Simulation \(\nu_0\)

## prior distribution of correlation matrix of latent factors
## 
## maximum correlation (in absolute value):
## 
##                    mean   median      sd   min     max
## nu0 = 3, S0 = 1   0.499    0.498   0.289     0   1.000
## nu0 = 4, S0 = 1   0.425    0.404   0.264     0   1.000
## nu0 = 5, S0 = 1   0.376    0.349   0.244     0   0.998
## nu0 = 6, S0 = 1   0.339    0.309   0.227     0   0.994
## nu0 = 7, S0 = 1   0.312    0.280   0.213     0   0.990
## nu0 = 8, S0 = 1   0.291    0.260   0.201     0   0.970
## 
##                      5%     10%     25%     75%     90%     95%
## nu0 = 3, S0 = 1   0.050   0.099   0.250   0.750   0.900   0.951
## nu0 = 4, S0 = 1   0.040   0.078   0.198   0.633   0.804   0.877
## nu0 = 5, S0 = 1   0.034   0.068   0.169   0.559   0.731   0.813
## nu0 = 6, S0 = 1   0.029   0.058   0.148   0.502   0.669   0.753
## nu0 = 7, S0 = 1   0.027   0.054   0.134   0.461   0.622   0.708
## nu0 = 8, S0 = 1   0.024   0.049   0.124   0.428   0.582   0.668
## 
## minimum eigenvalue of correlation matrix:
## 
##                    mean   median      sd     min   max
## nu0 = 3, S0 = 1   0.501    0.502   0.289   0.000     1
## nu0 = 4, S0 = 1   0.575    0.596   0.264   0.000     1
## nu0 = 5, S0 = 1   0.624    0.651   0.244   0.002     1
## nu0 = 6, S0 = 1   0.661    0.691   0.227   0.006     1
## nu0 = 7, S0 = 1   0.688    0.720   0.213   0.010     1
## nu0 = 8, S0 = 1   0.709    0.740   0.201   0.030     1
## 
##                      5%     10%     25%     75%     90%     95%
## nu0 = 3, S0 = 1   0.049   0.100   0.250   0.750   0.901   0.950
## nu0 = 4, S0 = 1   0.123   0.196   0.367   0.802   0.922   0.960
## nu0 = 5, S0 = 1   0.187   0.269   0.441   0.831   0.932   0.966
## nu0 = 6, S0 = 1   0.247   0.331   0.498   0.852   0.942   0.971
## nu0 = 7, S0 = 1   0.292   0.378   0.539   0.866   0.946   0.973
## nu0 = 8, S0 = 1   0.332   0.418   0.572   0.876   0.951   0.976

Simulation \(\kappa_0\)

## prior probabilities of numbers of factors:
##                   1       2     acc
## kappa = 0.1   0.921   0.079   0.899
## kappa = 0.2   0.849   0.151   0.832
## kappa = 0.3   0.784   0.216   0.786
## kappa = 0.4   0.727   0.273   0.753
## kappa = 0.5   0.678   0.322   0.726
## kappa = 0.6   0.632   0.368   0.709
## kappa = 0.7   0.594   0.406   0.694
## kappa = 0.8   0.559   0.441   0.683
## kappa = 0.9   0.528   0.472   0.674
## kappa = 1     0.500   0.500   0.666

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Copyright:
Benedikt Philipp Kleer, 2022 (Online-Appendix zur Promotion, eingereicht am 14. September 2022, Fachbereich 03, Justus-Liebig-Universität Gießen).