The k-means and hierarchical approaches are alternatives in estimating parameters in RLCA. Overall, in our simulation study, the k-means approach performed well, but the hierarchical approach didn’t perform well. At the early stage of hierarchical approach, each cluster contains only very few objects (i.e. at the initial stage, only one object for each cluster). It is not appropriate to use the sample covariance to represent the association between two random variables when the sample size is small. The wrong reallocation of objects at an early stage will result in wrong reallocation of objects at following stage. For the improvement of the proposed hierarchical approach, it may be a good idea to choice alternative measurements of the association between two random variables.
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Table 1: Values of α and 0 αLm in 3-class model
item 1 item 2 item 3 item 4 item 5
α 0
class 1 6.7479 3.4660 0.2348 -7.6250 11.8628 class 2 -1.3035 1.6160 -2.1880 -7.6992 -0.4100 class 3 -4.3977 -1.4305 -4.0995 -20.6690 -1.1043
αLm
z1m 0.3944 -0.6396 -0.0581 1.0860 -0.8558 z2m 0.0749 -0.0528 0.0289 0.3551 0.0189
Table 2: Values of β and 0 β in 3-class modelpj class 1 vs. class 3 class 2 vs. class 3
β 0
-1.8685 -0.2319
β pj 1
x i 1.1274 0.3254
2
x i 0.5260 0.0134
Table 3: Values of α and 0 αLm in 6-class model
item 1 item 2 item 3 item 4 item 5
level 1 v.s. level 3
α 0
class 1 5.8950 4.6522 1.0752 4.0627 3.4993 class 2 -0.1017 -0.3133 -4.4863 0.8992 0.3045 class 3 1.9543 2.8491 -2.6076 2.2020 1.9947 class 4 0.8544 0.4180 0.4860 4.7660 0.5688 class 5 -5.6842 -9.5250 -3.8248 -3.9258 -1.8959 class 6 -6.0287 -2.2211 -7.4452 -6.8831 0.1988
αLm
z1m -0.8438 -0.5129 -0.4503 -1.8826 -0.7673 z2m 0.0438 -0.0442 0.0069 0.0300 0.0003
level 2 v.s. level 3
α 0
class 1 3.3360 2.2059 0.3966 1.4379 1.3682
class 2 0.2934 0.0936 -1.8840 1.4048 0.5097
class 3 1.9570 2.7255 0.7330 3.4921 2.9509
class 4 2.9822 1.0677 0.6211 4.6124 0.8161
class 5 -4.4138 -4.3121 -1.8665 -2.3500 -0.3425 class 6 0.4196 0.5214 -2.6499 -0.2605 0.8891
αLm
z1m -0.2110 -0.2738 -0.7938 -0.7830 -0.5860 z2m 0.0179 -0.0076 0.0185 0.0075 -0.0115
Table 4: Values of β and 0 β in 6-class model pj
class 1 vs. class 6 class 2 vs. class 6 class 3 vs. class 6 class 4 vs. class 6 class 5 vs. class 6 β 0
-1.0866 0.4266 -0.6706 -0.4556 0.1665
β pj 1
x i 0.2739 -1.7432 -0.8519 -0.2596 -0.6237
2
x i 0.6879 0.0102 0.5634 0.2530 0.1428
Table 5: Values of α and 0 αLm in 2-class model
item 1 item 2 item 3 item 4 item 5
level 1 v.s. level 3
α 0
class 1 3.0464 2.0611 -0.4656 2.8398 1.6822 class 2 -3.7435 -3.9859 -4.8386 -2.8929 -1.2178
αLm
z1m 0.3906 0.3114 -0.0532 -0.4618 -0.2682 z2m 0.0511 -0.0138 0.0243 0.0416 0.0111
level 2 v.s. level 3
α 0
class 1 3.0959 1.6635 0.2100 2.9031 1.5960 class 2 -0.8657 -0.9226 -1.7795 -0.7267 0.3726
αLm
z1m 0.5012 0.3124 -0.4417 0.1048 -0.2919 z2m 0.0122 -0.0016 0.0192 0.0072 -0.0132
Table 6: Values of β and 0 β in 2-class modelpj class 1 vs. class 2
β 0
-0.9355
β pj
1
xi 0.4413
2
xi 0.4144
Table 7: Average parameters estimations for 100 replication in 3-class model, N=100 (standard error in multinomial regression / sample standard error for 100 replication)
item 1 item 1 item 1 item 1
TRUE K_Corr K_Cova H_Cova
intercept ----4.398 4.398 4.398 ----3.528 4.398 3.528 3.528 3.528 (2.075 / 2.184) ----4.444 4.444 4.444 4.444 (10.114 / 3.814) ----4.358 4.358 4.358 4.358 (4.315 / 3.276) class 1 11.146 11.146 11.146 11.146 8.019 8.019 8.019 8.019 (17.291 / 4.219) 9.778 9.778 9.778 9.778 (22.483 / 5.572) 7.329 7.329 7.329 7.329 (8.99 / 4.011) class 2 3.094 3.094 3.094 3.094 3.910 3.910 3.910 3.910 (4.998 / 3.001) 7.503 7.503 7.503 7.503 (24.921 / 6.628) 8.339 8.339 8.339 8.339 (35.991 / 6.713)
sex 0.394 0.394 0.394 0.394 0.594 0.594 0.594 0.594 (1.054 / 1.213) 0.864 0.864 0.864 0.864 (4.422 / 1.785) 0.839 0.839 0.839 0.839 (2.494 / 1.922) age 0.075 0.075 0.075 0.075 0.049 0.049 0.049 0.049 (0.046 / 0.047) 0.051 0.051 0.051 0.051 (0.233 / 0.061) 0.041 0.041 0.041 0.041 (0.057 / 0.07)
item 2 item 2 item 2 item 2
TRUE K_Corr K_Cova H_Cova
intercept ----1.431 1.431 1.431 ----1.291 1.431 1.291 1.291 1.291 (4.304 / 2.99) ----2.119 2.119 2.119 2.119 (7.229 / 4.003) ----2.190 2.190 2.190 2.190 (5.213 / 3.778) class 1 4.897 4.897 4.897 4.897 5.623 5.623 5.623 5.623 (3.913 / 2.962) 7.651 7.651 7.651 7.651 (8.37 / 5.032) 6.154 6.154 6.154 6.154 (5.031 / 3.565) class 2 3.046 3.046 3.046 3.046 3.259 3.259 3.259 3.259 (4.092 / 3.278) 2.839 2.839 2.839 2.839 (15.678 / 7.492) 0.250 0.250 0.250 0.250 (23.224 / 7.469)
sex ----0.640 0.640 0.640 ----0.564 0.640 0.564 0.564 0.564 (0.608 / 0.643) ----0.715 0.715 0.715 0.715 (1.8 / 1.525) ----0.544 0.544 0.544 0.544 (0.796 / 1.019) age ----0.053 0.053 0.053 ----0.079 0.053 0.079 0.079 0.079 (0.04 / 0.036) ----0.088 0.088 0.088 0.088 (0.046 / 0.049) ----0.080 0.080 0.080 0.080 (0.04 / 0.047)
item 3 item 3 item 3 item 3
TRUE K_Corr K_Cova H_Cova
intercept ----4.100 4.100 4.100 ----5.595 4.100 5.595 5.595 5.595 (7.938 / 3.768) ----6.424 6.424 6.424 6.424 (7.862 / 4.322) ----6.369 6.369 6.369 6.369 (6.834 / 4.121) class 1 4.334 4.334 4.334 4.334 6.440 6.440 6.440 6.440 (7.523 / 4.213) 7.838 7.838 7.838 7.838 (8.554 / 4.67) 6.709 6.709 6.709 6.709 (6.721 / 3.944) class 2 1.912 1.912 1.912 1.912 3.426 3.426 3.426 3.426 (9.758 / 5.219) 1.985 1.985 1.985 1.985 (11.701 / 6.661) ----2.054 2.054 2.054 2.054 (19.358 / 5.666)
sex ----0.058 0.058 0.058 0.162 0.058 0.162 0.162 0.162 (0.998 / 1.374) ----0.009 0.009 0.009 0.009 (0.752 / 1.066) 0.135 0.135 0.135 0.135 (0.561 / 0.648) age 0.029 0.029 0.029 0.029 0.001 0.001 0.001 0.001 (0.037 / 0.039) 0.002 0.002 0.002 0.002 (0.039 / 0.043) 0.008 0.008 0.008 0.008 (0.036 / 0.036)
item 4 item 4 item 4 item 4
TRUE K_Corr K_Cova H_Cova
intercept ----20.669 20.669 20.669 ----6.283 20.669 6.283 6.283 6.283 (4.109 / 5.524) ----7.280 7.280 7.280 7.280 (7.075 / 5.89) ----10.886 10.886 10.886 10.886 (8.832 / 13.008) class 1 13.044 13.044 13.044 13.044 6.194 6.194 6.194 6.194 (5.067 / 3.709) 7.740 7.740 7.740 7.740 (10.621 / 4.95) 8.858 8.858 8.858 8.858 (8.238 / 7.563) class 2 12.970 12.970 12.970 12.970 4.506 4.506 4.506 4.506 (4.411 / 3.837) 7.454 7.454 7.454 7.454 (22.45 / 6.907) 10.801 10.801 10.801 10.801 (NaN / 11.956) sex 1.086 1.086 1.086 1.086 0.819 0.819 0.819 0.819 (1.34 / 1.47) 0.766 0.766 0.766 0.766 (1.723 / 1.646) 0.944 0.944 0.944 0.944 (2.687 / 2.484) age 0.355 0.355 0.355 0.355 0.097 0.097 0.097 0.097 (0.051 / 0.109) 0.105 0.105 0.105 0.105 (0.057 / 0.077) 0.166 0.166 0.166 0.166 (0.092 / 0.26)
Table 7: (Continued)
item 5 item 5 item 5 item 5
TRUE K_Corr K_Cova H_Cova
intercept ----1.104 1.104 1.104 1.104 ----0.893 0.893 0.893 0.893 (1.277 / 1.401) ----0.825 0.825 0.825 0.825 (1.937 / 1.996) ----0.895 0.895 0.895 0.895 (1.542 / 1.635) class 1 12.967 12.967 12.967 12.967 3.864 3.864 3.864 3.864 (0.817 / 1.419) 5.404 5.404 5.404 5.404 (9.679 / 4.146) 3.578 3.578 3.578 3.578 (2.704 / 2.075) class 2 0.694 0.694 0.694 1.804 0.694 1.804 1.804 1.804 (1.819 / 2.111) 1.702 1.702 1.702 1.702 (8.345 / 5.394) ----3.136 3.136 3.136 3.136 (18.43 / 6.21)
sex ----0.856 0.856 0.856 0.856 ----0.710 0.710 0.710 0.710 (0.566 / 0.622) ----0.710 0.710 0.710 0.710 (0.576 / 0.609) ----0.683 0.683 0.683 0.683 (0.588 / 0.699) age 0.019 0.019 0.019 0.003 0.019 0.003 0.003 0.003 (0.035 / 0.037) 0.002 0.002 0.002 0.002 (0.036 / 0.041) 0.003 0.003 0.003 0.003 (0.036 / 0.04)
Table 8: Average parameters estimations for 100 replication in 3-class model, N=100 (standard error in multinomial regression / sample standard error for 100 replication)
Class 1 vs. Class 3 Class 1 vs. Class 3 Class 1 vs. Class 3 Class 1 vs. Class 3
TRUE K_Corr K_Cova H_Cova
intercept ----1.868 1.868 1.868 ----1.116 1.868 1.116 1.116 1.116 (0.617 / 0.825) ----1.192 1.192 1.192 1.192 (0.634 / 1.053) ----0.650 0.650 0.650 0.650 (0.545 / 0.832) occup 1.127 1.127 1.127 1.127 0.80.80.863 0.863 63 63 (0.549 / 0.583) 0.882 0.882 0.882 0.882 (0.555 / 0.538) 0.871 0.871 0.871 0.871 (0.528 / 0.554) dprime 0.526 0.526 0.526 0.526 0.324 0.324 0.324 0.324 (0.17 / 0.191) 0.350 0.350 0.350 0.350 (0.174 / 0.208) 0.292 0.292 0.292 0.292 (0.154 / 0.174)
Class 2 vs. Class 3 Class 2 vs. Class 3 Class 2 vs. Class 3 Class 2 vs. Class 3
TRUE K_Corr K_Cova H_Cova
intercept ----0.232 0.232 0.232 ----0.825 0.232 0.825 0.825 0.825 (0.606 / 0.682) ----1.220 1.220 1.220 1.220 (0.71 / 1.091) ----3.108 3.108 3.108 3.108 (2.574 / 4.536) occup 0.325 0.325 0.325 0.325 0.243 0.243 0.243 0.243 (1.448 / 1.333) ----0.075 0.075 0.075 0.075 (6.056 / 2.408) ----1.609 1.609 1.609 1.609 (19.879 / 4.498) dprime 0.013 0.013 0.013 0.013 0.097 0.097 0.097 0.097 (0.177 / 0.19) 0.118 0.118 0.118 0.118 (0.205 / 0.235) ----0.191 0.191 0.191 0.191 (1.139 / 2.937)
Table 9: Average conditional Probability for 100 replication in 3- class model, N=100
(sample standard deviance in parentheses)
Class 1 Class 1 Class 1 Class 1
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 1.000 1.000 1.000 1.000 0.971 0.971 0.971 0.971 (0.044) 0.972 0.972 0.972 0.972 (0.031) 0.955 0.955 0.955 0.955 (0.036) Level 2 0.000 0.000 0.000 0.000 0.029 0.029 0.029 0.029 (0.044) 0.028 0.028 0.028 0.028 (0.031) 0.045 0.045 0.045 0.045 (0.036)
