This function generates random drift matrices \(\boldsymbol{\Phi}\) using the Monte Carlo method.
Arguments
- phi
Numeric matrix. The drift matrix (\(\boldsymbol{\Phi}\)).
phishould have row and column names pertaining to the variables in the system.- vcov_phi_vec
Numeric matrix. The sampling variance-covariance matrix of \(\mathrm{vec} \left( \boldsymbol{\Phi} \right)\).
- R
Positive integer. Number of replications.
- test_phi
Logical. If
test_phi = TRUE, the function tests the stability of the generated drift matrix \(\boldsymbol{\Phi}\). If the test returnsFALSE, the function generates a new drift matrix \(\boldsymbol{\Phi}\) and runs the test recursively until the test returnsTRUE.- ncores
Positive integer. Number of cores to use. If
ncores = NULL, use a single core. Consider using multiple cores when number of replicationsRis a large value.- seed
Random seed.
Value
Returns an object
of class ctmedmc which is a list with the following elements:
- call
Function call.
- args
Function arguments.
- fun
Function used ("MCPhi").
- output
A list simulated drift matrices.
Details
Monte Carlo Method
Let \(\boldsymbol{\theta}\) be \(\mathrm{vec} \left( \boldsymbol{\Phi} \right)\), that is, the elements of the \(\boldsymbol{\Phi}\) matrix in vector form sorted column-wise. Let \(\hat{\boldsymbol{\theta}}\) be \(\mathrm{vec} \left( \hat{\boldsymbol{\Phi}} \right)\). Based on the asymptotic properties of maximum likelihood estimators, we can assume that estimators are normally distributed around the population parameters. $$ \hat{\boldsymbol{\theta}} \sim \mathcal{N} \left( \boldsymbol{\theta}, \mathbb{V} \left( \hat{\boldsymbol{\theta}} \right) \right) $$ Using this distributional assumption, a sampling distribution of \(\hat{\boldsymbol{\theta}}\) which we refer to as \(\hat{\boldsymbol{\theta}}^{\ast}\) can be generated by replacing the population parameters with sample estimates, that is, $$ \hat{\boldsymbol{\theta}}^{\ast} \sim \mathcal{N} \left( \hat{\boldsymbol{\theta}}, \hat{\mathbb{V}} \left( \hat{\boldsymbol{\theta}} \right) \right) . $$
Linear Stochastic Differential Equation Model
The measurement model is given by $$ \mathbf{y}_{i, t} = \boldsymbol{\nu} + \boldsymbol{\Lambda} \boldsymbol{\eta}_{i, t} + \boldsymbol{\varepsilon}_{i, t}, \quad \mathrm{with} \quad \boldsymbol{\varepsilon}_{i, t} \sim \mathcal{N} \left( \mathbf{0}, \boldsymbol{\Theta} \right) $$ where \(\mathbf{y}_{i, t}\), \(\boldsymbol{\eta}_{i, t}\), and \(\boldsymbol{\varepsilon}_{i, t}\) are random variables and \(\boldsymbol{\nu}\), \(\boldsymbol{\Lambda}\), and \(\boldsymbol{\Theta}\) are model parameters. \(\mathbf{y}_{i, t}\) represents a vector of observed random variables, \(\boldsymbol{\eta}_{i, t}\) a vector of latent random variables, and \(\boldsymbol{\varepsilon}_{i, t}\) a vector of random measurement errors, at time \(t\) and individual \(i\). \(\boldsymbol{\nu}\) denotes a vector of intercepts, \(\boldsymbol{\Lambda}\) a matrix of factor loadings, and \(\boldsymbol{\Theta}\) the covariance matrix of \(\boldsymbol{\varepsilon}\).
An alternative representation of the measurement error is given by $$ \boldsymbol{\varepsilon}_{i, t} = \boldsymbol{\Theta}^{\frac{1}{2}} \mathbf{z}_{i, t}, \quad \mathrm{with} \quad \mathbf{z}_{i, t} \sim \mathcal{N} \left( \mathbf{0}, \mathbf{I} \right) $$ where \(\mathbf{z}_{i, t}\) is a vector of independent standard normal random variables and \( \left( \boldsymbol{\Theta}^{\frac{1}{2}} \right) \left( \boldsymbol{\Theta}^{\frac{1}{2}} \right)^{\prime} = \boldsymbol{\Theta} . \)
The dynamic structure is given by $$ \mathrm{d} \boldsymbol{\eta}_{i, t} = \left( \boldsymbol{\iota} + \boldsymbol{\Phi} \boldsymbol{\eta}_{i, t} \right) \mathrm{d}t + \boldsymbol{\Sigma}^{\frac{1}{2}} \mathrm{d} \mathbf{W}_{i, t} $$ where \(\boldsymbol{\iota}\) is a term which is unobserved and constant over time, \(\boldsymbol{\Phi}\) is the drift matrix which represents the rate of change of the solution in the absence of any random fluctuations, \(\boldsymbol{\Sigma}\) is the matrix of volatility or randomness in the process, and \(\mathrm{d}\boldsymbol{W}\) is a Wiener process or Brownian motion, which represents random fluctuations.
