Simulation \(\nu_0\)
## prior distribution of correlation matrix of latent factors
##
## maximum correlation (in absolute value):
##
## mean median sd min max
## nu0 = 5, S0 = 1 0.780 0.810 0.160 0.097 1.000
## nu0 = 6, S0 = 1 0.708 0.724 0.165 0.081 1.000
## nu0 = 7, S0 = 1 0.652 0.658 0.164 0.078 0.998
## nu0 = 8, S0 = 1 0.607 0.609 0.160 0.095 0.999
## nu0 = 9, S0 = 1 0.570 0.570 0.156 0.060 0.992
## nu0 = 10, S0 = 1 0.541 0.537 0.151 0.068 0.975
## nu0 = 11, S0 = 1 0.513 0.509 0.146 0.071 0.975
## nu0 = 12, S0 = 1 0.490 0.484 0.142 0.066 0.949
## nu0 = 13, S0 = 1 0.471 0.464 0.138 0.043 0.947
## nu0 = 14, S0 = 1 0.453 0.447 0.134 0.058 0.945
##
## 5% 10% 25% 75% 90% 95%
## nu0 = 5, S0 = 1 0.476 0.548 0.675 0.912 0.966 0.983
## nu0 = 6, S0 = 1 0.414 0.477 0.592 0.840 0.917 0.949
## nu0 = 7, S0 = 1 0.371 0.429 0.535 0.777 0.866 0.908
## nu0 = 8, S0 = 1 0.339 0.393 0.491 0.726 0.820 0.866
## nu0 = 9, S0 = 1 0.315 0.366 0.456 0.684 0.780 0.829
## nu0 = 10, S0 = 1 0.297 0.344 0.431 0.648 0.744 0.795
## nu0 = 11, S0 = 1 0.280 0.325 0.407 0.616 0.710 0.761
## nu0 = 12, S0 = 1 0.265 0.309 0.387 0.589 0.682 0.734
## nu0 = 13, S0 = 1 0.253 0.295 0.371 0.566 0.658 0.709
## nu0 = 14, S0 = 1 0.243 0.282 0.356 0.544 0.634 0.684
##
## minimum eigenvalue of correlation matrix:
##
## mean median sd min max
## nu0 = 5, S0 = 1 0.152 0.122 0.124 0.000 0.846
## nu0 = 6, S0 = 1 0.213 0.189 0.136 0.000 0.878
## nu0 = 7, S0 = 1 0.264 0.246 0.140 0.001 0.901
## nu0 = 8, S0 = 1 0.306 0.292 0.141 0.000 0.880
## nu0 = 9, S0 = 1 0.341 0.330 0.141 0.006 0.905
## nu0 = 10, S0 = 1 0.370 0.362 0.139 0.019 0.912
## nu0 = 11, S0 = 1 0.398 0.392 0.136 0.019 0.923
## nu0 = 12, S0 = 1 0.422 0.416 0.135 0.040 0.931
## nu0 = 13, S0 = 1 0.442 0.438 0.132 0.028 0.926
## nu0 = 14, S0 = 1 0.461 0.457 0.130 0.042 0.940
##
## 5% 10% 25% 75% 90% 95%
## nu0 = 5, S0 = 1 0.011 0.021 0.055 0.218 0.328 0.399
## nu0 = 6, S0 = 1 0.035 0.056 0.107 0.294 0.403 0.471
## nu0 = 7, S0 = 1 0.066 0.095 0.157 0.353 0.458 0.522
## nu0 = 8, S0 = 1 0.099 0.132 0.200 0.398 0.500 0.561
## nu0 = 9, S0 = 1 0.128 0.164 0.236 0.434 0.533 0.591
## nu0 = 10, S0 = 1 0.156 0.196 0.269 0.463 0.557 0.613
## nu0 = 11, S0 = 1 0.184 0.225 0.299 0.490 0.581 0.634
## nu0 = 12, S0 = 1 0.210 0.250 0.324 0.514 0.601 0.653
## nu0 = 13, S0 = 1 0.230 0.272 0.347 0.532 0.618 0.669
## nu0 = 14, S0 = 1 0.253 0.294 0.368 0.550 0.633 0.682Simulation \(\kappa_0\)
## prior probabilities of numbers of factors:
## 1 2 3 4 acc
## kappa = 0.1 0.637 0.334 0.029 0.000 0.764
## kappa = 0.2 0.426 0.485 0.088 0.002 0.637
## kappa = 0.3 0.296 0.545 0.154 0.005 0.560
## kappa = 0.4 0.212 0.560 0.219 0.009 0.508
## kappa = 0.5 0.157 0.552 0.277 0.014 0.471
## kappa = 0.6 0.119 0.532 0.330 0.020 0.444
## kappa = 0.7 0.092 0.507 0.374 0.027 0.423
## kappa = 0.8 0.073 0.480 0.413 0.034 0.406
## kappa = 0.9 0.058 0.454 0.447 0.041 0.392
## kappa = 1 0.047 0.428 0.477 0.047 0.381
Copyright: 
Benedikt Philipp Kleer, 2022 (Online-Appendix zur Promotion, eingereicht am 14. September 2022, Fachbereich 03, Justus-Liebig-Universität Gießen).