item2
Level 1 0.802 0.802 0.802 0.802 0.767 0.767 0.767 0.767 (0.100) 0.775 0.775 0.775 0.775 (0.115) 0.702 0.702 0.702 0.702 (0.089) Level 2 0.198 0.198 0.198 0.198 0.233 0.233 0.233 0.233 (0.100) 0.225 0.225 0.225 0.225 (0.115) 0.298 0.298 0.298 0.298 (0.089)
item3
Level 1 0.760 0.760 0.760 0.760 0.687 0.687 0.687 0.687 (0.111) 0.702 0.702 0.702 0.702 (0.143) 0.629 0.629 0.629 0.629 (0.098) Level 2 0.240 0.240 0.240 0.240 0.313 0.313 0.313 0.313 (0.111) 0.298 0.298 0.298 0.298 (0.143) 0.371 0.371 0.371 0.371 (0.098)
item4
Level 1 0.990 0.990 0.990 0.990 0.928 0.928 0.928 0.928 (0.049) 0.920 0.920 0.920 0.920 (0.058) 0.913 0.913 0.913 0.913 (0.046) Level 2 0.010 0.010 0.010 0.010 0.072 0.072 0.072 0.072 (0.049) 0.080 0.080 0.080 0.080 (0.058) 0.087 0.087 0.087 0.087 (0.046)
item5
Level 1 1.000 1.000 1.000 1.000 0.907 0.907 0.907 0.907 (0.064) 0.905 0.905 0.905 0.905 (0.076) 0.868 0.868 0.868 0.868 (0.075) Level 2 0.000 0.000 0.000 0.000 0.093 0.093 0.093 0.093 (0.064) 0.095 0.095 0.095 0.095 (0.076) 0.132 0.132 0.132 0.132 (0.075)
Class 2 Class 2 Class 2 Class 2
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.797 0.797 0.797 0.797 0.782 0.782 0.782 0.782 (0.180) 0.810 0.810 0.810 0.810 (0.285) 0.818 0.818 0.818 0.818 (0.340) Level 2 0.203 0.203 0.203 0.203 0.218 0.218 0.218 0.218 (0.180) 0.190 0.190 0.190 0.190 (0.285) 0.182 0.182 0.182 0.182 (0.340)
item2
Level 1 0.389 0.389 0.389 0.389 0.383 0.383 0.383 0.383 (0.193) 0.366 0.366 0.366 0.366 (0.308) 0.243 0.243 0.243 0.243 (0.377) Level 2 0.611 0.611 0.611 0.611 0.617 0.617 0.617 0.617 (0.193) 0.634 0.634 0.634 0.634 (0.308) 0.757 0.757 0.757 0.757 (0.377)
item3
Level 1 0.220 0.220 0.220 0.220 0.292 0.292 0.292 0.292 (0.209) 0.268 0.268 0.268 0.268 (0.286) 0.098 0.098 0.098 0.098 (0.266) Level 2 0.780 0.780 0.780 0.780 0.708 0.708 0.708 0.708 (0.209) 0.732 0.732 0.732 0.732 (0.286) 0.902 0.902 0.902 0.902 (0.266)
item4
Level 1 0.989 0.989 0.989 0.989 0.746 0.746 0.746 0.746 (0.195) 0.775 0.775 0.775 0.775 (0.314) 0.805 0.805 0.805 0.805 (0.349) Level 2 0.011 0.011 0.011 0.011 0.254 0.254 0.254 0.254 (0.195) 0.225 0.225 0.225 0.225 (0.314) 0.195 0.195 0.195 0.195 (0.349)
item5
Level 1 0.442 0.442 0.442 0.442 0.581 0.581 0.581 0.581 (0.196) 0.547 0.547 0.547 0.547 (0.311) 0.246 0.246 0.246 0.246 (0.326) Level 2 0.558 0.558 0.558 0.558 0.419 0.419 0.419 0.419 (0.196) 0.453 0.453 0.453 0.453 (0.311) 0.754 0.754 0.754 0.754 (0.326)
Table 9: (Continued)
Class 3 Class 3 Class 3 Class 3
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.151 0.151 0.151 0.151 0.217 0.217 0.217 0.217 (0.119) 0.191 0.191 0.191 0.191 (0.114) 0.144 0.144 0.144 0.144 (0.079) Level 2 0.849 0.849 0.849 0.849 0.783 0.783 0.783 0.783 (0.119) 0.809 0.809 0.809 0.809 (0.114) 0.856 0.856 0.856 0.856 (0.079)
item2
Level 1 0.029 0.029 0.029 0.029 0.061 0.061 0.061 0.061 (0.063) 0.059 0.059 0.059 0.059 (0.056) 0.051 0.051 0.051 0.051 (0.046) Level 2 0.971 0.971 0.971 0.971 0.940 0.940 0.940 0.940 (0.063) 0.941 0.941 0.941 0.941 (0.056) 0.949 0.949 0.949 0.949 (0.046)
item3
Level 1 0.040 0.040 0.040 0.040 0.044 0.044 0.044 0.044 (0.057) 0.039 0.039 0.039 0.039 (0.044) 0.033 0.033 0.033 0.033 (0.033) Level 2 0.960 0.960 0.960 0.960 0.956 0.956 0.956 0.956 (0.057) 0.961 0.961 0.961 0.961 (0.044) 0.967 0.967 0.967 0.967 (0.033)
item4
Level 1 0.000 0.000 0.000 0.000 0.162 0.162 0.162 0.162 (0.113) 0.141 0.141 0.141 0.141 (0.105) 0.086 0.086 0.086 0.086 (0.071) Level 2 1.000 1.000 1.000 1.000 0.838 0.838 0.838 0.838 (0.113) 0.859 0.859 0.859 0.859 (0.105) 0.914 0.914 0.914 0.914 (0.071)
item5
Level 1 0.284 0.284 0.284 0.284 0.273 0.273 0.273 0.273 (0.118) 0.287 0.287 0.287 0.287 (0.130) 0.279 0.279 0.279 0.279 (0.092) Level 2 0.716 0.716 0.716 0.716 0.727 0.727 0.727 0.727 (0.118) 0.713 0.713 0.713 0.713 (0.130) 0.721 0.721 0.721 0.721 (0.092)
Table 10: Average Latent Prevalences for 100 replication in 3 class model, N=100 (sample standard deviance in parentheses)
TRUE K_Corr K_Cova H_Cova
class1 0.392 0.392 0.392 0.392 0.416 0.416 0.416 0.416 (0.087) 0.439 0.439 0.439 0.439 (0.131) 0.570 0.570 0.570 0.570 (0.103) class2 0.286 0.286 0.286 0.286 0.229 0.229 0.229 0.229 (0.055) 0.199 0.199 0.199 0.199 (0.113) 0.078 0.078 0.078 0.078 (0.060) class3 0.322 0.322 0.322 0.322 0.355 0.355 0.355 0.355 (0.082) 0.362 0.362 0.362 0.362 (0.092) 0.351 0.351 0.351 0.351 (0.082)
Table 11: Average Correlation Coefficients for 100 replication in 3-class model, N=100 (total number of not NA values in parentheses)
K_Corr K_Cova H_Cova
class1 0.120 0.120 0.120 0.120 (100)(100)(100)(100) 0.199 0.199 0.199 0.199 (100)(100) (100)(100) 0.164 0.164 0.164 0.164 (100)(100) (100)(100) class2 0.119 0.119 0.119 0.119 (100)(100)(100)(100) 0.303 0.303 0.303 0.303 (100)(100) (100)(100) 0.636 0.636 0.636 0.636 (81)(81) (81)(81) class3 0.149 0.149 0.149 0.149 (100)(100)(100)(100) 0.183 0.183 0.183 0.183 (100)(100) (100)(100) 0.189 0.189 0.189 0.189 (100)(100) (100)(100)
Table 12: Average parameters estimations for 100 replication in 3-class model, N=500 (standard error in multinomial regression / sample standard error for 100 replication)
item 1 item 1item 1 item 1
TRUE K_Corr K_Cova H_Cova
intercept ----4.398 4.398 4.398 4.398 ----3.013 3.013 3.013 3.013 (0.713 / 1.222) ----3.138 3.138 3.138 3.138 (0.749 / 1.216) ----3.192 3.192 3.192 3.192 (0.775 / 0.888) class 1 11.146 11.146 11.146 11.146 5.468 5.468 5.468 5.468 (0.818 / 1.242) 6.166 6.166 6.166 6.166 (3.297 / 2.611) 4.878 4.878 4.878 4.878 (0.393 / 0.555) class 2 3.094 3.094 3.094 3.094 2.751 2.751 2.751 2.751 (0.435 / 1.926) 3.387 3.387 3.387 3.387 (4.474 / 4.401) 9.473 9.473 9.473 9.473 (14.246 / 3.82) sex 0.394 0.394 0.394 0.394 0.468 0.468 0.468 0.468 (0.304 / 0.319) 0.421 0.421 0.421 0.421 (0.321 / 0.357) 0.448 0.448 0.448 0.448 (0.336 / 0.348) age 0.075 0.075 0.075 0.075 0.044 0.044 0.044 0.044 (0.019 / 0.022) 0.045 0.045 0.045 0.045 (0.02 / 0.02) 0.040 0.040 0.040 0.040 (0.021 / 0.023)
item 2 item 2item 2 item 2
TRUE K_Corr K_Cova H_Cova
intercept ----1.431 1.431 1.431 1.431 ----0.365 0.365 0.365 0.365 (0.624 / 0.963) ----0.455 0.455 0.455 0.455 (0.633 / 1.425) ----0.621 0.621 0.621 0.621 (0.586 / 0.787) class 1 4.897 4.897 4.897 4.897 4.336 4.336 4.336 4.336 (0.419 / 0.937) 4.275 4.275 4.275 4.275 (0.439 / 1.996) 3.930 3.930 3.930 3.930 (0.378 / 0.456) class 2 3.046 3.046 3.046 3.046 1.938 1.938 1.938 1.938 (0.763 / 1.912) 0.851 0.851 0.851 0.851 (2.193 / 4.882) ----2.901 2.901 2.901 2.901 (3.141 / 4.75)
sex ----0.640 0.640 0.640 0.640 ----0.504 0.504 0.504 0.504 (0.262 / 0.285) ----0.535 0.535 0.535 0.535 (0.262 / 0.291) ----0.439 0.439 0.439 0.439 (0.247 / 0.292) age ----0.053 0.053 0.053 0.053 ----0.069 0.069 0.069 0.069 (0.017 / 0.018) ----0.068 0.068 0.068 0.068 (0.017 / 0.022) ----0.065 0.065 0.065 0.065 (0.015 / 0.018)
item 3 item 3item 3 item 3
TRUE K_Corr K_Cova H_Cova
intercept ----4.100 4.100 4.100 4.100 ----3.712 3.712 3.712 3.712 (0.673 / 1.149) ----3.699 3.699 3.699 3.699 (0.668 / 1.373) ----3.924 3.924 3.924 3.924 (0.641 / 1.212) class 1 4.334 4.334 4.334 4.334 4.120 4.120 4.120 4.120 (0.433 / 1.203) 4.252 4.252 4.252 4.252 (0.429 / 1.527) 3.785 3.785 3.785 3.785 (0.404 / 1.084) class 2 1.912 1.912 1.912 1.912 1.761 1.761 1.761 1.761 (0.846 / 2.152) 0.829 0.829 0.829 0.829 (2.586 / 4.277) ----3.955 3.955 3.955 3.955 (5.093 / 4.278) sex ----0.058 0.058 0.058 0.058 0.031 0.031 0.031 0.031 (0.249 / 0.356) 0.021 0.021 0.021 0.021 (0.255 / 0.339) 0.138 0.138 0.138 0.138 (0.236 / 0.315) age 0.029 0.029 0.029 0.029 0.014 0.014 0.014 0.014 (0.015 / 0.017) 0.013 0.013 0.013 0.013 (0.016 / 0.018) 0.018 0.018 0.018 0.018 (0.014 / 0.015)
item 4 item 4item 4 item 4
TRUE K_Corr K_Cova H_Cova
intercept ----20.669 20.669 20.669 20.669 ----4.588 4.588 4.588 4.588 (0.76 / 1.494) ----4.937 4.937 4.937 4.937 (0.796 / 2.004) ----5.956 5.956 5.956 5.956 (0.946 / 1.481) class 1 13.044 13.044 13.044 13.044 4.760 4.760 4.760 4.760 (0.434 / 1.081) 4.980 4.980 4.980 4.980 (0.494 / 1.492) 5.199 5.199 5.199 5.199 (0.42 / 0.709) class 2 12.970 12.970 12.970 12.970 2.746 2.746 2.746 2.746 (0.438 / 1.933) 2.953 2.953 2.953 2.953 (2.499 / 4.765) 9.129 9.129 9.129 9.129 (10.859 / 4.31)
sex 1.086 1.086 1.086 1.086 0.435 0.435 0.435 0.435 (0.292 / 0.36) 0.407 0.407 0.407 0.407 (0.305 / 0.38) 0.518 0.518 0.518 0.518 (0.344 / 0.398) age 0.355 0.355 0.355 0.355 0.078 0.078 0.078 0.078 (0.019 / 0.025) 0.082 0.082 0.082 0.082 (0.02 / 0.027) 0.097 0.097 0.097 0.097 (0.023 / 0.03)
Table 12: (Continued)
item 5 item 5item 5 item 5
TRUE K_Corr K_Cova H_Cova
intercept ----1.104 1.104 1.104 ----0.870 1.104 0.870 0.870 0.870 (0.546 / 0.839) ----0.911 0.911 0.911 0.911 (0.611 / 1.017) ----0.896 0.896 0.896 0.896 (0.525 / 0.616) class 1 12.967 12.967 12.967 12.967 3.694 3.694 3.694 3.694 (0.579 / 1.355) 4.260 4.260 4.260 4.260 (1.11 / 2.73) 2.873 2.873 2.873 2.873 (0.253 / 0.413) class 2 0.694 0.694 0.694 0.694 1.158 1.158 1.158 1.158 (0.367 / 2.226) 1.898 1.898 1.898 1.898 (0.82 / 3.56) ----2.579 2.579 2.579 2.579 (0.774 / 4.566) sex ----0.856 0.856 0.856 ----0.721 0.856 0.721 0.721 0.721 (0.247 / 0.294) ----0.727 0.727 0.727 0.727 (0.246 / 0.274) ----0.599 0.599 0.599 0.599 (0.24 / 0.292) age 0.019 0.019 0.019 0.019 0.006 0.006 0.006 0.006 (0.015 / 0.016) 0.006 0.006 0.006 0.006 (0.015 / 0.016) 0.009 0.009 0.009 0.009 (0.015 / 0.017)