See also
Other Continuous Time Mediation Functions:
DeltaBeta(),
DeltaIndirectCentral(),
DeltaMed(),
DeltaTotalCentral(),
Direct(),
Indirect(),
IndirectCentral(),
MCBeta(),
MCIndirectCentral(),
MCMed(),
MCTotalCentral(),
Med(),
PosteriorBeta(),
PosteriorIndirectCentral(),
PosteriorMed(),
PosteriorPhi(),
PosteriorTotalCentral(),
Total(),
TotalCentral(),
Trajectory()
Examples
set.seed(42)
phi <- matrix(
data = c(
-0.357, 0.771, -0.450,
0.0, -0.511, 0.729,
0, 0, -0.693
),
nrow = 3
)
colnames(phi) <- rownames(phi) <- c("x", "m", "y")
MCPhi(
phi = phi,
vcov_phi_vec = 0.1 * diag(9),
R = 100L # use a large value for R in actual research
)
#> [[1]]
#> x m y
#> x -0.3295 0.2220 -0.2679
#> m 0.7555 -0.8565 0.0091
#> y -0.4690 1.5626 -0.7618
#>
#> [[2]]
#> x m y
#> x -0.3830 0.0943 -0.4144
#> m 0.9453 -0.4066 -0.3812
#> y -0.1887 0.7553 -0.8437
#>
#> [[3]]
#> x m y
#> x -0.1077 -0.0344 0.001
#> m 0.4363 -0.7873 -0.033
#> y -0.9239 0.9293 -0.606
#>
#> [[4]]
#> x m y
#> x -0.7750 0.1073 -0.1698
#> m 1.2028 -0.5626 -0.0798
#> y 0.0148 0.6496 -0.5988
#>
#> [[5]]
#> x m y
#> x -1.0155 0.2169 -0.4148
#> m 0.8304 -0.3326 -0.1625
#> y -0.0059 0.3293 -0.4056
#>
#> [[6]]
#> x m y
#> x -0.5023 -0.3002 0.2227
#> m 0.5239 -0.0857 0.3440
#> y -0.0757 0.5680 -0.9511
#>
#> [[7]]
#> x m y
#> x -0.1279 -0.4010 -0.1586
#> m 0.7976 -0.4652 -0.6030
#> y -0.3153 0.3125 -0.7378
#>
#> [[8]]
#> x m y
#> x -0.6284 0.2739 -0.1972
#> m 0.4140 -0.7338 0.1835
#> y -0.1817 0.6000 -0.6670
#>
#> [[9]]
#> x m y
#> x -0.3203 -0.4097 -0.1738
#> m 1.0749 -0.4948 0.2990
#> y -0.4625 0.9025 -0.8753
#>
#> [[10]]
#> x m y
#> x -0.4946 -0.6680 0.8914
#> m 0.4559 -0.7414 -0.3237
#> y 0.0138 0.7617 -0.7599
#>
#> [[11]]
#> x m y
#> x -0.3574 -0.3296 -0.3109
#> m 0.9960 -1.0598 0.0318
#> y -0.6253 0.8023 -0.3250
#>
#> [[12]]
#> x m y
#> x -0.2388 0.1046 0.1173
#> m 0.5637 -0.5110 -0.0937
#> y -0.4943 0.3738 -0.8324
#>
#> [[13]]
#> x m y
#> x -0.4017 -0.1042 -0.1136
#> m 0.4225 -1.0385 -0.7173
#> y -0.2042 0.4482 -0.7084
#>
#> [[14]]
#> x m y
#> x -0.5168 -0.1229 0.2009
#> m 0.4649 -0.5269 0.1268
#> y -0.4530 0.6824 -1.1855
#>
#> [[15]]
#> x m y
#> x -0.4401 0.1808 -0.1407
#> m 0.5675 -0.7721 -0.0552
#> y 0.0013 -0.1627 -0.8033
#>
#> [[16]]
#> x m y
#> x -0.7018 -0.287 -0.4060
#> m 0.4014 -0.926 -0.6191
#> y -0.4522 1.042 -0.9174
#>
#> [[17]]
#> x m y
#> x -0.2428 -0.1850 0.3692
#> m 0.1528 -0.5686 -0.1734
#> y -0.1697 0.4695 -0.5461
#>
#> [[18]]
#> x m y
#> x -0.8570 -0.0544 -0.0911
#> m 1.4080 -0.4738 -1.0594
#> y 0.0874 0.8196 -0.4478
#>
#> [[19]]
#> x m y
#> x -0.4047 -0.2895 0.1201
#> m 0.7085 -0.7802 0.3837
#> y 0.3360 0.2906 -0.3345
#>
#> [[20]]
#> x m y
#> x -0.1396 -0.0238 -0.1357
#> m 0.3961 -0.4810 0.0038
#> y 0.1203 0.4805 -0.1099
#>
#> [[21]]
#> x m y
#> x -0.5919 0.0691 -0.0411
#> m 0.7065 -0.8078 -0.0403
#> y -0.7677 0.9824 -0.9226
#>
#> [[22]]
#> x m y
#> x -0.3922 -0.0144 -0.1370
#> m 0.5602 -0.4864 -0.6544
#> y -0.7721 0.4842 -0.0734
#>
#> [[23]]
#> x m y
#> x -0.0552 -0.2630 -0.2973
#> m 1.6914 -0.6528 -0.0127
#> y -0.4832 0.2784 -0.6221
#>
#> [[24]]
#> x m y
#> x -0.4761 -0.1023 0.0572
#> m 1.0788 -0.6270 -0.1512
#> y -1.0433 0.8290 -1.1084
#>
#> [[25]]
#> x m y
#> x -0.5386 0.3221 0.0621
#> m 0.4560 -0.7578 0.2615
#> y -0.5445 -0.2587 -0.8716
#>
#> [[26]]
#> x m y
#> x -0.8226 -0.0375 0.1275
#> m 0.9053 -0.3728 -0.0042
#> y -0.1520 0.6408 -0.3339
#>
#> [[27]]
#> x m y
#> x -0.3714 -0.2501 0.0273
#> m 0.3441 -0.5902 0.4339
#> y -0.1173 0.6587 -0.6179
#>
#> [[28]]
#> x m y
#> x -0.2288 0.1370 0.0740
#> m 0.6924 -0.8384 -0.6592
#> y -0.6282 0.4929 -0.9160
#>
#> [[29]]
#> x m y
#> x -0.9407 0.4237 0.1673
#> m 1.0778 -0.5615 -0.1271
#> y -0.1173 0.1810 -0.3245
#>
#> [[30]]
#> x m y
#> x -0.4081 0.0028 0.0232
#> m 0.4974 -0.4713 -0.4130
#> y -0.4946 0.2607 -0.5754
#>
#> [[31]]
#> x m y
#> x -0.1392 -0.4151 0.1329
#> m 0.4121 -0.3814 -0.0712
#> y -0.8051 0.4695 -0.5703
#>
#> [[32]]
#> x m y
#> x -1.0668 -0.3412 -0.0488
#> m 1.5288 -0.5792 -0.6432
#> y -0.0236 0.6782 -0.9510
#>
