 -1.146814136 -0.5802626204 -0.9177504479 -1.390190989 -1.206905013
#> 483 -0.517420484 -0.6930956931 -0.2857279087 -1.488629309  0.422219140
#> 484 -0.362123773  0.4176777658  0.0334189892 -1.406044634  0.454629589
#> 485  2.350554326  1.7009253407  1.8637513403 -1.496235482 -0.163020873
#> 486  2.446531376  1.4772814634  1.6610259451  0.686145924  1.764219220
#> 487 -0.166703279 -0.7689569577  0.4375831414 -0.236761631  0.708307550
#> 488 -1.043667439 -0.6177181183 -0.3948745548  1.999142429  1.556264730
#> 489 -1.972934934 -0.4574453740 -1.4967514890  0.633238683 -1.256751438
#> 490  0.514671633  0.8486522150  0.7560714283  1.648197547  1.493250586
#> 491 -1.090573584 -1.0105952561 -0.2574819052  0.502718643  0.344762456
#> 492  2.284659326  0.7250536608  0.6281918277  0.845467412 -0.220400492
#> 493 -0.885617573 -0.0710937366 -0.6645192072  0.467247396  0.137229672
#> 494  0.111106430  0.9312337223  1.1845111392 -0.402055064 -1.050506383
#> 495  3.810276681  2.2340507344  3.0012591306  0.923526703  1.525119170
#> 496 -1.108909998 -0.8805504382 -0.4912841819 -0.008055641 -0.146875426
#> 497  0.307566624 -0.5573918794 -0.3496832267  1.033784238 -0.526256809
#> 498 -1.106894472 -0.9672369941  0.8100186652 -0.799126982 -0.330229100
#> 499  0.347653649 -1.0337627600 -1.1709151582  1.004233021 -0.507554021
#> 500 -0.873264535 -1.0667511126 -1.3289289550 -0.311973356 -1.278660869
#>               y6
#> 1   -1.302942894
#> 2   -1.376772140
#> 3    0.318337577
#> 4    0.524683654
#> 5   -0.264099300
#> 6    1.034987017
#> 7   -0.706194369
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#> 9   -1.359121581
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#> 11  -1.426151033
#> 12  -0.418235051
#> 13  -1.122857398
#> 14   0.043411009
#> 15   0.991176304
#> 16   0.940944023
#> 17  -1.670669562
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#> 20   0.999719225
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#> 311  0.782679779
#> 312  2.648330760
#> 313  0.687530952
#> 314  0.207993146
#> 315 -0.005685039
#> 316  0.230697611
#> 317 -1.264391421
#> 318 -1.386095385
#> 319 -0.234235652
#> 320  1.294782128
#> 321  0.207684363
#> 322  0.043329760
#> 323  0.939870228
#> 324  0.421330813
#> 325  1.320335299
#> 326  0.458298098
#> 327 -0.042697714
#> 328  2.006947166
#> 329  0.379430345
#> 330 -2.129192367
#> 331  0.196098717
#> 332  1.393003495
#> 333 -0.073310229
#> 334  2.480113598
#> 335  0.079921666
#> 336  0.774492174
#> 337  0.953274118
#> 338 -1.740718098
#> 339 -0.970030921
#> 340 -0.570304347
#> 341  0.636752609
#> 342 -1.696814630
#> 343  0.471351775
#> 344 -0.184596347
#> 345  2.471610155
#> 346  0.787760295
#> 347  0.691019611
#> 348  0.760257155
#> 349 -0.087764149
#> 350  0.937409857
#> 351  0.498558581
#> 352  2.338596403
#> 353  1.146643825
#> 354  1.280210896
#> 355 -0.985301005
#> 356 -1.637812102
#> 357 -2.837346535
#> 358 -0.626029096
#> 359 -1.704020284
#> 360  0.100538608
#> 361 -0.494989370
#> 362  0.065471913
#> 363  2.259576921
#> 364  0.381827457
#> 365  0.625836483
#> 366  0.720615097
#> 367  0.331540091
#> 368 -0.121268436