Table 13: Average parameters estimations for 100 replication in 3-class model, N=500 (standard error in multinomial regression / sample standard error for 100 replication)
Class 1 vs. Class 3 Class 1 vs. Class 3 Class 1 vs. Class 3 Class 1 vs. Class 3
TRUE K_Corr K_Cova H_Cova
intercept ----1.868 1.868 1.868 ----0.990 1.868 0.990 0.990 0.990 (0.256 / 0.567) ----1.001 1.001 1.001 1.001 (0.26 / 0.639) ----0.578 0.578 0.578 0.578 (0.225 / 0.289) occup 1.127 1.127 1.127 1.127 0.80.80.835 0.835 35 35 (0.242 / 0.285) 0.848 0.848 0.848 0.848 (0.245 / 0.252) 0.804 0.804 0.804 0.804 (0.23 / 0.227) dprime 0.526 0.526 0.526 0.526 0.296 0.296 0.296 0.296 (0.072 / 0.085) 0.298 0.298 0.298 0.298 (0.074 / 0.09) 0.259 0.259 0.259 0.259 (0.065 / 0.067)
Class 2 vs. Class 3 Class 2 vs. Class 3 Class 2 vs. Class 3 Class 2 vs. Class 3
TRUE K_Corr K_Cova H_Cova
intercept ----0.232 0.232 0.232 ----1.181 0.232 1.181 1.181 1.181 (0.296 / 0.71) ----1.264 1.264 1.264 1.264 (0.314 / 0.902) ----2.121 2.121 2.121 2.121 (0.462 / 0.887) occup 0.325 0.325 0.325 0.325 0.376 0.376 0.376 0.376 (0.328 / 0.446) 0.346 0.346 0.346 0.346 (0.347 / 0.459) 0.162 0.162 0.162 0.162 (0.814 / 0.867) dprime 0.013 0.013 0.013 0.013 0.092 0.092 0.092 0.092 (0.088 / 0.123) 0.102 0.102 0.102 0.102 (0.093 / 0.152) 0.030 0.030 0.030 0.030 (0.139 / 0.172)
Table 14 : Average conditional Probability for 100 replication in 3- class model, N=500
(sample standard deviance in parentheses)
Class 1 Class 1 Class 1 Class 1
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 1.000 1.000 1.000 1.000 0.977 0.977 0.977 0.977 (0.015) 0.977 0.977 0.977 0.977 (0.016) 0.957 0.957 0.957 0.957 (0.016) Level 2 0.000 0.000 0.000 0.000 0.023 0.023 0.023 0.023 (0.015) 0.024 0.024 0.024 0.024 (0.016) 0.043 0.043 0.043 0.043 (0.016)
item2
Level 1 0.797 0.797 0.797 0.797 0.762 0.762 0.762 0.762 (0.093) 0.745 0.745 0.745 0.745 (0.117) 0.698 0.698 0.698 0.698 (0.038) Level 2 0.203 0.203 0.203 0.203 0.238 0.238 0.238 0.238 (0.093) 0.255 0.255 0.255 0.255 (0.117) 0.302 0.302 0.302 0.302 (0.038)
item3
Level 1 0.763 0.763 0.763 0.763 0.694 0.694 0.694 0.694 (0.090) 0.703 0.703 0.703 0.703 (0.113) 0.628 0.628 0.628 0.628 (0.049) Level 2 0.237 0.237 0.237 0.237 0.306 0.306 0.306 0.306 (0.090) 0.297 0.297 0.297 0.297 (0.113) 0.373 0.373 0.373 0.373 (0.049)
item4
Level 1 0.992 0.992 0.992 0.992 0.937 0.937 0.937 0.937 (0.025) 0.935 0.935 0.935 0.935 (0.025) 0.921 0.921 0.921 0.921 (0.018) Level 2 0.008 0.008 0.008 0.008 0.063 0.063 0.063 0.063 (0.025) 0.065 0.065 0.065 0.065 (0.025) 0.079 0.079 0.079 0.079 (0.018)
item5
Level 1 1.000 1.000 1.000 1.000 0.910 0.910 0.910 0.910 (0.053) 0.903 0.903 0.903 0.903 (0.066) 0.866 0.866 0.866 0.866 (0.039) Level 2 0.000 0.000 0.000 0.000 0.090 0.090 0.090 0.090 (0.053) 0.097 0.097 0.097 0.097 (0.066) 0.135 0.135 0.135 0.135 (0.039)
Class 2 Class 2 Class 2 Class 2
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.803 0.803 0.803 0.803 0.737 0.737 0.737 0.737 (0.253) 0.724 0.724 0.724 0.724 (0.310) 0.962 0.962 0.962 0.962 (0.093) Level 2 0.197 0.197 0.197 0.197 0.263 0.263 0.263 0.263 (0.253) 0.276 0.276 0.276 0.276 (0.310) 0.038 0.038 0.038 0.038 (0.093)
item2
Level 1 0.381 0.381 0.381 0.381 0.325 0.325 0.325 0.325 (0.218) 0.330 0.330 0.330 0.330 (0.272) 0.100 0.100 0.100 0.100 (0.183) Level 2 0.619 0.619 0.619 0.619 0.675 0.675 0.675 0.675 (0.218) 0.670 0.670 0.670 0.670 (0.272) 0.900 0.900 0.900 0.900 (0.183)
item3
Level 1 0.222 0.222 0.222 0.222 0.264 0.264 0.264 0.264 (0.223) 0.248 0.248 0.248 0.248 (0.248) 0.061 0.061 0.061 0.061 (0.151) Level 2 0.778 0.778 0.778 0.778 0.736 0.736 0.736 0.736 (0.223) 0.752 0.752 0.752 0.752 (0.248) 0.940 0.940 0.940 0.940 (0.151)
item4
Level 1 0.991 0.991 0.991 0.991 0.667 0.667 0.667 0.667 (0.263) 0.647 0.647 0.647 0.647 (0.335) 0.929 0.929 0.929 0.929 (0.158) Level 2 0.009 0.009 0.009 0.009 0.333 0.333 0.333 0.333 (0.263) 0.353 0.353 0.353 0.353 (0.335) 0.071 0.071 0.071 0.071 (0.158)
item5
Level 1 0.444 0.444 0.444 0.444 0.554 0.554 0.554 0.554 (0.256) 0.567 0.567 0.567 0.567 (0.271) 0.207 0.207 0.207 0.207 (0.213) Level 2 0.556 0.556 0.556 0.556 0.446 0.446 0.446 0.446 (0.256) 0.433 0.433 0.433 0.433 (0.271) 0.793 0.793 0.793 0.793 (0.213)
Table 14 : (Continued)
Class 3 Class 3 Class 3 Class 3
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.156 0.156 0.156 0.156 0.245 0.245 0.245 0.245 (0.111) 0.230 0.230 0.230 0.230 (0.111) 0.178 0.178 0.178 0.178 (0.046) Level 2 0.844 0.844 0.844 0.844 0.755 0.755 0.755 0.755 (0.111) 0.770 0.770 0.770 0.770 (0.111) 0.822 0.822 0.822 0.822 (0.046)
item2
Level 1 0.029 0.029 0.029 0.029 0.071 0.071 0.071 0.071 (0.049) 0.073 0.073 0.073 0.073 (0.050) 0.061 0.061 0.061 0.061 (0.023) Level 2 0.972 0.972 0.972 0.972 0.929 0.929 0.929 0.929 (0.049) 0.927 0.927 0.927 0.927 (0.050) 0.939 0.939 0.939 0.939 (0.023)
item3
Level 1 0.041 0.041 0.041 0.041 0.049 0.049 0.049 0.049 (0.041) 0.050 0.050 0.050 0.050 (0.041) 0.045 0.045 0.045 0.045 (0.020) Level 2 0.959 0.959 0.959 0.959 0.951 0.951 0.951 0.951 (0.041) 0.950 0.950 0.950 0.950 (0.041) 0.955 0.955 0.955 0.955 (0.020)
item4
Level 1 0.000 0.000 0.000 0.000 0.192 0.192 0.192 0.192 (0.107) 0.177 0.177 0.177 0.177 (0.104) 0.106 0.106 0.106 0.106 (0.037) Level 2 1.000 1.000 1.000 1.000 0.808 0.808 0.808 0.808 (0.107) 0.823 0.823 0.823 0.823 (0.104) 0.894 0.894 0.894 0.894 (0.037)
item5
Level 1 0.285 0.285 0.285 0.285 0.289 0.289 0.289 0.289 (0.089) 0.282 0.282 0.282 0.282 (0.083) 0.293 0.293 0.293 0.293 (0.036) Level 2 0.715 0.715 0.715 0.715 0.711 0.711 0.711 0.711 (0.089) 0.718 0.718 0.718 0.718 (0.083) 0.707 0.707 0.707 0.707 (0.036)
Table 15: Average Latent Prevalences for 100 replication in 3 class model , N=500 (sample standard deviance in parentheses)
TRUE K_Corr K_Cova H_Cova
class1 0.393 0.393 0.393 0.393 0.449 0.449 0.449 0.449 (0.094) 0.453 0.453 0.453 0.453 (0.114) 0.570 0.570 0.570 0.570 (0.047) class2 0.284 0.284 0.284 0.284 0.176 0.176 0.176 0.176 (0.069) 0.177 0.177 0.177 0.177 (0.093) 0.062 0.062 0.062 0.062 (0.035) class3 0.323 0.323 0.323 0.323 0.374 0.374 0.374 0.374 (0.081) 0.370 0.370 0.370 0.370 (0.084) 0.368 0.368 0.368 0.368 (0.036)
Table 16: Average Correlation Coefficients for 100 replication in 3-class model, N=500 (total number of not NA values in parentheses)
K_Corr K_Cova H_Cova
class1 0.061 0.061 0.061 0.061 (100) 0.086 0.086 0.086 0.086 (100) 0.109 0.109 0.109 0.109 (100) class2 0.041 0.041 0.041 0.041 (100) 0.091 0.091 0.091 0.091 (100) 0.386 0.386 0.386 0.386 (100) class3 0.095 0.095 0.095 0.095 (100) 0.088 0.088 0.088 0.088 (100) 0.079 0.079 0.079 0.079 (100)
Table 17: Average parameters estimations for 100 replication in 6-class model, N=300 (standard error in multinomial regression / sample standard error for 100 replication)
item 1 item 1item 1 item 1
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----6.029 6.029 6.029 6.029 1.737 1.737 1.737 1.737 (1.172 / 7.757) 1.844 1.844 1.844 1.844 (1.25 / 9.46) ----18.193 18.193 18.193 18.193 (0.587 / 8.816) class 1 11.924 11.924 11.924 7.056 11.924 7.056 7.056 7.056 (1.015 / 10.156) 11.540 11.540 11.540 11.540 (0.512 / 13.163) 20.592 20.592 20.592 20.592 (0.473 / 9.543) class 2 5.927 5.927 5.927 5.927 ----0.524 0.524 0.524 0.524 (0.734 / 10.784) 6.671 6.671 6.671 6.671 (0.988 / 48.88) ----4.585 4.585 4.585 4.585 (NaN / 9.622) class 3 7.983 7.983 7.983 7.983 2.137 2.137 2.137 2.137 (0.904 / 8.185) 3.102 3.102 3.102 3.102 (0.771 / 11.635) ----5.584 5.584 5.584 5.584 (NaN / 10.72) class 4 6.883 6.883 6.883 6.883 4.156 4.156 4.156 4.156 (0.868 / 15.471) 3.248 3.248 3.248 3.248 (NaN / 12.919) ----6.038 6.038 6.038 6.038 (NaN / 8.985) class 5 0.345 0.345 0.345 0.345 ----6.390 6.390 6.390 6.390 (0.844 / 8.454) ----11.281 11.281 11.281 11.281 (0.813 / 11.652) 5.012 5.012 5.012 5.012 (0.215 / 7.417)
sex ----0.844 0.844 0.844 0.844 ----0.062 0.062 0.062 0.062 (0.493 / 0.679) 0.021 0.021 0.021 0.021 (0.556 / 1.54) 0.007 0.007 0.007 0.007 (0.45 / 0.605) age 0.044 0.044 0.044 0.044 0.025 0.025 0.025 0.025 (0.031 / 0.033) 0.031 0.031 0.031 0.031 (0.035 / 0.035) 0.012 0.012 0.012 0.012 (0.027 / 0.027)
level 2 v.s. level 3
intercept 0.420 0.420 0.420 0.420 1.944 1.944 1.944 1.944 (1.041 / 6.915) 3.062 3.062 3.062 3.062 (1.169 / 7.594) ----6.591 6.591 6.591 6.591 (0.833 / 19.015) class 1 2.916 2.916 2.916 2.916 3.160 3.160 3.160 3.160 (0.846 / 11.05) 4.487 4.487 4.487 4.487 (NaN / 12.456) 7.261 7.261 7.261 7.261 (0.583 / 18.744) class 2 ----0.126 0.126 0.126 0.126 ----0.824 0.824 0.824 0.824 (0.645 / 9.806) 4.154 4.154 4.154 4.154 (0.678 / 48.578) ----8.932 8.932 8.932 8.932 (0.19 / 22.377) class 3 1.537 1.537 1.537 1.537 1.734 1.734 1.734 1.734 (0.837 / 8.172) 1.403 1.403 1.403 1.403 (0.666 / 11.047) ----14.967 14.967 14.967 14.967 (0.076 / 21.241) class 4 2.563 2.563 2.563 2.563 5.146 5.146 5.146 5.146 (0.844 / 14.696) 4.037 4.037 4.037 4.037 (0.768 / 12.696) ----13.289 13.289 13.289 13.289 (0.097 / 21.671) class 5 ----4.833 4.833 4.833 4.833 ----4.491 4.491 4.491 4.491 (0.626 / 7.344) ----8.430 8.430 8.430 8.430 (0.794 / 10.288) ----3.427 3.427 3.427 3.427 (0.484 / 20.184)