#> [[33]]
#> x m y
#> x -0.6313 0.1458 0.5649
#> m 1.0035 -1.0179 -0.0652
#> y -0.7079 0.5710 -0.9275
#>
#> [[34]]
#> x m y
#> x -0.5981 0.5447 0.2370
#> m 0.5518 -0.8220 0.1444
#> y -0.2837 0.7441 -0.8026
#>
#> [[35]]
#> x m y
#> x -0.3760 -0.6159 -0.1619
#> m 0.7455 -0.4486 0.3184
#> y -0.5399 0.8208 -0.9259
#>
#> [[36]]
#> x m y
#> x -0.8211 0.3333 0.5403
#> m 0.4818 -0.6742 0.1147
#> y -0.4575 1.0438 -0.6069
#>
#> [[37]]
#> x m y
#> x -0.0438 -0.1913 -0.2189
#> m 1.0121 -1.0879 0.4560
#> y -0.7420 0.9661 -0.4182
#>
#> [[38]]
#> x m y
#> x -0.6305 0.0519 -0.3075
#> m 0.2891 -0.8919 -0.1079
#> y -0.5822 0.8868 -0.8725
#>
#> [[39]]
#> x m y
#> x -0.9969 0.6508 -0.2677
#> m 0.4777 -0.5442 -0.0148
#> y -0.8395 0.8875 -1.0651
#>
#> [[40]]
#> x m y
#> x -0.4153 -0.3777 0.0552
#> m 0.6768 -0.7006 -0.3646
#> y -0.5796 0.6035 -0.3262
#>
#> [[41]]
#> x m y
#> x -0.4109 -0.2373 -0.0544
#> m 0.5736 -0.9596 -0.2123
#> y -0.3284 1.0132 -0.3790
#>
#> [[42]]
#> x m y
#> x -0.1467 -0.3364 -0.4359
#> m 0.2769 -0.4348 0.0457
#> y -0.5458 0.6445 -0.6675
#>
#> [[43]]
#> x m y
#> x -0.3225 0.0097 0.4471
#> m 0.2850 -0.5174 0.2141
#> y -1.0253 1.4949 -0.8394
#>
#> [[44]]
#> x m y
#> x -0.7559 -0.1536 0.4511
#> m 0.9942 -0.9598 0.5648
#> y -0.4914 0.5642 -1.0631
#>
#> [[45]]
#> x m y
#> x -0.1769 0.0374 -0.4160
#> m 0.9637 -0.4728 -0.2756
#> y -0.6885 0.3754 -0.5568
#>
#> [[46]]
#> x m y
#> x -0.3169 -0.1641 0.0323
#> m 1.2726 -0.4854 0.2306
#> y -0.9982 0.6590 -0.7262
#>
#> [[47]]
#> x m y
#> x -0.5678 0.2690 0.0708
#> m 0.4662 -0.5777 0.0837
#> y -0.5875 0.0619 -0.9957
#>
#> [[48]]
#> x m y
#> x -0.9053 -0.4573 -0.0542
#> m 0.6444 -0.5776 -0.2122
#> y -0.0040 0.9637 -0.3440
#>
#> [[49]]
#> x m y
#> x -0.3641 0.2027 0.0351
#> m 0.7360 -0.7475 -0.3221
#> y -0.4191 0.3433 -1.0359
#>
#> [[50]]
#> x m y
#> x -0.1074 -0.1336 -0.3040
#> m 1.0164 -0.4057 -0.1125
#> y -0.5545 1.0478 -1.0712
#>
#> [[51]]
#> x m y
#> x -0.3634 -0.0708 -0.3003
#> m 0.9753 -0.7200 1.1534
#> y -0.4025 0.9655 -0.8761
#>
#> [[52]]
#> x m y
#> x -0.4116 0.1819 0.0896
#> m 0.2703 -0.4336 0.1018
#> y -0.5597 0.6048 -0.6692
#>
#> [[53]]
#> x m y
#> x -0.9718 -0.1154 -0.1710
#> m 1.2792 -0.6169 -0.1020
#> y -0.5817 0.8355 -0.3922
#>
#> [[54]]
#> x m y
#> x -0.3671 -0.0507 0.2011
#> m 0.4971 -0.9741 -0.2671
#> y -0.3027 1.1691 -0.6000
#>
#> [[55]]
#> x m y
#> x -0.9081 -0.2732 -0.1377
#> m 0.7826 -0.2509 0.0539
#> y -0.4285 0.7691 -0.6318
#>
#> [[56]]
#> x m y
#> x -0.6330 -0.1352 0.4032
#> m 1.3981 -0.4071 -0.4848
#> y -0.0628 0.8709 -0.6484
#>
#> [[57]]
#> x m y
#> x -0.5716 -0.2904 -0.9815
#> m 0.6002 -0.5104 0.3351
#> y -0.5145 0.9666 -0.5926
#>
#> [[58]]
#> x m y
#> x -0.0853 -0.1908 0.5859
#> m -0.0739 -0.7610 -0.2784
#> y -1.0674 0.6428 -0.8445
#>
#> [[59]]
#> x m y
#> x -0.3777 0.0656 0.1128
#> m 0.8989 -0.5156 -0.4871
#> y -0.4501 0.3930 -0.4726
#>
#> [[60]]
#> x m y
#> x -1.1444 0.2666 -0.0877
#> m 0.2862 -0.3202 -0.2117
#> y -0.5150 1.3012 -0.5467
#>
#> [[61]]
#> x m y
#> x -0.5269 0.0676 -0.0710
#> m 0.7264 -1.0256 0.0231
#> y -0.0178 0.4719 -0.4232
#>
#> [[62]]
#> x m y
#> x -0.2998 -0.1015 0.1827
#> m 0.4915 -0.6801 0.3549
#> y -0.0945 0.9665 -0.9195
#>
#> [[63]]
#> x m y
#> x -0.0936 -0.1392 0.3097
#> m 1.0521 -0.4798 -0.4324
#> y -0.5027 0.6471 -0.7498
#>
#> [[64]]
#> x m y
#> x -0.6689 -0.0929 -0.2490
#> m 1.0424 -0.1300 0.1806
#> y -0.9117 1.0659 -1.1202
#>
#> [[65]]
#> x m y
#> x -0.4898 -0.1196 0.4541
#> m 0.6970 -0.1351 -0.3419
#> y -0.3528 0.1951 -0.7034
#>
#> [[66]]
#> x m y
#> x -0.2360 -0.0164 -0.3757
#> m 0.9830 -0.6066 -0.2857
#> y -0.1591 0.7775 -1.0288
#>
#> [[67]]
#> x m y
#> x -0.6339 0.0342 0.0401
#> m 0.8270 -1.0489 0.4998
#> y 0.0652 0.5969 -0.5418
#>
#> [[68]]
#> x m y
#> x -0.5422 -0.0616 0.0014
#> m 0.6718 -0.3817 0.4155
#> y -0.7427 0.3234 -0.9757
#>
#> [[69]]
#> x m y
#> x -0.0403 -0.0506 -0.5266
#> m 0.7176 -0.8780 -0.1823
#> y -0.4755 1.0920 -0.7177
#>
#> [[70]]
#> x m y
#> x -0.4184 0.0873 0.2936
#> m 0.5819 -0.5672 -0.2931
#> y -0.5228 0.6846 -1.1257
#>
#> [[71]]
#> x m y
#> x -0.6265 0.2090 -0.1042
#> m 0.7528 -0.9778 0.0057
#> y -0.5539 0.7630 -0.0298