#> 369 -1.537755296
#> 370  2.012887941
#> 371  0.708969618
#> 372  0.657291463
#> 373 -0.666789919
#> 374  0.468845678
#> 375  0.533643775
#> 376 -1.518870653
#> 377 -0.760217407
#> 378 -0.679703929
#> 379  0.300431341
#> 380  0.304665615
#> 381  1.329330929
#> 382  1.046483572
#> 383  1.787344306
#> 384 -1.402507247
#> 385 -0.909786602
#> 386 -0.704867387
#> 387 -0.564740564
#> 388 -0.836288720
#> 389  0.571051759
#> 390 -1.207015377
#> 391 -1.586633856
#> 392  0.904801613
#> 393  0.265729530
#> 394  0.312717612
#> 395  0.441379141
#> 396  0.426278785
#> 397  0.510187447
#> 398 -0.564465239
#> 399 -1.290216233
#> 400  0.394272480
#> 401  0.327800052
#> 402  0.279282416
#> 403  0.651673140
#> 404 -0.808126587
#> 405  0.615793511
#> 406 -2.871322103
#> 407 -0.075067841
#> 408  0.804329189
#> 409  0.670879561
#> 410  0.745120415
#> 411  0.994762203
#> 412 -1.844456978
#> 413  0.732382716
#> 414 -1.115667742
#> 415  2.403255637
#> 416 -1.160117365
#> 417 -1.240561747
#> 418  0.493699304
#> 419 -0.303278520
#> 420  0.804797367
#> 421  0.025470891
#> 422 -0.714142152
#> 423  0.408829514
#> 424  0.770657049
#> 425  0.746798149
#> 426  0.358219237
#> 427 -1.374362800
#> 428 -0.193929766
#> 429 -0.123695428
#> 430 -1.439863978
#> 431 -0.118545461
#> 432  0.020905805
#> 433  1.982415803
#> 434  0.257272358
#> 435 -0.689158196
#> 436  0.954899641
#> 437  0.801289014
#> 438  0.648044552
#> 439  1.674060443
#> 440 -0.134809518
#> 441 -1.283356464
#> 442  0.527616764
#> 443  1.226695957
#> 444 -0.047491499
#> 445  0.503722027
#> 446 -0.143320524
#> 447 -0.338717146
#> 448 -1.019502455
#> 449 -0.564628420
#> 450  1.419964151
#> 451 -0.455663939
#> 452  0.194340069
#> 453 -3.080063265
#> 454  1.180386436
#> 455 -0.846740998
#> 456  0.187221358
#> 457  1.052486528
#> 458  0.437110820
#> 459  0.400636475
#> 460  1.620881774
#> 461  0.179217851
#> 462  0.082431587
#> 463  0.663066476
#> 464  0.068360763
#> 465 -1.238691073
#> 466 -1.306197686
#> 467 -1.164491687
#> 468  0.026234636
#> 469 -0.262302823
#> 470  0.485095687
#> 471  1.837058011
#> 472  0.102234549
#> 473 -0.212199140
#> 474  1.447509995
#> 475 -0.533763655
#> 476  0.112339027
#> 477  2.177340316
#> 478 -0.824079949
#> 479 -1.350292628
#> 480 -0.278783882
#> 481  1.361629211
#> 482 -0.944265283
#> 483  0.537436771
#> 484 -0.021406887
#> 485 -0.509549309
#> 486 -1.619875103
#> 487  0.686323545
#> 488  0.536991870
#> 489 -0.368985995
#> 490  0.458823736
#> 491  1.810228459
#> 492 -0.773543026
#> 493 -2.112870550
#> 494  0.094154247
#> 495  1.325119464
#> 496 -0.195478976
#> 497  0.055960572
#> 498  1.041076386
#> 499 -1.611102531
#> 500 -1.317739585
r$params$sigma_implied  # implied covariance matrix
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 1.00 0.56 0.48 0.00 0.00 0.00
#> [2,] 0.56 1.00 0.42 0.00 0.00 0.00
#> [3,] 0.48 0.42 1.00 0.00 0.00 0.00
#> [4,] 0.00 0.00 0.00 1.00 0.56 0.48
#> [5,] 0.00 0.00 0.00 0.56 1.00 0.42
#> [6,] 0.00 0.00 0.00 0.48 0.42 1.00

# Oblique model
phi <- matrix(c(1, 0.4, 0.4, 1), nrow = 2)
r2  <- simulate_fa(loadings = loadings, phi = phi, n = 500, seed = 1)