sex ----0.211 0.211 0.211 0.211 0.195 0.195 0.195 0.195 (0.454 / 0.658) 0.321 0.321 0.321 0.321 (0.523 / 1.471) 0.272 0.272 0.272 0.272 (0.46 / 0.6) age 0.018 0.018 0.018 0.018 0.013 0.013 0.013 0.013 (0.029 / 0.033) 0.018 0.018 0.018 0.018 (0.033 / 0.037) 0.007 0.007 0.007 0.007 (0.028 / 0.032)
item 2 item 2item 2 item 2
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----2.221 2.221 2.221 2.221 ----2.164 2.164 2.164 2.164 (1.175 / 12.823) ----6.534 6.534 6.534 6.534 (1.081 / 14.855) ----17.409 17.409 17.409 17.409 (0.411 / 5.298) class 1 6.873 6.873 6.873 6.873 12.051 12.051 12.051 12.051 (NaN / 39.33) 14.547 14.547 14.547 14.547 (0.786 / 15.798) 19.805 19.805 19.805 19.805 (0.382 / 6.667) class 2 1.908 1.908 1.908 1.908 1.197 1.197 1.197 1.197 (NaN / 16.979) 4.786 4.786 4.786 4.786 (0.634 / 19.049) ----5.189 5.189 5.189 5.189 (NaN / 8.769) class 3 5.070 5.070 5.070 5.070 3.983 3.983 3.983 3.983 (0.885 / 14.828) 9.973 9.973 9.973 9.973 (0.639 / 15.834) ----4.981 4.981 4.981 4.981 (NaN / 6.646) class 4 2.639 2.639 2.639 2.639 2.165 2.165 2.165 2.165 (0.762 / 18.335) 6.946 6.946 6.946 6.946 (0.598 / 18.129) ----4.645 4.645 4.645 4.645 (NaN / 6.238) class 5 ----7.304 7.304 7.304 7.304 ----5.225 5.225 5.225 5.225 (0.619 / 14.321) ----6.648 6.648 6.648 6.648 (0.353 / 14.421) ----0.197 0.197 0.197 0.197 (NaN / 3.487) sex ----0.513 0.513 0.513 0.513 ----0.056 0.056 0.056 0.056 (0.476 / 0.551) ----0.125 0.125 0.125 0.125 (0.481 / 0.558) ----0.077 0.077 0.077 0.077 (0.358 / 0.363) age ----0.044 0.044 0.044 0.044 ----0.042 0.042 0.042 0.042 (0.03 / 0.034) ----0.043 0.043 0.043 0.043 (0.03 / 0.031) ----0.032 0.032 0.032 0.032 (0.022 / 0.023)
Table 17: (Continued)
level 2 v.s. level 3
intercept 0.521 0.521 0.521 0.521 ----0.177 0.177 0.177 0.177 (0.9 / 4.198) 0.688 0.688 0.688 0.688 (0.859 / 9.632) ----14.797 14.797 14.797 14.797 (0.567 / 12.287) class 1 1.685 1.685 1.685 1.685 ----0.313 0.313 0.313 0.313 (0.649 / 20.431) 2.958 2.958 2.958 2.958 (NaN / 10.485) 15.760 15.760 15.760 15.760 (0.457 / 12.282) class 2 ----0.428 0.428 0.428 ----2.130 0.428 2.130 2.130 2.130 (0.481 / 8.227) ----1.686 1.686 1.686 1.686 (0.457 / 13.856) ----6.299 6.299 6.299 6.299 (0.118 / 16.771) class 3 2.204 2.204 2.204 2.204 2.565 2.565 2.565 2.565 (0.641 / 5.587) 3.966 3.966 3.966 3.966 (0.5 / 12.154) ----7.688 7.688 7.688 7.688 (0.052 / 15.491) class 4 0.546 0.546 0.546 0.546 3.276 3.276 3.276 3.276 (0.605 / 16.832) 0.820 0.820 0.820 0.820 (0.511 / 13.506) ----7.565 7.565 7.565 7.565 (0.065 / 14.053) class 5 ----4.833 4.833 4.833 ----3.179 4.833 3.179 3.179 3.179 (0.586 / 6.489) ----5.85.85.827 5.827 27 27 (0.507 / 11.646) 2.191 2.191 2.191 2.191 (0.214 / 12.536) sex ----0.274 0.274 0.274 ----0.016 0.274 0.016 0.016 0.016 (0.365 / 0.444) ----0.056 0.056 0.056 0.056 (0.372 / 0.448) ----0.001 0.001 0.001 0.001 (0.323 / 0.351) age ----0.008 0.008 0.008 ----0.007 0.008 0.007 0.007 0.007 (0.023 / 0.025) ----0.008 0.008 0.008 0.008 (0.023 / 0.026) ----0.007 0.007 0.007 0.007 (0.02 / 0.021)
item 3 item 3item 3 item 3
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----7.445 7.445 7.445 ----7.876 7.445 7.876 7.876 7.876 (1.11 / 14.908) ----13.160 13.160 13.160 13.160 (0.847 / 14.946) ----17.015 17.015 17.015 17.015 (0.425 / 2.719) class 1 8.520 8.520 8.520 8.520 9.461 9.461 9.461 9.461 (0.974 / 14.59) 14.795 14.795 14.795 14.795 (0.548 / 14.646) 16.709 16.709 16.709 16.709 (0.387 / 3.143) class 2 2.959 2.959 2.959 2.959 3.506 3.506 3.506 3.506 (0.646 / 16.817) 5.581 5.581 5.581 5.581 (0.344 / 18.171) ----4.871 4.871 4.871 4.871 (NaN / 7.409) class 3 4.838 4.838 4.838 4.838 4.650 4.650 4.650 4.650 (NaN / 15.864) 8.864 8.864 8.864 8.864 (0.461 / 15.489) ----3.483 3.483 3.483 3.483 (NaN / 7.756) class 4 7.931 7.931 7.931 7.931 9.387 9.387 9.387 9.387 (0.905 / 17.781) 9.811 9.811 9.811 9.811 (0.429 / 16.866) ----3.928 3.928 3.928 3.928 (NaN / 6.145) class 5 3.620 3.620 3.620 3.620 ----1.814 1.814 1.814 1.814 (0.583 / 16.499) 1.398 1.398 1.398 1.398 (0.336 / 13.851) ----0.858 0.858 0.858 0.858 (0.098 / 6.024)
sex ----0.450 0.450 0.450 0.024 0.450 0.024 0.024 0.024 (0.49 / 0.669) ----0.047 0.047 0.047 0.047 (0.442 / 0.553) ----0.026 0.026 0.026 0.026 (0.348 / 0.465) age 0.007 0.007 0.007 0.007 0.001 0.001 0.001 0.001 (0.03 / 0.032) 0.003 0.003 0.003 0.003 (0.028 / 0.034) ----0.001 0.001 0.001 0.001 (0.022 / 0.02)
level 2 v.s. level 3
intercept ----2.650 2.650 2.650 ----3.047 2.650 3.047 3.047 3.047 (0.752 / 6.555) ----5.241 5.241 5.241 5.241 (0.793 / 12.547) ----14.044 14.044 14.044 14.044 (0.507 / 7.571) class 1 3.046 3.046 3.046 3.046 3.135 3.135 3.135 3.135 (0.511 / 6.924) 5.938 5.938 5.938 5.938 (0.638 / 12.714) 14.007 14.007 14.007 14.007 (0.39 / 7.439) class 2 0.766 0.766 0.766 0.766 0.205 0.205 0.205 0.205 (0.448 / 9.96) 2.768 2.768 2.768 2.768 (0.533 / 10.725) ----4.661 4.661 4.661 4.661 (0.116 / 13.138) class 3 3.383 3.383 3.383 3.383 4.564.564.564.565 5 5 5 (NaN / 8.395) 6.147 6.147 6.147 6.147 (0.542 / 13.399) 2.191 2.191 2.191 2.191 (0.153 / 18.248) class 4 3.271 3.271 3.271 3.271 1.230 1.230 1.230 1.230 (0.415 / 7.296) 4.325 4.325 4.325 4.325 (0.554 / 13.633) ----0.970 0.970 0.970 0.970 (0.131 / 15.97) class 5 0.783 0.783 0.783 0.783 0.804 0.804 0.804 0.804 (0.575 / 6.619) 2.992 2.992 2.992 2.992 (0.616 / 12.729) 4.074 4.074 4.074 4.074 (0.295 / 11.242)
sex ----0.794 0.794 0.794 ----0.40.794 0.40.40.495 95 95 95 (0.313 / 0.332) ----0.547 0.547 0.547 0.547 (0.319 / 0.378) ----0.443 0.443 0.443 0.443 (0.286 / 0.304) age 0.019 0.019 0.019 0.019 0.012 0.012 0.012 0.012 (0.02 / 0.018) 0.014 0.014 0.014 0.014 (0.02 / 0.02) 0.008 0.008 0.008 0.008 (0.018 / 0.017)
Table 17: (Continued)
item 4 item 4item 4 item 4
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----6.883 6.883 6.883 6.883 ----0.819 0.819 0.819 0.819 (1.134 / 6.3) ----0.232 0.232 0.232 0.232 (1.11 / 8.601) ----17.852 17.852 17.852 17.852 (0.6 / 7.573) class 1 10.946 10.946 10.946 10.946 7.891 7.891 7.891 7.891 (1.221 / 8.307) 14.228 14.228 14.228 14.228 (NaN / 23.778) 20.849 20.849 20.849 20.849 (0.478 / 9.591) class 2 7.782 7.782 7.782 7.782 2.412 2.412 2.412 2.412 (0.745 / 7.801) 5.210 5.210 5.210 5.210 (0.597 / 12.414) ----3.024 3.024 3.024 3.024 (NaN / 12.86) class 3 9.085 9.085 9.085 9.085 3.977 3.977 3.977 3.977 (0.741 / 7.998) 5.279 5.279 5.279 5.279 (0.78 / 11.649) ----3.640 3.640 3.640 3.640 (NaN / 15.571) class 4 11.649 11.649 11.649 11.649 5.875 5.875 5.875 5.875 (0.721 / 8.92) 6.106 6.106 6.106 6.106 (0.577 / 11.194) ----6.823 6.823 6.823 6.823 (NaN / 8.339) class 5 2.957 2.957 2.957 2.957 ----3.419 3.419 3.419 3.419 (0.756 / 7.367) ----6.178 6.178 6.178 6.178 (0.687 / 9.665) 3.662 3.662 3.662 3.662 (0.163 / 7.743)
sex ----1.883 1.883 1.883 1.883 ----0.876 0.876 0.876 0.876 (0.476 / 0.645) ----1.053 1.053 1.053 1.053 (0.516 / 0.749) ----0.647 0.647 0.647 0.647 (0.412 / 0.506) age 0.030 0.030 0.030 0.030 0.017 0.017 0.017 0.017 (0.029 / 0.031) 0.020 0.020 0.020 0.020 (0.031 / 0.031) 0.003 0.003 0.003 0.003 (0.025 / 0.026)
level 2 v.s. level 3
intercept ----0.0.0.0.261 261 261 ----0.793 261 0.793 0.793 0.793 (1.045 / 5.424) 0.123 0.123 0.123 0.123 (1.025 / 6.465) ----14.601 14.601 14.601 14.601 (0.734 / 14.925) class 1 1.698 1.698 1.698 1.698 5.215 5.215 5.215 5.215 (1.108 / 7.847) 4.434 4.434 4.434 4.434 (NaN / 21.747) 16.064 16.064 16.064 16.064 (0.52 / 13.532) class 2 1.665 1.665 1.665 1.665 2.730 2.730 2.730 2.730 (0.683 / 7.125) 3.804 3.804 3.804 3.804 (0.547 / 10.582) ----2.888 2.888 2.888 2.888 (0.165 / 25.005) class 3 3.753 3.753 3.753 3.753 5.776 5.776 5.776 5.776 (0.715 / 7.502) 5.606 5.606 5.606 5.606 (0.747 / 10.134) ----6.064 6.064 6.064 6.064 (0.126 / 15.897) class 4 4.873 4.873 4.873 4.873 5.226 5.226 5.226 5.226 (0.708 / 8.282) 5.971 5.971 5.971 5.971 (0.546 / 10.546) ----7.845 7.845 7.845 7.845 (0.081 / 14.333) class 5 ----2.089 2.089 2.089 2.089 ----1.519 1.519 1.519 1.519 (0.627 / 6.265) ----4.647 4.647 4.647 4.647 (0.606 / 10.304) 4.238 4.238 4.238 4.238 (0.361 / 17.071) sex ----0.783 0.783 0.783 0.783 ----0.132 0.132 0.132 0.132 (0.434 / 0.557) ----0.289 0.289 0.289 0.289 (0.479 / 0.632) ----0.107 0.107 0.107 0.107 (0.418 / 0.503) age 0.008 0.008 0.008 0.008 ----0.002 0.002 0.002 0.002 (0.027 / 0.029) 0.001 0.001 0.001 0.001 (0.029 / 0.027) ----0.009 0.009 0.009 0.009 (0.026 / 0.026)
item 5 item 5item 5 item 5