#>
#> [[72]]
#> x m y
#> x -0.3142 -0.4175 -0.3436
#> m 0.6047 -0.6731 0.4674
#> y -0.0897 0.5923 -1.0471
#>
#> [[73]]
#> x m y
#> x -0.7625 -0.1079 -0.1096
#> m 0.5141 -0.8554 0.3487
#> y -0.6520 0.6899 -1.4064
#>
#> [[74]]
#> x m y
#> x -0.3623 -0.2808 -0.0804
#> m 0.8808 -0.4030 0.1781
#> y -0.6301 0.8759 -1.0519
#>
#> [[75]]
#> x m y
#> x -0.5995 -0.4198 -0.5094
#> m 0.6576 -0.2874 0.3968
#> y -0.2405 0.7774 -0.6126
#>
#> [[76]]
#> x m y
#> x -0.2502 0.0400 -0.2393
#> m 1.0703 -0.0552 -0.2317
#> y -0.2040 0.5293 -0.4795
#>
#> [[77]]
#> x m y
#> x -0.3583 0.4105 -0.3260
#> m 0.4468 -0.7572 -0.4285
#> y 0.0135 0.4630 -0.4630
#>
#> [[78]]
#> x m y
#> x -0.6778 0.0109 -0.5704
#> m 0.8244 -0.3219 -0.1490
#> y -0.5195 0.4863 -1.0459
#>
#> [[79]]
#> x m y
#> x -0.1261 -0.2689 0.1719
#> m 1.2347 -0.8141 -0.5353
#> y -0.5857 1.1799 -0.7561
#>
#> [[80]]
#> x m y
#> x -0.2520 -0.4989 0.4904
#> m 0.5242 -0.4786 -0.2059
#> y -0.3187 0.9093 -0.7219
#>
#> [[81]]
#> x m y
#> x -0.4483 0.5324 -0.0998
#> m 0.1837 -0.3331 0.2339
#> y -0.3454 0.9350 -1.0312
#>
#> [[82]]
#> x m y
#> x -0.4740 0.4396 -0.0832
#> m 0.6544 -0.7612 0.3754
#> y -0.2096 0.5643 -0.9836
#>
#> [[83]]
#> x m y
#> x -0.8703 -0.2334 0.4392
#> m 1.4877 -0.6639 -0.1450
#> y -0.2625 0.8243 -0.8017
#>
#> [[84]]
#> x m y
#> x -0.1962 -0.3202 0.0654
#> m 1.3910 -0.3775 -0.3593
#> y -0.5640 0.3310 -0.3806
#>
#> [[85]]
#> x m y
#> x -0.3905 -0.2777 -0.3170
#> m 0.3367 -0.6976 0.0301
#> y 0.6498 0.8609 -0.6813
#>
#> [[86]]
#> x m y
#> x -0.6248 -0.4520 0.2134
#> m 0.8028 -0.2845 0.0879
#> y -0.9383 0.9861 -0.6502
#>
#> [[87]]
#> x m y
#> x -0.1593 -0.5304 -0.0042
#> m 0.9188 -0.6926 -0.0764
#> y -0.2094 0.5743 -0.4895
#>
#> [[88]]
#> x m y
#> x -0.4309 -0.1042 -0.0629
#> m 0.7116 -0.6306 0.1055
#> y -0.4704 0.3523 -0.9833
#>
#> [[89]]
#> x m y
#> x -0.1073 0.0902 0.3519
#> m 0.0455 -0.5125 0.2619
#> y -0.4501 0.8671 -0.6955
#>
#> [[90]]
#> x m y
#> x -0.1855 -0.1612 -0.1172
#> m 0.9788 -0.8409 -0.3104
#> y -0.5546 0.6565 -0.6502
#>
#> [[91]]
#> x m y
#> x -0.2742 -0.0278 -0.0435
#> m 0.3944 -0.2534 -0.2422
#> y 0.6082 0.6999 -0.5411
#>
#> [[92]]
#> x m y
#> x -0.8169 0.2507 0.1256
#> m 0.2168 -0.8083 0.4825
#> y 0.0757 0.5949 -0.5242
#>
#> [[93]]
#> x m y
#> x -0.3167 0.0613 -0.1022
#> m 0.6812 -0.6474 -0.5121
#> y -0.3802 0.8593 -0.4606
#>
#> [[94]]
#> x m y
#> x -0.4927 0.0970 0.1964
#> m 0.6259 -0.5075 0.2843
#> y -0.2871 0.1613 -1.0010
#>
#> [[95]]
#> x m y
#> x -0.2908 -0.0831 -0.3284
#> m 0.7124 -0.3808 0.0491
#> y -0.4735 0.7616 -0.4224
#>
#> [[96]]
#> x m y
#> x -0.2382 -0.0210 0.2435
#> m 0.8107 -0.9013 0.0443
#> y -0.5787 0.8863 -1.0013
#>
#> [[97]]
#> x m y
#> x -0.3714 -0.2303 -0.3200
#> m 1.2856 -0.9282 0.2868
#> y -0.1415 1.1378 -0.8186
#>
#> [[98]]
#> x m y
#> x -0.2475 -0.4155 0.3497
#> m 0.6953 -0.4973 0.1498
#> y -0.3532 0.7291 -0.4281
#>
#> [[99]]
#> x m y
#> x -0.2293 -0.2961 0.2112
#> m 0.6084 -0.7606 0.1396
#> y -0.7304 0.3160 -0.4800
#>
#> [[100]]
#> x m y
#> x -0.5496 -0.0348 0.0700
#> m 0.9226 -0.5533 -0.0088
#> y -0.5031 0.8429 -0.5873
#>
phi <- matrix(
data = c(
-6, 5.5, 0, 0,
1.25, -2.5, 5.9, -7.3,
0, 0, -6, 2.5,
5, 0, 0, -6
),
nrow = 4
)
colnames(phi) <- rownames(phi) <- paste0("y", 1:4)
MCPhi(
phi = phi,
vcov_phi_vec = 0.1 * diag(16),
R = 100L, # use a large value for R in actual research
test_phi = FALSE
)
#> [[1]]
#> y1 y2 y3 y4
#> y1 -5.7668 0.9230 0.2233 4.2634
#> y2 5.6636 -2.6310 0.5893 0.1656
#> y3 0.1348 5.7811 -6.3375 -0.0939
#> y4 0.3147 -7.4983 2.6865 -6.3097
#>
#> [[2]]
#> y1 y2 y3 y4
#> y1 -5.6895 1.3958 -0.1064 4.9329
#> y2 5.6879 -2.2832 -0.0758 -0.3114
#> y3 -0.5317 5.7714 -5.9755 -0.0333
#> y4 -0.2057 -7.3658 2.2075 -5.4863
#>
#> [[3]]
#> y1 y2 y3 y4
#> y1 -5.9580 1.5836 0.3723 4.6407
#> y2 5.5283 -2.0794 0.2199 0.0805
#> y3 -0.5804 5.7189 -6.2748 0.1087
#> y4 -0.1854 -7.1197 2.6285 -6.3340
#>
#> [[4]]
#> y1 y2 y3 y4
#> y1 -5.6135 1.3059 -0.1520 3.7929
#> y2 6.2636 -3.0146 0.5791 -0.4636
#> y3 0.1067 5.7501 -5.8046 -0.4455
#> y4 0.3517 -7.0425 2.5319 -5.9514
#>
#> [[5]]
#> y1 y2 y3 y4
#> y1 -6.1717 1.0766 -0.3349 4.7839