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept 0.190.190.190.199 9 9 9 0.580 0.580 0.580 0.580 (0.973 / 5.077) 2.523 2.523 2.523 2.523 (0.939 / 10.278) ----8.121 8.121 8.121 8.121 (0.699 / 11.996) class 1 3.300 3.300 3.300 3.300 2.947 2.947 2.947 2.947 (0.815 / 4.854) 4.531 4.531 4.531 4.531 (0.908 / 12.099) 10.991 10.991 10.991 10.991 (0.519 / 12.657) class 2 0.106 0.106 0.106 0.106 0.541 0.541 0.541 0.541 (0.662 / 8.4) 0.139 0.139 0.139 0.139 (0.594 / 14.111) ----7.807 7.807 7.807 7.807 (NaN / 14.952) class 3 1.796 1.796 1.796 1.796 1.273 1.273 1.273 1.273 (0.712 / 6.059) 1.275 1.275 1.275 1.275 (0.616 / 11.492) ----5.210 5.210 5.210 5.210 (NaN / 17.885) class 4 0.370 0.370 0.370 0.370 0.195 0.195 0.195 0.195 (0.707 / 6.955) ----0.008 0.008 0.008 0.008 (0.515 / 12.751) ----4.438 4.438 4.438 4.438 (NaN / 16.454) class 5 ----2.095 2.095 2.095 2.095 ----2.681 2.681 2.681 2.681 (0.727 / 5.521) ----5.033 5.033 5.033 5.033 (0.647 / 11.443) 2.450 2.450 2.450 2.450 (0.514 / 14.639)
sex ----0.767 0.767 0.767 0.767 ----0.533 0.533 0.533 0.533 (0.38 / 0.372) ----0.570 0.570 0.570 0.570 (0.385 / 0.427) ----0.452 0.452 0.452 0.452 (0.346 / 0.384) age 0.000 0.000 0.000 0.000 0.002 0.002 0.002 0.002 (0.024 / 0.027) 0.003 0.003 0.003 0.003 (0.024 / 0.026) ----0.005 0.005 0.005 0.005 (0.021 / 0.022)
Table 17: (Continued)
level 2 v.s. level 3
intercept 0.889 0.889 0.889 0.889 0.695 0.695 0.695 0.695 (0.923 / 4.54) 3.893.893.893.891 1 1 1 (0.917 / 11.262) ----0.849 0.849 0.849 0.849 (0.734 / 17.149) class 1 0.479 0.479 0.479 0.479 1.045 1.045 1.045 1.045 (0.878 / 5.248) ----0.487 0.487 0.487 0.487 (0.928 / 10.74) 2.432 2.432 2.432 2.432 (0.496 / 16.137) class 2 ----0.379 0.379 0.379 ----0.338 0.379 0.338 0.338 0.338 (0.649 / 6.642) ----1.726 1.726 1.726 1.726 (0.58 / 13.667) ----4.965 4.965 4.965 4.965 (0.146 / 26.834) class 3 2.062 2.062 2.062 2.062 2.744 2.744 2.744 2.744 (0.678 / 5.879) 0.590 0.590 0.590 0.590 (0.608 / 11.761) ----5.547 5.547 5.547 5.547 (0.2 / 24.622) class 4 ----0.073 0.073 0.073 0.008 0.073 0.008 0.008 0.008 (0.715 / 6.208) ----0.948 0.948 0.948 0.948 (0.582 / 13.179) ----4.960 4.960 4.960 4.960 (0.173 / 26.296) class 5 ----1.232 1.232 1.232 ----1.516 1.232 1.516 1.516 1.516 (0.586 / 5.423) ----4.696 4.696 4.696 4.696 (0.593 / 11.888) ----1.360 1.360 1.360 1.360 (0.614 / 17.428) sex ----0.586 0.586 0.586 ----0.458 0.586 0.458 0.458 0.458 (0.364 / 0.437) ----0.494 0.494 0.494 0.494 (0.371 / 0.473) ----0.384 0.384 0.384 0.384 (0.361 / 0.433) age ----0.011 0.011 0.011 ----0.011 0.011 0.011 0.011 0.011 (0.023 / 0.023) ----0.012 0.012 0.012 0.012 (0.023 / 0.024) ----0.014 0.014 0.014 0.014 (0.022 / 0.022)
Table 18: Average parameters estimations for 100 replication in 6-class model, N=300 (standard error in multinomial regression / sample standard error for 100 replication)
Class 1 vs. Class 6
Table 19: Average conditional Probability for 100 replication in 6-class model, N=300
(sample standard deviance in parentheses)
Class 1 Class 1 Class 1 Class 1
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.955 0.955 0.955 0.955 0.874 0.874 0.874 0.874 (0.079) 0.914 0.914 0.914 0.914 (0.077) 0.563 0.563 0.563 0.563 (0.118) Level 2 0.044 0.044 0.044 0.044 0.114 0.114 0.114 0.114 (0.072) 0.079 0.079 0.079 0.079 (0.068) 0.345 0.345 0.345 0.345 (0.094) Level 3 0.001 0.001 0.001 0.001 0.012 0.012 0.012 0.012 (0.017) 0.007 0.007 0.007 0.007 (0.014) 0.093 0.093 0.093 0.093 (0.036)
item2
Level 1 0.727 0.727 0.727 0.727 0.703 0.703 0.703 0.703 (0.160) 0.758 0.758 0.758 0.758 (0.136) 0.345 0.345 0.345 0.345 (0.159) Level 2 0.235 0.235 0.235 0.235 0.241 0.241 0.241 0.241 (0.134) 0.200 0.200 0.200 0.200 (0.111) 0.438 0.438 0.438 0.438 (0.106) Level 3 0.038 0.038 0.038 0.038 0.056 0.056 0.056 0.056 (0.048) 0.042 0.042 0.042 0.042 (0.043) 0.218 0.218 0.218 0.218 (0.065)
item3
Level 1 0.508 0.508 0.508 0.508 0.440 0.440 0.440 0.440 (0.236) 0.531 0.531 0.531 0.531 (0.155) 0.237 0.237 0.237 0.237 (0.111) Level 2 0.318 0.318 0.318 0.318 0.369 0.369 0.369 0.369 (0.169) 0.320.320.320.327 7 7 7 (0.132) 0.373 0.373 0.373 0.373 (0.052) Level 3 0.174 0.174 0.174 0.174 0.191 0.191 0.191 0.191 (0.103) 0.142 0.142 0.142 0.142 (0.072) 0.390 0.390 0.390 0.390 (0.084)
item4
Level 1 0.929 0.929 0.929 0.929 0.855 0.855 0.855 0.855 (0.083) 0.900 0.900 0.900 0.900 (0.083) 0.523 0.523 0.523 0.523 (0.127) Level 2 0.056 0.056 0.056 0.056 0.127 0.127 0.127 0.127 (0.080) 0.087 0.087 0.087 0.087 (0.076) 0.360 0.360 0.360 0.360 (0.097) Level 3 0.015 0.015 0.015 0.015 0.018 0.018 0.018 0.018 (0.018) 0.013 0.013 0.013 0.013 (0.019) 0.117 0.117 0.117 0.117 (0.041)
item5
Level 1 0.883 0.883 0.883 0.883 0.820 0.820 0.820 0.820 (0.083) 0.861 0.861 0.861 0.861 (0.088) 0.525 0.525 0.525 0.525 (0.122) Level 2 0.078 0.078 0.078 0.078 0.124 0.124 0.124 0.124 (0.069) 0.095 0.095 0.095 0.095 (0.070) 0.309 0.309 0.309 0.309 (0.083) Level 3 0.039 0.039 0.039 0.039 0.056 0.056 0.056 0.056 (0.037) 0.044 0.044 0.044 0.044 (0.036) 0.166 0.166 0.166 0.166 (0.049)
Class 2 Class 2 Class 2 Class 2
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.439 0.439 0.439 0.439 0.385 0.385 0.385 0.385 (0.244) 0.457 0.457 0.457 0.457 (0.273) 0.044 0.044 0.044 0.044 (0.172) Level 2 0.384 0.384 0.384 0.384 0.424 0.424 0.424 0.424 (0.203) 0.378 0.378 0.378 0.378 (0.226) 0.214 0.214 0.214 0.214 (0.363) Level 3 0.177 0.177 0.177 0.177 0.191 0.191 0.191 0.191 (0.217) 0.165 0.165 0.165 0.165 (0.260) 0.742 0.742 0.742 0.742 (0.387)
item2
Level 1 0.071 0.071 0.071 0.071 0.170 0.170 0.170 0.170 (0.253) 0.211 0.211 0.211 0.211 (0.282) 0.0.0.0.028 028 028 028 (0.148) Level 2 0.397 0.397 0.397 0.397 0.372 0.372 0.372 0.372 (0.251) 0.363 0.363 0.363 0.363 (0.245) 0.096 0.096 0.096 0.096 (0.244) Level 3 0.532 0.532 0.532 0.532 0.457 0.457 0.457 0.457 (0.313) 0.427 0.427 0.427 0.427 (0.338) 0.876 0.876 0.876 0.876 (0.284)
Table 19 : (Continued)
item3
Level 1 0.009 0.009 0.009 0.009 0.134 0.134 0.134 0.134 (0.237) 0.104 0.104 0.104 0.104 (0.196) 0.024 0.024 0.024 0.024 (0.136) Level 2 0.156 0.156 0.156 0.156 0.266 0.266 0.266 0.266 (0.184) 0.277 0.277 0.277 0.277 (0.206) 0.096 0.096 0.096 0.096 (0.238) Level 3 0.834 0.834 0.834 0.834 0.600 0.600 0.600 0.600 (0.250) 0.619 0.619 0.619 0.619 (0.266) 0.880 0.880 0.880 0.880 (0.277)
item4
Level 1 0.361 0.361 0.361 0.361 0.360 0.360 0.360 0.360 (0.225) 0.409 0.409 0.409 0.409 (0.252) 0.070 0.070 0.070 0.070 (0.193) Level 2 0.498 0.498 0.498 0.498 0.443 0.443 0.443 0.443 (0.206) 0.443 0.443 0.443 0.443 (0.232) 0.183 0.183 0.183 0.183 (0.331) Level 3 0.141 0.141 0.141 0.141 0.197 0.197 0.197 0.197 (0.170) 0000.148 .148 .148 .148 (0.200) 0.747 0.747 0.747 0.747 (0.373)
item5
Level 1 0.335 0.335 0.335 0.335 0.400 0.400 0.400 0.400 (0.243) 0.411 0.411 0.411 0.411 (0.280) 0.057 0.057 0.057 0.057 (0.167) Level 2 0.306 0.306 0.306 0.306 0.311 0.311 0.311 0.311 (0.181) 0.302 0.302 0.302 0.302 (0.196) 0.354 0.354 0.354 0.354 (0.444) Level 3 0.359 0.359 0.359 0.359 0.289 0.289 0.289 0.289 (0.240) 0.287 0.287 0.287 0.287 (0.276) 0.589 0.589 0.589 0.589 (0.460)
Class 3 Class 3 Class 3 Class 3
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.609 0.609 0.609 0.609 0.500 0.500 0.500 0.500 (0.186) 0.505 0.505 0.505 0.505 (0.192) 0.031 0.031 0.031 0.031 (0.154) Level 2 0.360 0.360 0.360 0.360 0.428 0.428 0.428 0.428 (0.178) 0.430 0.430 0.430 0.430 (0.181) 0.114 0.114 0.114 0.114 (0.291) Level 3 0.031 0.031 0.031 0.031 0.072 0.072 0.072 0.072 (0.159) 0.065 0.065 0.065 0.065 (0.145) 0.855 0.855 0.855 0.855 (0.338)
item2
Level 1 0.217 0.217 0.217 0.217 0.182 0.182 0.182 0.182 (0.172) 0.194 0.194 0.194 0.194 (0.175) 0.015 0.015 0.015 0.015 (0.104) Level 2 0.714 0.714 0.714 0.714 0.668 0.668 0.668 0.668 (0.175) 0.653 0.653 0.653 0.653 (0.206) 0.068 0.068 0.068 0.068 (0.225) Level 3 0.069 0.069 0.069 0.069 0.150 0.150 0.150 0.150 (0.120) 0.153 0.153 0.153 0.153 (0.176) 0.917 0.917 0.917 0.917 (0.256)
item3
Level 1 0.020 0.020 0.020 0.020 0.086 0.086 0.086 0.086 (0.151) 0.088 0.088 0.088 0.088 (0.140) 0.017 0.017 0.017 0.017 (0.107) Level 2 0.705 0.705 0.705 0.705 0.562 0.562 0.562 0.562 (0.210) 0.573 0.573 0.573 0.573 (0.206) 0.235 0.235 0.235 0.235 (0.376) Level 3 0.275 0.275 0.275 0.275 0.351 0.351 0.351 0.351 (0.200) 0.340 0.340 0.340 0.340 (0.202) 0.748 0.748 0.748 0.748 (0.391)
item4
Level 1 0.242 0.242 0.242 0.242 0.330 0.330 0.330 0.330 (0.176) 0.346 0.346 0.346 0.346 (0.210) 0.061 0.061 0.061 0.061 (0.192) Level 2 0.732 0.732 0.732 0.732 0.602 0.602 0.602 0.602 (0.185) 0.589 0.589 0.589 0.589 (0.217) 0.101 0.101 0.101 0.101 (0.242) Level 3 0.0260.0260.0260.026 0.068 0.068 0.068 0.068 (0.122) 0.065 0.065 0.065 0.065 (0.123) 0.837 0.837 0.837 0.837 (0.326)
item5
Level 1 0.319 0.319 0.319 0.319 0.351 0.351 0.351 0.351 (0.163) 0.368 0.368 0.368 0.368 (0.183) 0.102 0.102 0.102 0.102 (0.256) Level 2 0.618 0.618 0.618 0.618 0.538 0.538 0.538 0.538 (0.185) 0.503 0.503 0.503 0.503 (0.194) 0.311 0.311 0.311 0.311 (0.404) Level 3 0.063 0.063 0.063 0.063 0.111 0.111 0.111 0.111 (0.079) 0.129 0.129 0.129 0.129 (0.138) 0.587 0.587 0.587 0.587 (0.444)
Table 19 : (Continued)
Class 4 Class 4 Class 4 Class 4
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.164 0.164 0.164 0.164 0.476 0.476 0.476 0.476 (0.255) 0.408 0.408 0.408 0.408 (0.271) 0.024 0.024 0.024 0.024 (0.129) Level 2 0.811 0.811 0.811 0.811 0.451 0.451 0.451 0.451 (0.235) 0.493 0.493 0.493 0.493 (0.273) 0.122 0.122 0.122 0.122 (0.291) Level 3 0.025 0.025 0.025 0.025 0.073 0.073 0.073 0.073 (0.129) 0.099 0.099 0.099 0.099 (0.230) 0.854 0.854 0.854 0.854 (0.329)
item2
Level 1 0.085 0.085 0.085 0.085 0.251 0.251 0.251 0.251 (0.241) 0.202 0.202 0.202 0.202 (0.227) 0.010 0.010 0.010 0.010 (0.064) Level 2 0.607 0.607 0.607 0.607 0.525 0.525 0.525 0.525 (0.234) 0.520 0.520 0.520 0.520 (0.251) 0.058 0.058 0.058 0.058 (0.189) Level 3 0.307 0.307 0.307 0.307 0.224 0.224 0.224 0.224 (0.220) 0.278 0.278 0.278 0.278 (0.286) 0.932 0.932 0.932 0.932 (0.220)
item3
Level 1 0.330 0.330 0.330 0.330 0.341 0.341 0.341 0.341 (0.362) 0.204 0.204 0.204 0.204 (0.252) 0.018 0.018 0.018 0.018 (0.109) Level 2 0.466 0.466 0.466 0.466 0.322 0.322 0.322 0.322 (0.236) 0.390.390.390.397 7 7 7 (0.235) 0.177 0.177 0.177 0.177 (0.335) Level 3 0.203 0.203 0.203 0.203 0.337 0.337 0.337 0.337 (0.262) 0.399 0.399 0.399 0.399 (0.277) 0.804 0.804 0.804 0.804 (0.351)
item4
Level 1 0.581 0.581 0.581 0.581 0.522 0.522 0.522 0.522 (0.252) 0.440 0.440 0.440 0.440 (0.246) 0.028 0.028 0.028 0.028 (0.150) Level 2 0.414 0.414 0.414 0.414 0.395 0.395 0.395 0.395 (0.216) 0.419 0.419 0.419 0.419 (0.219) 0.069 0.069 0.069 0.069 (0.210) Level 3 0.005 0.005 0.005 0.005 0.083 0.083 0.083 0.083 (0.112) 0.141 0.141 0.141 0.141 (0.256) 0.903 0.903 0.903 0.903 (0.265)
item5
Level 1 0.360 0.360 0.360 0.360 0.460 0.460 0.460 0.460 (0.250) 0.404 0.404 0.404 0.404 (0.241) 0.123 0.123 0.123 0.123 (0.282) Level 2 0.343 0.343 0.343 0.343 0.316 0.316 0.316 0.316 (0.198) 0.341 0.341 0.341 0.341 (0.217) 0.322 0.322 0.322 0.322 (0.422) Level 3 0.296 0.296 0.296 0.296 0.224 0.224 0.224 0.224 (0.230) 0.255 0.255 0.255 0.255 (0.264) 0.555 0.555 0.555 0.555 (0.458)
Class 5 Class 5 Class 5 Class 5
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.009 0.009 0.009 0.009 0.056 0.056 0.056 0.056 (0.052) 0.025 0.025 0.025 0.025 (0.029) 0.012 0.012 0.012 0.012 (0.024) Level 2 0.019 0.019 0.019 0.019 0.176 0.176 0.176 0.176 (0.086) 0.098 0.098 0.098 0.098 (0.070) 0.046 0.046 0.046 0.046 (0.062) Level 3 0.972 0.972 0.972 0.972 0.767 0.767 0.767 0.767 (0.108) 0.877 0.877 0.877 0.877 (0.086) 0.943 0.943 0.943 0.943 (0.078)
item2
Level 1 0.000 0.000 0.000 0.000 0.012 0.012 0.012 0.012 (0.014) 0.003 0.003 0.003 0.003 (0.008) 0.0.0.0.001 001 001 001 (0.006) Level 2 0.009 0.009 0.009 0.009 0.119 0.119 0.119 0.119 (0.084) 0.075 0.075 0.075 0.075 (0.057) 0.019 0.019 0.019 0.019 (0.042) Level 3 0.991 0.991 0.991 0.991 0.869 0.869 0.869 0.869 (0.087) 0.922 0.922 0.922 0.922 (0.060) 0.980 0.980 0.980 0.980 (0.044)
item3
Level 1 0.018 0.018 0.018 0.018 0.015 0.015 0.015 0.015 (0.019) 0.014 0.014 0.014 0.014 (0.019) 0.006 0.006 0.006 0.006 (0.019) Level 2 0.157 0.157 0.157 0.157 0.135 0.135 0.135 0.135 (0.065) 0.141 0.141 0.141 0.141 (0.065) 0.052 0.052 0.052 0.052 (0.068) Level 3 0.825 0.825 0.825 0.825 0.850 0.850 0.850 0.850 (0.069) 0.845 0.845 0.845 0.845 (0.070) 0.941 0.941 0.941 0.941 (0.073)
Table 19 : (Continued)
item4
Level 1 0.019 0.019 0.019 0.019 0.061 0.061 0.061 0.061 (0.052) 0.036 0.036 0.036 0.036 (0.036) 0.010 0.010 0.010 0.010 (0.025) Level 2 0.075 0.075 0.075 0.075 0.146 0.146 0.146 0.146 (0.077) 0.095 0.095 0.095 0.095 (0.059) 0.038 0.038 0.038 0.038 (0.055) Level 3 0.907 0.907 0.907 0.907 0.792 0.792 0.792 0.792 (0.110) 0.80.80.80.869 69 69 69 (0.076) 0.952 0.952 0.952 0.952 (0.073)
item5
Level 1 0.070 0.070 0.070 0.070 0.109 0.109 0.109 0.109 (0.063) 0.104 0.104 0.104 0.104 (0.053) 0.064 0.064 0.064 0.064 (0.060) Level 2 0.248 0.248 0.248 0.248 0.255 0.255 0.255 0.255 (0.093) 0.235 0.235 0.235 0.235 (0.098) 0.171 0.171 0.171 0.171 (0.136) Level 3 0.682 0.682 0.682 0.682 0.636 0.636 0.636 0.636 (0.115) 0.661 0.661 0.661 0.661 (0.123) 0.765 0.765 0.765 0.765 (0.163)
Class 6 Class 6 Class 6 Class 6
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.002 0.002 0.002 0.002 0.317 0.317 0.317 0.317 (0.297) 0.282 0.282 0.282 0.282 (0.292) 0.006 0.006 0.006 0.006 (0.038) Level 2 0.709 0.709 0.709 0.709 0.450 0.450 0.450 0.450 (0.249) 0.494 0.494 0.494 0.494 (0.288) 0.319 0.319 0.319 0.319 (0.420) Level 3 0.289 0.289 0.289 0.289 0.234 0.234 0.234 0.234 (0.248) 0.224 0.224 0.224 0.224 (0.270) 0.675 0.675 0.675 0.675 (0.419)
item2
Level 1 0.009 0.009 0.009 0.009 0.181 0.181 0.181 0.181 (0.304) 0.121 0.121 0.121 0.121 (0.246) 0.002 0.002 0.002 0.002 (0.020) Level 2 0.529 0.529 0.529 0.529 0.412 0.412 0.412 0.412 (0.247) 0.438 0.438 0.438 0.438 (0.257) 0.098 0.098 0.098 0.098 (0.251) Level 3 0.462 0.462 0.462 0.462 0.407 0.407 0.407 0.407 (0.279) 0.441 0.441 0.441 0.441 (0.286) 0.900 0.900 0.900 0.900 (0.254)
item3
Level 1 0.001 0.001 0.001 0.001 0.138 0.138 0.138 0.138 (0.286) 0.065 0.065 0.065 0.065 (0.207) 0.000 0.000 0.000 0.000 0.000 Level 2 0000.080 .080 .080 .080 0.230 0.230 0.230 0.230 (0.201) 0.182 0.182 0.182 0.182 (0.188) 0.056 0.056 0.056 0.056 (0.207) Level 3 0.919 0.919 0.919 0.919 0.632 0.632 0.632 0.632 (0.302) 0.753 0.753 0.753 0.753 (0.259) 0.944 0.944 0.944 0.944 (0.207)
item4
Level 1 0.001 0.001 0.001 0.001 0.297 0.297 0.297 0.297 (0.284) 0.257 0.257 0.257 0.257 (0.285) 0.016 0.016 0.016 0.016 (0.075) Level 2 0.400 0.400 0.400 0.400 0.342 0.342 0.342 0.342 (0.215) 0.341 0.341 0.341 0.341 (0.238) 0.110 0.110 0.110 0.110 (0.273) Level 3 0.600 0.600 0.600 0.600 0.361 0.361 0.361 0.361 (0.298) 0.401 0.401 0.401 0.401 (0.331) 0.874 0.874 0.874 0.874 (0.283)
item5
Level 1 0.272 0.272 0.272 0.272 0.340 0.340 0.340 0.340 (0.252) 0.330 0.330 0.330 0.330 (0.238) 0.110 0.110 0.110 0.110 (0.251) Level 2 0.404 0.404 0.404 0.404 0.362 0.362 0.362 0.362 (0.199) 0.396 0.396 0.396 0.396 (0.233) 0.392 0.392 0.392 0.392 (0.438) Level 3 0.324 0.324 0.324 0.324 0.299 0.299 0.299 0.299 (0.238) 0.274 0.274 0.274 0.274 (0.245) 0.498 0.498 0.498 0.498 (0.454)
Table 20: Average Latent Prevalences for 100 replication in 6-class model, N=300 (sample standard deviance in parentheses)
TRUE K_Corr K_Cova H_Cova
class1 0.2640.264 0.2640.264 0.233 0.233 0.233 0.233 (0.078) 0.217 0.217 0.217 0.217 (0.086) 0.795 0.795 0.795 0.795 (0.192) class2 0.1380.138 0.1380.138 0.122 0.122 0.122 0.122 (0.047) 0.132 0.132 0.132 0.132 (0.079) 0.029 0.029 0.029 0.029 (0.111) class3 0.1950.195 0.1950.195 0.183 0.183 0.183 0.183 (0.074) 0.199 0.199 0.199 0.199 (0.097) 0.026 0.026 0.026 0.026 (0.089) class4 0.1190.119 0.1190.119 0.132 0.132 0.132 0.132 (0.055) 0.156 0.156 0.156 0.156 (0.101) 0.024 0.024 0.024 0.024 (0.096) class5 0.1590.159 0.1590.159 0.205 0.205 0.205 0.205 (0.074) 0.183 0.183 0.183 0.183 (0.051) 0.109 0.109 0.109 0.109 (0.063) class6 0.1250.125 0.1250.125 0.125 0.125 0.125 0.125 (0.055) 0.113 0.113 0.113 0.113 (0.060) 0.017 0.017 0.017 0.017 (0.012)
Table 21: Average Correlation Coefficients for 100 replication in 6-class model, N=300. (total number of not NA values in parentheses)
K_Corr K_Cova H_Cova
class1 0.159 0.159 0.159 0.159 (100) 0.168 0.168 0.168 0.168 (100) 0.211 0.211 0.211 0.211 (100) class2 0.191 0.191 0.191 0.191 (100) 0.198 0.198 0.198 0.198 (100) 0.848 0.848 0.848 0.848 (61) class3 0.153 0.153 0.153 0.153 (100) 0.149 0.149 0.149 0.149 (100) 0.858 0.858 0.858 0.858 (61) class4 0.183 0.183 0.183 0.183 (100) 0.184 0.184 0.184 0.184 (100) 0.913 0.913 0.913 0.913 (43) class5 0.256 0.256 0.256 0.256 (100) 0.226 0.226 0.226 0.226 (100) 0.406 0.406 0.406 0.406 (100) class6 0.214 0.214 0.214 0.214 (100) 0.216 0.216 0.216 0.216 (100) 0.863 0.863 0.863 0.863 (71)
Table 22: Average parameters estimations for 100 replication in 6-class model, N=1000 (standard error in multinomial regression / sample standard error for 100 replication)
item 1 item 1item 1 item 1
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----6.029 6.029 6.029 6.029 ----1.350 1.350 1.350 1.350 (0.712 / 3.492) ----0.415 0.415 0.415 0.415 (0.753 / 4.672) ----11.734 11.734 11.734 11.734 (0.533 / 6.209) class 1 11.924 11.924 11.924 11.924 5.659 5.659 5.659 5.659 (0.828 / 4.682) 9.291 9.291 9.291 9.291 (0.603 / 7.259) 14.051 14.051 14.051 14.051 (0.414 / 6.747) class 2 5.927 5.927 5.927 1.459 5.927 1.459 1.459 1.459 (0.547 / 5.186) 1111.597 .597 .597 .597 (0.501 / 7.569) ----2.041 2.041 2.041 2.041 (NaN / 9.953) class 3 7.983 7.983 7.983 3.223 7.983 3.223 3.223 3.223 (0.571 / 3.695) 2.845 2.845 2.845 2.845 (0.525 / 11.486) ----5.018 5.018 5.018 5.018 (NaN / 7.408) class 4 6.883 6.883 6.883 2.915 6.883 2.915 2.915 2.915 (0.62 / 6.534) 2.536 2.536 2.536 2.536 (0.511 / 8.388) ----6.204 6.204 6.204 6.204 (NaN / 6.04) class 5 0.345 0.345 0.345 ----3.843 0.345 3.843 3.843 3.843 (0.599 / 4.203) ----6.766.766.763 6.763 3 3 (NaN / 7.542) 4.023 4.023 4.023 4.023 (0.531 / 7.237)
sex ----0.844 0.844 0.844 0.844 0.041 0.041 0.041 0.041 (0.277 / 0.401) ----0.017 0.017 0.017 0.017 (0.297 / 0.476) 0.079 0.079 0.079 0.079 (0.231 / 0.25) age 0.044 0.044 0.035 0.044 0.044 0.035 0.035 0.035 (0.018 / 0.02) 0.041 0.041 0.041 0.041 (0.019 / 0.023) 0.012 0.012 0.012 0.012 (0.015 / 0.016)
level 2 v.s. level 3