#> y2 5.3780 -2.5961 -0.5326 -0.2039
#> y3 -0.3308 6.3404 -6.2413 0.6843
#> y4 0.1681 -7.0827 2.7400 -6.0146
#>
#> [[6]]
#> y1 y2 y3 y4
#> y1 -5.3812 1.2558 0.6623 5.2363
#> y2 5.0359 -3.1022 0.0187 -0.0110
#> y3 0.4751 6.0529 -6.0927 -0.3454
#> y4 0.3612 -7.0734 2.4150 -6.4608
#>
#> [[7]]
#> y1 y2 y3 y4
#> y1 -6.0145 0.9127 -0.1050 5.0986
#> y2 5.7418 -2.8818 -0.3098 0.1868
#> y3 0.0207 5.8365 -5.9757 -0.1299
#> y4 0.2673 -7.3022 2.9458 -6.2110
#>
#> [[8]]
#> y1 y2 y3 y4
#> y1 -5.8044 1.0844 0.1378 4.9405
#> y2 5.5657 -2.3141 -0.4056 -0.3457
#> y3 0.2661 5.9458 -5.6681 -0.1354
#> y4 -0.5021 -7.0220 2.6626 -5.6208
#>
#> [[9]]
#> y1 y2 y3 y4
#> y1 -6.5522 1.3479 0.3668 4.7705
#> y2 5.4461 -2.9554 -0.1138 0.2969
#> y3 -0.2456 5.4209 -5.9634 -0.1664
#> y4 0.2009 -6.9219 2.9102 -6.1279
#>
#> [[10]]
#> y1 y2 y3 y4
#> y1 -5.9269 1.3184 0.0610 4.7207
#> y2 5.7802 -2.7238 -0.0001 -0.1507
#> y3 0.6121 5.6427 -6.2988 -0.3708
#> y4 -0.2834 -7.9467 2.7768 -5.6733
#>
#> [[11]]
#> y1 y2 y3 y4
#> y1 -6.0108 1.6800 -0.2495 4.5300
#> y2 5.3815 -2.8865 -0.1977 0.1310
#> y3 0.3771 5.5380 -5.5998 0.0828
#> y4 -0.2887 -6.5693 2.5902 -6.1295
#>
#> [[12]]
#> y1 y2 y3 y4
#> y1 -5.8948 2.1404 0.5304 4.8120
#> y2 5.2657 -2.7172 0.2243 0.2726
#> y3 0.3392 6.2523 -6.4579 0.5665
#> y4 -0.0974 -7.1006 3.0208 -5.9235
#>
#> [[13]]
#> y1 y2 y3 y4
#> y1 -6.3194 1.2196 0.2219 4.5833
#> y2 5.6737 -2.2696 0.5674 -0.1532
#> y3 -0.6263 5.6929 -6.1867 0.5924
#> y4 0.5117 -6.6057 2.8267 -5.7002
#>
#> [[14]]
#> y1 y2 y3 y4
#> y1 -5.4823 1.1359 -0.5189 4.7700
#> y2 6.0158 -2.4379 0.1708 -0.3368
#> y3 0.2634 6.1350 -6.1545 -0.1257
#> y4 0.2983 -7.1599 2.4814 -5.8683
#>
#> [[15]]
#> y1 y2 y3 y4
#> y1 -6.6469 1.6101 0.0410 4.7742
#> y2 5.3425 -2.5490 0.2587 -0.0487
#> y3 -0.0882 6.2703 -5.8678 0.1974
#> y4 0.3573 -7.0197 2.0987 -5.7518
#>
#> [[16]]
#> y1 y2 y3 y4
#> y1 -6.1222 1.2925 -0.0562 4.6711
#> y2 5.6139 -2.3581 -0.0177 -0.3112
#> y3 0.0130 5.6994 -6.3263 0.4808
#> y4 0.3061 -7.7456 2.2897 -6.1503
#>
#> [[17]]
#> y1 y2 y3 y4
#> y1 -5.9608 1.4888 0.0045 5.1459
#> y2 5.5950 -1.9211 -0.1746 -0.2890
#> y3 0.0078 5.8701 -5.8714 -0.1302
#> y4 -0.4365 -7.1767 2.8803 -5.8976
#>
#> [[18]]
#> y1 y2 y3 y4
#> y1 -5.8132 1.1155 -0.2077 4.7644
#> y2 5.5631 -2.8843 -0.0421 -0.3663
#> y3 0.5158 5.6960 -6.5660 -0.7380
#> y4 -0.0856 -7.5594 2.2929 -6.0541
#>
#> [[19]]
#> y1 y2 y3 y4
#> y1 -5.8361 1.6981 -0.2099 5.1071
#> y2 5.8118 -2.6273 0.1838 0.2969
#> y3 0.2353 6.0135 -6.2679 0.1417
#> y4 0.2306 -6.8748 2.5869 -5.7116
#>
#> [[20]]
#> y1 y2 y3 y4
#> y1 -6.1133 1.2747 0.2049 4.9287
#> y2 5.3474 -2.4081 0.1822 -0.0050
#> y3 0.0505 6.2017 -5.5979 0.1538
#> y4 0.6316 -7.7229 2.5705 -5.7057
#>
#> [[21]]
#> y1 y2 y3 y4
#> y1 -6.3539 1.4517 -0.0312 5.0953
#> y2 5.1892 -2.3262 -0.4178 0.0068
#> y3 -0.3209 5.9855 -6.0231 0.0657
#> y4 0.0838 -7.5616 2.6139 -5.8151
#>
#> [[22]]
#> y1 y2 y3 y4
#> y1 -5.3427 1.6514 0.3106 4.5388
#> y2 5.6862 -2.8037 -0.0708 -0.7003
#> y3 0.0372 5.6301 -6.3433 0.0265
#> y4 0.1000 -7.7933 2.7021 -6.1851
#>
#> [[23]]
#> y1 y2 y3 y4
#> y1 -5.6847 1.0275 0.5207 4.9294
#> y2 5.9071 -2.4629 -0.2393 0.4546
#> y3 0.5209 5.9664 -5.9180 -0.1018
#> y4 0.1192 -8.2784 2.4460 -5.6730
#>
#> [[24]]
#> y1 y2 y3 y4
#> y1 -6.0209 1.0396 -0.1932 4.5331
#> y2 5.1288 -2.1827 -0.0835 0.2775
#> y3 0.0706 6.0495 -6.0031 -0.1035
#> y4 -0.3772 -7.1062 2.0684 -6.1947
#>
#> [[25]]
#> y1 y2 y3 y4
#> y1 -5.7677 1.2751 0.1769 5.0236
#> y2 5.6191 -1.9918 0.0119 0.4368
#> y3 -0.2083 5.3403 -6.4606 0.2666
#> y4 -0.4714 -7.6268 2.8729 -6.0815
#>
#> [[26]]
#> y1 y2 y3 y4
#> y1 -6.1515 1.4525 0.2027 4.6271
#> y2 5.4472 -2.8296 0.0494 -0.0455
#> y3 -0.4805 5.5610 -6.6059 -0.7099
#> y4 0.5108 -7.5901 2.7159 -5.6216
#>
#> [[27]]
#> y1 y2 y3 y4
#> y1 -6.0670 1.3287 -0.0973 5.0208
#> y2 6.2865 -2.8627 -0.1693 -0.5216
#> y3 -0.0158 5.6777 -5.7077 0.2599
#> y4 0.0596 -6.6147 3.0623 -5.9546
#>
#> [[28]]
#> y1 y2 y3 y4
#> y1 -5.2771 1.3007 0.3736 4.5974
#> y2 5.7214 -3.1083 0.4978 -0.1548
#> y3 0.2311 5.4551 -5.7353 -0.0374
#> y4 0.2129 -7.3875 2.9406 -6.6204
#>
#> [[29]]
#> y1 y2 y3 y4
#> y1 -6.3433 0.8689 0.0856 5.2539