intercept 0.420 0.420 0.420 ----0.098 0.420 0.098 0.098 0.098 (0.637 / 3.172) 0.863 0.863 0.863 0.863 (0.666 / 4.14) ----2.396 2.396 2.396 2.396 (0.715 / 10.572) class 1 2.916 2.916 2.916 2.536 2.916 2.536 2.536 2.536 (0.833 / 4.525) 5.074 5.074 5.074 5.074 (0.476 / 6.726) 3.354 3.354 3.354 3.354 (0.534 / 10.36) class 2 ----0.126 0.126 0.126 0.126 0.594 0.594 0.594 0.594 (0.494 / 4.979) 0.332 0.332 0.332 0.332 (0.409 / 6.99) ----6.030 6.030 6.030 6.030 (0.373 / 15.412) class 3 1.537 1.537 1.537 2.386 1.537 2.386 2.386 2.386 (0.533 / 3.561) 1.924 1.924 1.924 1.924 (0.484 / 11.036) ----11.606 11.606 11.606 11.606 (0.216 / 10.8) class 4 2.563 2.563 2.563 3.101 2.563 3.101 3.101 3.101 (0.591 / 6.67) 2.093 2.093 2.093 2.093 (0.471 / 7.575) ----11.039 11.039 11.039 11.039 (0.255 / 14.127) class 5 ----4.833 4.833 4.833 4.833 ----3.281 3.281 3.281 3.281 (0.426 / 4.406) ----4.573 4.573 4.573 4.573 (0.5 / 4.285) ----1.356 1.356 1.356 1.356 (0.658 / 10.929) sex ----0.211 0.211 0.211 0.211 0.242 0.242 0.242 0.242 (0.254 / 0.392) 0.202 0.202 0.202 0.202 (0.276 / 0.43) 0.299 0.299 0.299 0.299 (0.237 / 0.273) age 0.018 0.018 0.018 0.018 0.018 0.018 0.018 0.018 (0.016 / 0.018) 0.025 0.025 0.025 0.025 (0.018 / 0.021) 0.006 0.006 0.006 0.006 (0.015 / 0.015)
item 2 item 2item 2 item 2
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----2.221 2.221 2.221 2.221 ----2.008 2.008 2.008 2.008 (0.771 / 5.309) ----2.634 2.634 2.634 2.634 (0.672 / 5.215) ----16.332 16.332 16.332 16.332 (0.259 / 4.974) class 1 6.873 6.873 6.873 7.532 6.873 7.532 7.532 7.532 (0.687 / 7.625) 8.602 8.602 8.602 8.602 (0.543 / 7.344) 18.353 18.353 18.353 18.353 (0.253 / 5.901) class 2 1.908 1.908 1.908 0.827 1.908 0.827 0.827 0.827 (0.669 / 7.332) 0.766 0.766 0.766 0.766 (0.498 / 8.021) ----5.787 5.787 5.787 5.787 (NaN / 4.308) class 3 5.070 5.070 5.070 3.128 5.070 3.128 3.128 3.128 (0.646 / 5.314) 3.895 3.895 3.895 3.895 (0.496 / 6.749) ----2.914 2.914 2.914 2.914 (NaN / 7.342) class 4 2.639 2.639 2.639 2.352 2.639 2.352 2.352 2.352 (0.675 / 6.556) 2.055 2.055 2.055 2.055 (0.441 / 8.23) ----3.939 3.939 3.939 3.939 (NaN / 5.43) class 5 ----7.304 7.304 7.304 7.304 ----3.709 3.709 3.709 3.709 (1.036 / 6.232) ----7.158 7.158 7.158 7.158 (0.434 / 5.833) 1.092 1.092 1.092 1.092 (0.076 / 4.923)
sex ----0.513 0.513 0.513 0.513 0.129 0.129 0.129 0.129 (0.249 / 0.243) 0.096 0.096 0.096 0.096 (0.25 / 0.271) 0.046 0.046 0.046 0.046 (0.192 / 0.194) age ----0.044 0.044 0.044 0.044 ----0.038 0.038 0.038 0.038 (0.016 / 0.017) ----0.042 0.042 0.042 0.042 (0.016 / 0.016) ----0.032 0.032 0.032 0.032 (0.012 / 0.013)
Table 22: (Continued)
level 2 v.s. level 3
intercept 0.521 0.521 0.521 0.521 ----0.665 0.665 0.665 0.665 (0.484 / 4.612) ----0.121 0.121 0.121 0.121 (0.495 / 3.301) ----14.460 14.460 14.460 14.460 (0.487 / 7.302) class 1 1.685 1.685 1.685 1.685 2.125 2.125 2.125 2.125 (0.429 / 4.665) 3.346 3.346 3.346 3.346 (0.457 / 5.542) 15.551 15.551 15.551 15.551 (0.423 / 7.481) class 2 ----0.428 0.428 0.428 0.809 0.428 0.809 0.809 0.809 (0.345 / 6.072) ----0.214 0.214 0.214 0.214 (0.345 / 6.264) ----7.7.7.7.503 503 503 503 (0.058 / 9.435) class 3 2.204 2.204 2.204 2.204 2.497 2.497 2.497 2.497 (0.341 / 4.588) 1.777 1.777 1.777 1.777 (0.346 / 3.815) ----4.110 4.110 4.110 4.110 (0.119 / 12.241) class 4 0.546 0.546 0.546 0.546 1.368 1.368 1.368 1.368 (0.363 / 5.041) 0.925 0.925 0.925 0.925 (0.354 / 5.278) ----5.993 5.993 5.993 5.993 (0.093 / 10.39) class 5 ----4.833 4.833 4.833 ----2.001 4.833 2.001 2.001 2.001 (0.496 / 5.127) ----3.038 3.038 3.038 3.038 (0.553 / 3.873) 7.875 7.875 7.875 7.875 (0.528 / 8.345)
sex ----0.274 0.274 0.274 0.103 0.274 0.103 0.103 0.103 (0.191 / 0.203) 0.070 0.070 0.070 0.070 (0.193 / 0.213) 0.094 0.094 0.094 0.094 (0.175 / 0.2) age ----0.008 0.008 0.008 ----0.006 0.008 0.006 0.006 0.006 (0.012 / 0.013) ----0.006 0.006 0.006 0.006 (0.012 / 0.015) ----0.006 0.006 0.006 0.006 (0.011 / 0.012)
item 3 item 3item 3 item 3
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----7.445 7.445 7.445 ----4.267 7.445 4.267 4.267 4.267 (0.683 / 7.031) ----6.275 6.275 6.275 6.275 (0.623 / 5.74) ----15.196 15.196 15.196 15.196 (0.375 / 5.66) class 1 8.520 8.520 8.520 8.520 6.414 6.414 6.414 6.414 (0.61 / 7.781) 7.516 7.516 7.516 7.516 (0.465 / 5.632) 15.660 15.660 15.660 15.660 (NaN / 7.94) class 2 2.959 2.959 2.959 2.959 ----0.495 0.495 0.495 0.495 (0.64 / 12.376) 2.130 2.130 2.130 2.130 (0.454 / 9.158) ----5.156 5.156 5.156 5.156 (NaN / 7.839) class 3 4.838 4.838 4.838 4.838 2.073 2.073 2.073 2.073 (0.565 / 7.372) 4.334 4.334 4.334 4.334 (0.504 / 6.554) ----1.426 1.426 1.426 1.426 (NaN / 9.861) class 4 7.931 7.931 7.931 7.931 4.478 4.478 4.478 4.478 (0.497 / 9.631) 3.845 3.845 3.845 3.845 (0.598 / 7.312) ----0.868 0.868 0.868 0.868 (NaN / 11.42) class 5 3.620 3.620 3.620 3.620 ----0.937 0.937 0.937 0.937 (0.814 / 7.222) 0.705 0.705 0.705 0.705 (0.682 / 6.616) 3.167 3.167 3.167 3.167 (0.284 / 8.308)
sex ----0.450 0.450 0.450 ----0.045 0.450 0.045 0.045 0.045 (0.245 / 0.287) ----0.048 0.048 0.048 0.048 (0.23 / 0.281) ----0.072 0.072 0.072 0.072 (0.186 / 0.185) age 0.007 0.007 0.007 0.007 0.003 0.003 0.003 0.003 (0.015 / 0.018) 0.001 0.001 0.001 0.001 (0.015 / 0.016) ----0.003 0.003 0.003 0.003 (0.012 / 0.013)
level 2 v.s. level 3
intercept ----2.650 2.650 2.650 ----1.705 2.650 1.705 1.705 1.705 (0.434 / 4.563) ----1.573 1.573 1.573 1.573 (0.476 / 2.675) ----13.615 13.615 13.615 13.615 (0.381 / 9.351) class 1 3.046 3.046 3.046 3.046 2.206 2.206 2.206 2.206 (0.447 / 5.462) 2.291 2.291 2.291 2.291 (0.391 / 2.653) 13.022 13.022 13.022 13.022 (NaN / 9.366) class 2 0.766 0.766 0.766 0.766 ----1.087 1.087 1.087 1.087 (NaN / 8.133) ----0.027 0.027 0.027 0.027 (0.425 / 3.721) ----3.081 3.081 3.081 3.081 (0.104 / 14.995) class 3 3.383 3.383 3.383 3.383 2.371 2.371 2.371 2.371 (0.295 / 4.12) 2.161 2.161 2.161 2.161 (0.359 / 3.131) 2.840 2.840 2.840 2.840 (0.261 / 15.501) class 4 3.271 3.271 3.271 3.271 1.246 1.246 1.246 1.246 (0.301 / 5.021) 1.314 1.314 1.314 1.314 (0.508 / 3.693) 3.606 3.606 3.606 3.606 (0.265 / 16.471) class 5 0.783 0.783 0.783 0.783 ----0.554 0.554 0.554 0.554 (0.33 / 4.42) ----0.435 0.435 0.435 0.435 (0.388 / 2.679) 10.427 10.427 10.427 10.427 (0.382 / 10.083) sex ----0.794 0.794 0.794 ----0.478 0.794 0.478 0.478 0.478 (0.168 / 0.167) ----0.496 0.496 0.496 0.496 (0.168 / 0.182) ----0.427 0.427 0.427 0.427 (0.153 / 0.153) age 0.019 0.019 0.019 0.019 0.012 0.012 0.012 0.012 (0.011 / 0.01) 0.011 0.011 0.011 0.011 (0.011 / 0.011) 0.007 0.007 0.007 0.007 (0.01 / 0.009)
Table 22: (Continued)
item 4 item 4item 4 item 4
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----6.883 6.883 6.883 ----1.018 6.883 1.018 1.018 1.018 (0.664 / 2.902) ----0.351 0.351 0.351 0.351 (0.677 / 4.27) ----14.773 14.773 14.773 14.773 (0.403 / 6.513) class 1 10.946 10.946 10.946 10.946 4.980 4.980 4.980 4.980 (0.615 / 3.237) 6.890 6.890 6.890 6.890 (0.771 / 5.578) 17.302 17.302 17.302 17.302 (0.313 / 7.112) class 2 7.782 7.782 7.782 7.782 1.768 1.768 1.768 1.768 (0.51 / 4.709) 1.865 1.865 1.865 1.865 (0.502 / 6.252) ----2.597 2.597 2.597 2.597 (NaN / 8.553) class 3 9.085 9.085 9.085 9.085 2.698 2.698 2.698 2.698 (0.592 / 3.736) 1.710 1.710 1.710 1.710 (0.518 / 5.186) ----5.185 5.185 5.185 5.185 (NaN / 7.701) class 4 11.649 11.649 11.649 11.649 2.769 2.769 2.769 2.769 (0.609 / 4.364) 2.508 2.508 2.508 2.508 (0.572 / 6.271) ----4.791 4.791 4.791 4.791 (NaN / 9.252) class 5 2.957 2.957 2.957 2.957 ----2.581 2.581 2.581 2.581 (0.545 / 3.182) ----4.056 4.056 4.056 4.056 (0.57 / 4.825) 7.666 7.666 7.666 7.666 (0.431 / 5.937)
sex ----1.883 1.883 1.883 ----0.846 1.883 0.846 0.846 0.846 (0.255 / 0.304) ----0.967 0.967 0.967 0.967 (0.265 / 0.328) ----0.567 0.567 0.567 0.567 (0.218 / 0.225) age 0.030 0.030 0.030 0.030 0.021 0.021 0.021 0.021 (0.016 / 0.016) 0.022 0.022 0.022 0.022 (0.017 / 0.018) 0.004 0.004 0.004 0.004 (0.014 / 0.016)
level 2 v.s. level 3
intercept ----0.0.0.261 0.261 261 261 0.224 0.224 0.224 0.224 (0.595 / 3.029) 0.629 0.629 0.629 0.629 (0.598 / 3.997) ----12.377 12.377 12.377 12.377 (0.428 / 11.687) class 1 1.698 1.698 1.698 1.698 1.826 1.826 1.826 1.826 (0.607 / 3.344) 3.416 3.416 3.416 3.416 (0.732 / 5.679) 13.211 13.211 13.211 13.211 (NaN / 11.715) class 2 1.665 1.665 1.665 1.665 1.546 1.546 1.546 1.546 (0.458 / 5.141) 1.553 1.553 1.553 1.553 (0.459 / 5.301) 4.561 4.561 4.561 4.561 (0.131 / 19.127) class 3 3.753 3.753 3.753 3.753 2.689 2.689 2.689 2.689 (0.537 / 3.485) 2.241 2.241 2.241 2.241 (0.475 / 4.993) ----6.065 6.065 6.065 6.065 (0.081 / 14.281) class 4 4.873 4.873 4.873 4.873 1.742 1.742 1.742 1.742 (0.576 / 4.291) 1.433 1.433 1.433 1.433 (0.5 / 5.438) ----4.001 4.001 4.001 4.001 (0.096 / 15.3) class 5 ----2.089 2.089 2.089 ----2.616 2.089 2.616 2.616 2.616 (0.409 / 3.572) ----3.551 3.551 3.551 3.551 (0.441 / 4.477) 8.364 8.364 8.364 8.364 (0.458 / 11.555)
sex ----0.783 0.783 0.783 ----0.144 0.783 0.144 0.144 0.144 (0.235 / 0.271) ----0.243 0.243 0.243 0.243 (0.244 / 0.305) ----0.075 0.075 0.075 0.075 (0.222 / 0.226) age 0.008 0.008 0.008 0.008 0.000 0.000 0.000 0.000 (0.015 / 0.014) 0.002 0.002 0.002 0.002 (0.015 / 0.016) ----0.006 0.006 0.006 0.006 (0.014 / 0.015)
item 5 item 5item 5 item 5