#> y2 5.4734 -2.3393 0.2726 0.2675
#> y3 -0.0526 5.7604 -6.0303 -0.0223
#> y4 -0.2449 -6.5926 2.7770 -6.1566
#>
#> [[30]]
#> y1 y2 y3 y4
#> y1 -5.7536 1.3618 0.3328 4.9249
#> y2 5.3979 -2.3363 -0.0817 0.4274
#> y3 0.0238 5.7449 -5.6317 -0.1724
#> y4 -0.1627 -7.4029 2.1575 -6.6403
#>
#> [[31]]
#> y1 y2 y3 y4
#> y1 -6.2718 1.3489 0.3620 4.9804
#> y2 6.0443 -2.5327 -0.1802 -0.5506
#> y3 0.0275 6.1188 -6.0708 -0.0636
#> y4 -0.3418 -7.5190 2.5217 -6.1727
#>
#> [[32]]
#> y1 y2 y3 y4
#> y1 -6.2242 1.4407 -0.0388 4.9602
#> y2 5.8011 -2.4977 -0.1438 0.0753
#> y3 -0.4079 6.0727 -6.0324 -0.3399
#> y4 -0.5544 -7.0974 2.2145 -5.9584
#>
#> [[33]]
#> y1 y2 y3 y4
#> y1 -6.3039 0.8956 -0.1184 5.5026
#> y2 5.4044 -2.6264 -0.2561 0.0758
#> y3 0.0288 5.4258 -6.5411 -0.0384
#> y4 -0.0572 -7.4542 2.8864 -5.9262
#>
#> [[34]]
#> y1 y2 y3 y4
#> y1 -5.9672 1.1480 -0.0393 4.6688
#> y2 5.8418 -2.6531 -0.0048 0.4096
#> y3 0.3215 5.8236 -5.6790 -0.2734
#> y4 0.2377 -7.5154 2.2944 -6.6422
#>
#> [[35]]
#> y1 y2 y3 y4
#> y1 -5.7728 1.5450 -0.0139 5.5630
#> y2 5.7372 -2.1377 0.2431 -0.2941
#> y3 -0.2750 6.4422 -6.5744 -0.3441
#> y4 -0.3499 -7.4563 2.3695 -5.8145
#>
#> [[36]]
#> y1 y2 y3 y4
#> y1 -6.1589 1.1369 -0.1308 5.0856
#> y2 5.7150 -2.2752 -0.0253 0.8980
#> y3 -0.0521 6.1190 -5.9389 -0.0729
#> y4 0.3482 -6.6299 2.1511 -5.9658
#>
#> [[37]]
#> y1 y2 y3 y4
#> y1 -5.8945 0.9853 0.6941 4.9666
#> y2 5.1616 -3.0345 0.0107 -0.0917
#> y3 0.0343 5.8754 -5.5661 0.3381
#> y4 0.4594 -6.6046 2.0610 -5.9833
#>
#> [[38]]
#> y1 y2 y3 y4
#> y1 -6.0137 1.4075 -0.2587 4.7113
#> y2 5.1521 -2.3546 -0.1579 0.0894
#> y3 -0.0882 5.7019 -6.4509 -0.1253
#> y4 -0.4616 -7.0690 2.6749 -5.9659
#>
#> [[39]]
#> y1 y2 y3 y4
#> y1 -5.2570 1.5659 0.1064 4.6079
#> y2 5.4045 -2.2201 -0.2555 -0.0682
#> y3 -0.0509 5.8983 -6.4767 0.3584
#> y4 -0.3301 -7.8675 2.8030 -6.2076
#>
#> [[40]]
#> y1 y2 y3 y4
#> y1 -5.9080 1.3928 -0.1253 5.3514
#> y2 5.3735 -2.3501 -0.2915 0.0394
#> y3 -0.0680 5.8674 -6.0316 -0.0848
#> y4 -0.0270 -7.7892 2.2404 -6.3040
#>
#> [[41]]
#> y1 y2 y3 y4
#> y1 -6.4446 1.3247 -0.2761 4.5362
#> y2 5.7358 -2.1600 -0.5047 -0.6031
#> y3 -0.6084 5.5772 -5.6569 0.6039
#> y4 0.8787 -7.6333 2.4308 -5.5574
#>
#> [[42]]
#> y1 y2 y3 y4
#> y1 -5.8593 1.2839 -0.0032 4.7804
#> y2 5.8267 -2.5814 -0.0681 0.4127
#> y3 0.6440 5.9321 -5.8832 -0.1229
#> y4 0.1774 -6.8543 3.1020 -6.5602
#>
#> [[43]]
#> y1 y2 y3 y4
#> y1 -6.0673 0.8908 0.2522 5.3146
#> y2 5.5606 -2.4939 0.3249 0.3578
#> y3 -0.1531 5.7704 -5.2237 0.3980
#> y4 0.4033 -7.0085 2.2838 -6.7198
#>
#> [[44]]
#> y1 y2 y3 y4
#> y1 -5.8124 1.4435 0.0103 4.2477
#> y2 5.6099 -2.7047 -0.6513 0.4689
#> y3 0.0544 5.4757 -5.8748 0.2879
#> y4 -0.0655 -7.3180 3.0642 -5.7631
#>
#> [[45]]
#> y1 y2 y3 y4
#> y1 -5.9015 1.1435 -0.1690 4.9738
#> y2 4.9948 -2.8262 0.2239 0.0506
#> y3 -0.3837 6.4569 -6.3387 0.3022
#> y4 0.1928 -7.3322 2.5901 -6.3325
#>
#> [[46]]
#> y1 y2 y3 y4
#> y1 -6.0980 1.2951 -0.3674 4.6936
#> y2 5.5459 -3.1702 0.4847 -0.3380
#> y3 -0.1205 5.2876 -6.0921 -0.2235
#> y4 -0.1159 -7.3589 2.1731 -5.7440
#>
#> [[47]]
#> y1 y2 y3 y4
#> y1 -5.3795 0.6644 0.2127 4.3846
#> y2 5.3361 -2.5810 0.0289 0.3402
#> y3 -0.2481 5.8775 -4.8334 0.2223
#> y4 -0.4489 -7.3971 1.9999 -5.7160
#>
#> [[48]]
#> y1 y2 y3 y4
#> y1 -6.5926 1.3679 -0.0816 5.4116
#> y2 5.7363 -2.3326 -0.0569 -0.0734
#> y3 -0.5427 5.6793 -5.9737 0.0655
#> y4 -0.7339 -7.1181 2.5202 -5.7012
#>
#> [[49]]
#> y1 y2 y3 y4
#> y1 -5.7572 1.9445 -0.1988 4.9842
#> y2 5.6896 -2.7707 0.1606 0.0311
#> y3 0.3578 5.9488 -6.1304 -0.7058
#> y4 -0.0977 -7.0141 2.5897 -5.4540
#>
#> [[50]]
#> y1 y2 y3 y4
#> y1 -6.2746 1.0570 0.1394 4.9125
#> y2 5.6567 -2.6995 0.1489 -0.0157
#> y3 0.2149 6.1102 -6.1968 0.8091
#> y4 0.1977 -6.8883 2.3872 -5.8547
#>
#> [[51]]
#> y1 y2 y3 y4
#> y1 -5.9523 1.4773 0.4845 5.3901
#> y2 5.4737 -2.3223 0.4638 -0.0051
#> y3 0.1663 5.7208 -5.7078 -0.2873
#> y4 -0.2619 -7.5732 2.6116 -5.6516
#>
#> [[52]]
#> y1 y2 y3 y4
#> y1 -5.9569 1.1484 0.1413 4.9625
#> y2 5.4961 -1.9196 -0.2147 0.0860
#> y3 0.0434 5.1711 -6.0091 -0.4300
#> y4 0.0989 -6.9923 2.4675 -6.2801
#>
#> [[53]]
#> y1 y2 y3 y4
#> y1 -5.9964 1.5948 0.1424 4.8919
#> y2 4.9500 -2.3143 -0.2004 0.0746
#> y3 0.0413 6.1239 -6.1581 0.5520
#> y4 -0.1606 -6.6052 3.0729 -5.6252
#>
#> [[54]]
#> y1 y2 y3 y4
#> y1 -6.0056 0.5813 0.2066 4.1852
#> y2 5.6146 -2.5315 -0.2098 0.5014
#> y3 -0.0282 6.0132 -5.9744 -0.2524
#> y4 0.1977 -7.1909 2.0617 -5.5994
#>
#> [[55]]
#> y1 y2 y3 y4
#> y1 -6.2481 1.2533 0.0911 4.8759
#> y2 5.3307 -2.3027 -0.1617 0.5334
#> y3 0.1470 5.6411 -5.5382 -0.0052
#> y4 0.2635 -7.2861 2.4187 -6.3106
#>
#> [[56]]
#> y1 y2 y3 y4
#> y1 -5.9427 1.2370 -0.4303 4.2867
#> y2 5.4646 -2.7914 0.7996 -0.1051
#> y3 0.1021 6.0495 -5.6497 -0.1754
#> y4 0.2555 -7.3638 2.6484 -6.1278
#>
#> [[57]]
#> y1 y2 y3 y4
#> y1 -5.8707 1.4799 0.4191 5.0782
#> y2 5.6182 -2.4580 -0.0108 -0.2805
#> y3 -0.7355 5.7616 -6.2561 -0.4730
#> y4 0.0598 -7.7258 2.6587 -5.9206
#>
#> [[58]]
#> y1 y2 y3 y4
#> y1 -5.8946 1.0787 -0.4839 5.0753
#> y2 5.6657 -2.6659 -0.3270 0.1845
#> y3 -0.1998 5.6498 -5.6949 0.2662
#> y4 -0.2045 -7.1635 2.2299 -5.7683
#>
#> [[59]]
#> y1 y2 y3 y4
#> y1 -6.4531 0.9740 0.0054 4.9008
#> y2 5.8377 -2.9909 -0.2070 -0.4158
#> y3 -0.2417 5.5451 -5.8743 0.2004
#> y4 -0.5901 -7.1767 2.3551 -5.7033
#>
#> [[60]]
#> y1 y2 y3 y4
#> y1 -5.4631 1.0113 0.0522 5.1682
#> y2 4.9342 -2.6603 -0.3605 0.2755
#> y3 -0.4089 6.0702 -5.9465 -0.1638
#> y4 -0.2940 -7.0916 2.4145 -5.0471
#>
#> [[61]]
#> y1 y2 y3 y4
#> y1 -5.9779 1.0796 0.0267 4.8381
#> y2 5.4393 -2.5748 0.3063 -0.0395
#> y3 -0.2208 6.2879 -6.1863 -0.2941
#> y4 0.1071 -7.5201 1.8880 -6.3136
#>
#> [[62]]
#> y1 y2 y3 y4
#> y1 -5.6482 1.3129 -0.1826 4.8776
#> y2 6.0977 -1.9955 -0.5990 0.3349
#> y3 -0.3539 6.5941 -6.0968 -0.2040
#> y4 0.3579 -7.3144 2.8496 -5.5229
#>
#> [[63]]
#> y1 y2 y3 y4
#> y1 -5.6285 0.8844 0.2849 4.8488
#> y2 5.2297 -2.4012 0.0733 0.2061
#> y3 0.1713 5.3912 -6.4161 0.1879
#> y4 0.1810 -7.3348 2.8551 -6.0188
#>
#> [[64]]
#> y1 y2 y3 y4
#> y1 -5.5283 0.8311 0.1781 4.4061
#> y2 4.9419 -2.6348 -0.7101 -0.2532
#> y3 -0.0070 5.5456 -6.0511 0.0560
#> y4 0.5372 -8.1754 2.2046 -6.1299
#>
#> [[65]]
#> y1 y2 y3 y4
#> y1 -6.6001 1.6824 -0.0380 5.2231
#> y2 5.4676 -2.1973 0.5336 0.0204
#> y3 0.6301 5.1240 -5.9167 0.0347
#> y4 -0.0134 -7.2489 2.4992 -5.5505
#>
#> [[66]]
#> y1 y2 y3 y4
#> y1 -5.7521 0.7159 -0.2507 4.9922
#> y2 5.8027 -1.9508 0.5002 0.0441
#> y3 0.0835 6.1362 -5.8951 -0.1631
#> y4 -0.6097 -7.3279 2.7955 -6.1510
#>
#> [[67]]
#> y1 y2 y3 y4
#> y1 -6.6907 1.1029 -0.2930 5.1709
#> y2 4.9118 -2.5787 -0.0594 0.8663
#> y3 0.2808 6.0329 -6.1878 0.7187
#> y4 -0.0158 -7.4357 2.5586 -6.2412
#>
#> [[68]]
#> y1 y2 y3 y4
#> y1 -5.7003 1.5561 0.0553 5.6792
#> y2 5.4253 -2.8970 0.0461 -0.1316
#> y3 -1.0162 6.0995 -5.8691 0.1358
#> y4 0.5630 -7.3931 2.1565 -5.9070
#>
#> [[69]]
#> y1 y2 y3 y4
#> y1 -5.6939 1.5281 0.1444 4.8940
#> y2 5.6035 -2.9275 0.0641 -0.6012
#> y3 -0.0134 6.0038 -6.3259 -0.1658
#> y4 0.2364 -7.3385 2.3606 -5.9478
#>
#> [[70]]
#> y1 y2 y3 y4
#> y1 -5.9643 1.3434 -0.1344 5.0722
#> y2 5.1277 -2.5828 -0.1238 0.1204
#> y3 0.0389 5.8466 -6.0228 0.2002
#> y4 0.0429 -6.9442 2.5921 -6.1923
#>
#> [[71]]
#> y1 y2 y3 y4
#> y1 -5.9243 0.8865 0.0999 4.8679
#> y2 5.2796 -2.5638 -0.2983 0.1686
#> y3 0.0906 6.0471 -6.3269 -0.2134
#> y4 -0.5054 -7.1232 2.6130 -5.6755
#>
#> [[72]]
#> y1 y2 y3 y4
#> y1 -5.9200 1.2293 -0.0611 5.4255
#> y2 5.9229 -2.6953 0.1815 0.0032
#> y3 -0.2596 5.8636 -5.5987 -0.0868
#> y4 0.1786 -7.3480 2.7143 -5.7337
#>
#> [[73]]
#> y1 y2 y3 y4
#> y1 -6.4274 0.4931 0.2368 4.5700
#> y2 5.4101 -2.5940 0.3928 0.0951
#> y3 0.3073 5.5423 -6.2832 0.0019
#> y4 -0.6478 -7.5113 2.2986 -6.1988
#>
#> [[74]]
#> y1 y2 y3 y4
#> y1 -5.9378 1.2743 -0.1804 4.5888
#> y2 5.4514 -2.3675 -0.1271 0.2928
#> y3 -0.4136 5.6969 -5.6865 0.2059
#> y4 0.0874 -7.0510 2.6019 -6.0188
#>
#> [[75]]
#> y1 y2 y3 y4
#> y1 -6.5136 1.5369 0.0256 4.9086
#> y2 5.5642 -2.3868 -0.3224 0.1919
#> y3 0.1486 5.7668 -5.8998 0.1100
#> y4 -0.2103 -7.1476 2.6062 -5.8118
#>
#> [[76]]
#> y1 y2 y3 y4
#> y1 -6.7212 0.6250 0.0904 5.0172
#> y2 5.5723 -2.5360 0.1952 0.3232
#> y3 -0.3055 5.5932 -5.8743 -0.4162
#> y4 0.0984 -6.7820 2.4282 -5.8759
#>
#> [[77]]
#> y1 y2 y3 y4
#> y1 -6.2910 1.2902 -0.2498 5.4488
#> y2 5.1756 -2.4222 0.1451 0.1266
#> y3 -0.2061 5.6235 -6.2612 0.0346
#> y4 -0.3544 -6.9230 2.5766 -6.5837
#>
#> [[78]]
#> y1 y2 y3 y4
#> y1 -6.0322 0.9669 -0.3262 4.9366
#> y2 5.2301 -2.4229 -0.2520 -0.0096
#> y3 0.0000 5.7709 -6.3113 -0.2493
#> y4 0.0267 -7.0330 2.7660 -5.3736
#>
#> [[79]]
#> y1 y2 y3 y4
#> y1 -5.6171 1.3802 0.3513 5.4468
#> y2 5.5958 -2.1119 -0.3488 0.0908
#> y3 0.2067 5.6944 -5.7429 0.1289
#> y4 -0.1186 -7.4404 2.6279 -6.0663
#>
#> [[80]]
#> y1 y2 y3 y4
#> y1 -5.8217 1.6960 -0.1393 4.8420
#> y2 5.1737 -2.6817 -0.1878 -0.4379
#> y3 -0.0756 5.6943 -5.8635 0.0060
#> y4 -0.0536 -7.0538 3.0298 -5.6860
#>
#> [[81]]
#> y1 y2 y3 y4
#> y1 -5.9432 1.9662 0.1804 4.8325
#> y2 5.4171 -2.0434 -0.2288 0.0017
#> y3 -0.2531 6.1313 -5.6265 0.1767
#> y4 0.4081 -7.4475 2.6137 -5.4631
#>
#> [[82]]
#> y1 y2 y3 y4
#> y1 -6.1795 1.2062 -0.7283 4.5316
#> y2 6.0215 -2.4095 -0.5060 0.2728
#> y3 -0.0582 5.9522 -5.6993 0.7224
#> y4 0.1006 -7.1613 2.6657 -5.4758
#>
#> [[83]]
#> y1 y2 y3 y4
#> y1 -5.8417 1.2243 0.6788 5.1682
#> y2 5.4315 -2.4744 -0.2423 0.0133
#> y3 -0.3892 6.0071 -5.9319 0.2591
#> y4 -0.4600 -6.9390 2.4152 -5.9745
#>
#> [[84]]
#> y1 y2 y3 y4
#> y1 -6.2975 1.2838 0.2249 4.9901
#> y2 5.5440 -2.2441 -0.3645 0.2449
#> y3 0.1365 5.8487 -5.8212 -0.2674
#> y4 -0.0015 -7.1486 2.5200 -5.7578
#>
#> [[85]]
#> y1 y2 y3 y4
#> y1 -5.6978 1.4122 0.1484 4.5891
#> y2 5.4030 -2.3363 0.2806 -0.3610
#> y3 -0.1147 6.0320 -6.1666 -0.0848
#> y4 -0.1262 -7.8710 2.7927 -6.3336
#>
#> [[86]]
#> y1 y2 y3 y4
#> y1 -5.8476 0.9337 0.4785 5.2861
#> y2 5.3785 -3.1134 0.0101 -0.4904
#> y3 -0.6114 5.9998 -5.9727 -0.4166
#> y4 0.1387 -7.1715 2.9339 -5.7481
#>
#> [[87]]
#> y1 y2 y3 y4
#> y1 -5.8597 1.8850 -0.4586 4.9502
#> y2 5.4700 -2.7928 0.2341 -0.4140
#> y3 0.3105 5.9415 -6.0601 -0.5847
#> y4 -0.1970 -7.9899 2.2574 -6.3043
#>
#> [[88]]
#> y1 y2 y3 y4
#> y1 -6.3161 1.2327 0.0271 5.3631
#> y2 5.6828 -2.7258 -0.2832 -0.0979
#> y3 -0.2076 6.2184 -5.7706 0.4866
#> y4 0.3190 -7.3725 2.5438 -6.2305
#>
#> [[89]]
#> y1 y2 y3 y4
#> y1 -6.0877 1.2029 0.0267 5.0569
#> y2 5.2536 -2.4098 0.2891 -0.3400
#> y3 -0.0267 5.9468 -5.7560 -0.1364
#> y4 -0.4393 -7.5338 2.6983 -5.8723
#>
#> [[90]]
#> y1 y2 y3 y4
#> y1 -6.0322 1.4432 -0.0431 4.9221
#> y2 5.4464 -3.0324 -0.0247 0.0904
#> y3 0.3685 6.4214 -6.1455 0.2421
#> y4 -0.6743 -7.0642 2.5569 -5.7589
#>
#> [[91]]
#> y1 y2 y3 y4
#> y1 -6.0988 0.9930 -0.3469 4.7260
#> y2 5.3874 -3.0435 0.1365 0.5614
#> y3 0.1051 6.4381 -6.1544 -0.0754
#> y4 0.1931 -6.9494 1.8696 -6.0270
#>
#> [[92]]
#> y1 y2 y3 y4
#> y1 -5.5037 1.4817 -0.1673 4.8613
#> y2 5.2454 -1.6787 0.3387 0.1379
#> y3 -0.1108 5.8373 -6.0303 -0.0616
#> y4 0.2594 -7.3990 2.2196 -5.9596
#>
#> [[93]]
#> y1 y2 y3 y4
#> y1 -6.1597 0.9582 0.2737 5.4425
#> y2 5.6030 -2.1250 -0.4149 0.7565
#> y3 -0.3107 6.0609 -6.5682 -0.5186
#> y4 0.3355 -7.2279 2.7876 -5.9105
#>
#> [[94]]
#> y1 y2 y3 y4
#> y1 -5.8317 1.7254 0.3621 5.2930
#> y2 5.3161 -3.1388 0.0509 0.3506
#> y3 -0.1596 5.9242 -6.1536 0.3438
#> y4 0.0367 -6.7521 2.0423 -5.5868
#>
#> [[95]]
#> y1 y2 y3 y4
#> y1 -6.3414 1.2384 0.2634 5.4223
#> y2 5.2255 -2.3949 -0.5253 0.3888
#> y3 -0.1683 6.2406 -5.7544 0.2706
#> y4 -0.6913 -7.2530 2.0293 -5.5734
#>
#> [[96]]
#> y1 y2 y3 y4
#> y1 -5.5362 1.4831 0.1228 4.8351
#> y2 5.2138 -2.0728 0.5201 -0.0191
#> y3 0.0749 5.9327 -6.1675 0.2317
#> y4 -0.0376 -7.4086 2.4437 -5.9435
#>
#> [[97]]
#> y1 y2 y3 y4
#> y1 -5.5899 1.5127 -0.1531 5.1957
#> y2 5.2358 -1.6921 0.1887 0.1824
#> y3 0.3952 5.7920 -6.2844 -0.1212
#> y4 -0.3621 -6.9405 2.5557 -5.7922
#>
#> [[98]]
#> y1 y2 y3 y4
#> y1 -6.2095 1.4307 -0.0805 4.8610
#> y2 4.8708 -2.7822 0.1615 -0.0977
#> y3 0.1431 5.2626 -5.4246 0.3084
#> y4 -0.2285 -7.5144 2.0456 -5.5210
#>
#> [[99]]
#> y1 y2 y3 y4
#> y1 -5.7127 1.1469 0.1237 4.6626
#> y2 4.8916 -2.1677 -0.3059 0.2355
#> y3 0.0269 5.7291 -6.4156 -0.1528
#> y4 0.1273 -7.3281 1.8487 -5.8212
#>
#> [[100]]
#> y1 y2 y3 y4
#> y1 -5.4156 1.6693 -0.5459 5.0552
#> y2 5.5648 -2.6804 -0.7217 -0.1677
#> y3 -0.1679 5.6439 -5.7622 -0.8209
#> y4 0.0468 -7.1060 2.5218 -5.8344
#>