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept 0.199 0.199 0.199 0.199 ----0.146 0.146 0.146 0.146 (0.554 / 3.284) 1.120 1.120 1.120 1.120 (0.556 / 3.736) ----8.056 8.056 8.056 8.056 (0.422 / 9.196) class 1 3.300 3.300 3.300 3.300 3.172 3.172 3.172 3.172 (0.462 / 3.377) 2.625 2.625 2.625 2.625 (0.483 / 4.781) 10.676 10.676 10.676 10.676 (0.302 / 10.066) class 2 0.106 0.106 0.106 0.106 0.084 0.084 0.084 0.084 (0.456 / 5.887) 0.452 0.452 0.452 0.452 (0.413 / 5.994) ----4.471 4.471 4.471 4.471 (NaN / 14.093) class 3 1.796 1.796 1.796 1.796 1.6731.6731.6731.673 (0.663 / 4.025) 0.502 0.502 0.502 0.502 (0.396 / 4.967) ----3.616 3.616 3.616 3.616 (NaN / 12.054) class 4 0.370 0.370 0.370 0.370 ----0.057 0.057 0.057 0.057 (0.407 / 6.762) 0.217 0.217 0.217 0.217 (0.437 / 6.276) ----5.374 5.374 5.374 5.374 (NaN / 11.865) class 5 ----2.095 2.095 2.095 ----1.963 2.095 1.963 1.963 1.963 (0.435 / 3.643) ----3.409 3.409 3.409 3.409 (0.458 / 3.913) 5.647 5.647 5.647 5.647 (0.432 / 9.2)
sex ----0.767 0.767 0.767 ----0.503 0.767 0.503 0.503 0.503 (0.211 / 0.237) ----0.555 0.555 0.555 0.555 (0.21 / 0.241) ----0.441 0.441 0.441 0.441 (0.186 / 0.238) age 0.000 0.000 0.000 0.000 0.005 0.005 0.005 0.005 (0.013 / 0.013) 0.004 0.004 0.004 0.004 (0.013 / 0.011) ----0.006 0.006 0.006 0.006 (0.012 / 0.012)
Table 22: (Continued)
level 2 v.s. level 3
intercept 0.889 0.889 0.889 0.889 0.673 0.673 0.673 0.673 (0.537 / 4.004) 1.909 1.909 1.909 1.909 (0.522 / 4.74) 0.468 0.468 0.468 0.468 (0.447 / 15.952) class 1 0.479 0.479 0.479 0.479 0.784 0.784 0.784 0.784 (0.501 / 3.959) ----0.230 0.230 0.230 0.230 (0.514 / 5.11) 0.867 0.867 0.867 0.867 (0.317 / 15.836) class 2 ----0.379 0.379 0.379 ----0.530 0.379 0.530 0.530 0.530 (0.458 / 6.344) ----0.877 0.877 0.877 0.877 (0.379 / 6.786) ----8.928 8.928 8.928 8.928 (0.114 / 19.48) class 3 2.062 2.062 2.062 2.062 2.903 2.903 2.903 2.903 (0.574 / 6.413) 1.225 1.225 1.225 1.225 (0.378 / 6.41) ----3.861 3.861 3.861 3.861 (0.102 / 23.144) class 4 ----0.073 0.073 0.073 ----1.121 0.073 1.121 1.121 1.121 (0.42 / 7.132) ----0.640 0.640 0.640 0.640 (0.427 / 7.106) ----10.335 10.335 10.335 10.335 (0.041 / 19.255) class 5 ----1.232 1.232 1.232 ----1.346 1.232 1.346 1.346 1.346 (0.376 / 4.383) ----2.735 2.735 2.735 2.735 (0.36 / 4.973) ----1.514 1.514 1.514 1.514 (0.382 / 16.218) sex ----0.586 0.586 0.586 ----0.445 0.586 0.445 0.445 0.445 (0.202 / 0.203) ----0.486 0.486 0.486 0.486 (0.202 / 0.211) ----0.388 0.388 0.388 0.388 (0.191 / 0.211) age ----0.011 0.011 0.011 ----0.011 0.011 0.011 0.011 0.011 (0.013 / 0.013) ----0.010 0.010 0.010 0.010 (0.013 / 0.012) ----0.015 0.015 0.015 0.015 (0.012 / 0.013)
Table 23: Average parameters estimations for 100 replication in 6-class model, N=1000 (standard error in multinomial regression / sample standard error for 100 replication)
Class 1 vs. Class 6
Table 24: Average conditional Probability for 100 replication in 6-class model, N=1000
(sample standard deviance in parentheses)
Class 1 Class 1 Class 1 Class 1
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.955 0.955 0.955 0.955 0.879 0.879 0.879 0.879 (0.057) 0.910 0.910 0.910 0.910 (0.056) 0.566 0.566 0.566 0.566 (0.118) Level 2 0.044 0.044 0.044 0.044 0.111 0.111 0.111 0.111 (0.053) 0.084 0.084 0.084 0.084 (0.051) 0.340 0.340 0.340 0.340 (0.092) Level 3 0.001 0.001 0.001 0.001 0.010 0.010 0.010 0.010 (0.009) 0.005 0.005 0.005 0.005 (0.008) 0.095 0.095 0.095 0.095 (0.029)
item2
Level 1 0.727 0.727 0.727 0.727 0.710 0.710 0.710 0.710 (0.143) 0.733 0.733 0.733 0.733 (0.122) 0.335 0.335 0.335 0.335 (0.122) Level 2 0.235 0.235 0.235 0.235 0.232 0.232 0.232 0.232 (0.115) 0.222 0.222 0.222 0.222 (0.099) 0.446 0.446 0.446 0.446 (0.072) Level 3 0.038 0.038 0.038 0.038 0.059 0.059 0.059 0.059 (0.038) 0.045 0.045 0.045 0.045 (0.034) 0.219 0.219 0.219 0.219 (0.060)
item3
Level 1 0.509 0.509 0.509 0.509 0.485 0.485 0.485 0.485 (0.215) 0.504 0.504 0.504 0.504 (0.160) 0.258 0.258 0.258 0.258 (0.173) Level 2 0.317 0.317 0.317 0.317 0.343 0.343 0.343 0.343 (0.150) 0.340.340.340.345 5 5 5 (0.118) 0.359 0.359 0.359 0.359 (0.084) Level 3 0.175 0.175 0.175 0.175 0.172 0.172 0.172 0.172 (0.080) 0.151 0.151 0.151 0.151 (0.057) 0.384 0.384 0.384 0.384 (0.092)
item4
Level 1 0.927 0.927 0.927 0.927 0.858 0.858 0.858 0.858 (0.064) 0.893 0.893 0.893 0.893 (0.064) 0.524 0.524 0.524 0.524 (0.130) Level 2 0.057 0.057 0.057 0.057 0.120 0.120 0.120 0.120 (0.058) 0.094 0.094 0.094 0.094 (0.058) 0.359 0.359 0.359 0.359 (0.098) Level 3 0.016 0.016 0.016 0.016 0.022 0.022 0.022 0.022 (0.014) 0.014 0.014 0.014 0.014 (0.013) 0.118 0.118 0.118 0.118 (0.035)
item5
Level 1 0.883 0.883 0.883 0.883 0.829 0.829 0.829 0.829 (0.066) 0.850 0.850 0.850 0.850 (0.071) 0.532 0.532 0.532 0.532 (0.129) Level 2 0.078 0.078 0.078 0.078 0.119 0.119 0.119 0.119 (0.052) 0.103 0.103 0.103 0.103 (0.057) 0.309 0.309 0.309 0.309 (0.086) Level 3 0.039 0.039 0.039 0.039 0.052 0.052 0.052 0.052 (0.025) 0.047 0.047 0.047 0.047 (0.027) 0.159 0.159 0.159 0.159 (0.046)
Class 2 Class 2 Class 2 Class 2
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.436 0.436 0.436 0.436 0.395 0.395 0.395 0.395 (0.230) 0.376 0.376 0.376 0.376 (0.239) 0.058 0.058 0.058 0.058 (0.134) Level 2 0.385 0.385 0.385 0.385 0.430 0.430 0.430 0.430 (0.181) 0.441 0.441 0.441 0.441 (0.215) 0.246 0.246 0.246 0.246 (0.327) Level 3 0.178 0.178 0.178 0.178 0.176 0.176 0.176 0.176 (0.204) 0.183 0.183 0.183 0.183 (0.246) 0.696 0.696 0.696 0.696 (0.373)
item2
Level 1 0.071 0.071 0.071 0.071 0.144 0.144 0.144 0.144 (0.178) 0.140 0.140 0.140 0.140 (0.201) 0.0.0.0.000 000 000 000 (0.002) Level 2 0.396 0.396 0.396 0.396 0.461 0.461 0.461 0.461 (0.202) 0.413 0.413 0.413 0.413 (0.193) 0.033 0.033 0.033 0.033 (0.138) Level 3 0.533 0.533 0.533 0.533 0.395 0.395 0.395 0.395 (0.250) 0.447 0.447 0.447 0.447 (0.261) 0.967 0.967 0.967 0.967 (0.138)
Table 24 : (Continued)
item3
Level 1 0.009 0.009 0.009 0.009 0.123 0.123 0.123 0.123 (0.233) 0.129 0.129 0.129 0.129 (0.243) 0.015 0.015 0.015 0.015 (0.076) Level 2 0.155 0.155 0.155 0.155 0.248 0.248 0.248 0.248 (0.177) 0.230 0.230 0.230 0.230 (0.172) 0.120 0.120 0.120 0.120 (0.289) Level 3 0.836 0.836 0.836 0.836 0.629 0.629 0.629 0.629 (0.256) 0.641 0.641 0.641 0.641 (0.264) 0.865 0.865 0.865 0.865 (0.306)
item4
Level 1 0.356 0.356 0.356 0.356 0.346 0.346 0.346 0.346 (0.239) 0.357 0.357 0.357 0.357 (0.230) 0.036 0.036 0.036 0.036 (0.135) Level 2 0.500 0.500 0.500 0.500 0.459 0.459 0.459 0.459 (0.217) 0.458 0.458 0.458 0.458 (0.196) 0.310 0.310 0.310 0.310 (0.415) Level 3 0.143 0.143 0.143 0.143 0.195 0.195 0.195 0.195 (0.212) 0000.185 .185 .185 .185 (0.199) 0.655 0.655 0.655 0.655 (0.424)
item5
Level 1 0.333 0.333 0.333 0.333 0.376 0.376 0.376 0.376 (0.240) 0.386 0.386 0.386 0.386 (0.239) 0.065 0.065 0.065 0.065 (0.185) Level 2 0.306 0.306 0.306 0.306 0.325 0.325 0.325 0.325 (0.197) 0.300 0.300 0.300 0.300 (0.187) 0.265 0.265 0.265 0.265 (0.399) Level 3 0.361 0.361 0.361 0.361 0.299 0.299 0.299 0.299 (0.267) 0.314 0.314 0.314 0.314 (0.256) 0.670 0.670 0.670 0.670 (0.439)
Class 3 Class 3 Class 3 Class 3
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.606 0.606 0.606 0.606 0.484 0.484 0.484 0.484 (0.131) 0.496 0.496 0.496 0.496 (0.155) 0.051 0.051 0.051 0.051 (0.143) Level 2 0.362 0.362 0.362 0.362 0.465 0.465 0.465 0.465 (0.119) 0.423 0.423 0.423 0.423 (0.134) 0.133 0.133 0.133 0.133 (0.254) Level 3 0.032 0.032 0.032 0.032 0.051 0.051 0.051 0.051 (0.091) 0.081 0.081 0.081 0.081 (0.186) 0.816 0.816 0.816 0.816 (0.320)
item2
Level 1 0.217 0.217 0.217 0.217 0.151 0.151 0.151 0.151 (0.093) 0.184 0.184 0.184 0.184 (0.124) 0.027 0.027 0.027 0.027 (0.089) Level 2 0.714 0.714 0.714 0.714 0.696 0.696 0.696 0.696 (0.100) 0.655 0.655 0.655 0.655 (0.160) 0.082 0.082 0.082 0.082 (0.191) Level 3 0.069 0.069 0.069 0.069 0.152 0.152 0.152 0.152 (0.098) 0.161 0.161 0.161 0.161 (0.169) 0.890 0.890 0.890 0.890 (0.250)
item3
Level 1 0.020 0.020 0.020 0.020 0.071 0.071 0.071 0.071 (0.059) 0.083 0.083 0.083 0.083 (0.052) 0.051 0.051 0.051 0.051 (0.119) Level 2 0.703 0.703 0.703 0.703 0.584 0.584 0.584 0.584 (0.145) 0.570 0.570 0.570 0.570 (0.149) 0.256 0.256 0.256 0.256 (0.334) Level 3 0.277 0.277 0.277 0.277 0.346 0.346 0.346 0.346 (0.151) 0.347 0.347 0.347 0.347 (0.167) 0.693 0.693 0.693 0.693 (0.353)
item4
Level 1 0.239 0.239 0.239 0.239 0.304 0.304 0.304 0.304 (0.134) 0.314 0.314 0.314 0.314 (0.137) 0.036 0.036 0.036 0.036 (0.120) Level 2 0.735 0.735 0.735 0.735 0.629 0.629 0.629 0.629 (0.138) 0.592 0.592 0.592 0.592 (0.163) 0.093 0.093 0.093 0.093 (0.231) Level 3 0.0260.0260.0260.026 0.067 0.067 0.067 0.067 (0.107) 0.094 0.094 0.094 0.094 (0.176) 0.871 0.871 0.871 0.871 (0.297)
item5
Level 1 0.318 0.318 0.318 0.318 0.300 0.300 0.300 0.300 (0.138) 0.336 0.336 0.336 0.336 (0.135) 0.079 0.079 0.079 0.079 (0.185) Level 2 0.618 0.618 0.618 0.618 0.586 0.586 0.586 0.586 (0.165) 0.544 0.544 0.544 0.544 (0.165) 0.378 0.378 0.378 0.378 (0.440) Level 3 0.064 0.064 0.064 0.064 0.114 0.114 0.114 0.114 (0.085) 0.120 0.120 0.120 0.120 (0.140) 0.543 0.543 0.543 0.543 (0.470)
Table 24 : (Continued)
Class 4 Class 4 Class 4 Class 4
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.163 0.163 0.163 0.163 0.415 0.415 0.415 0.415 (0.277) 0.412 0.412 0.412 0.412 (0.288) 0.018 0.018 0.018 0.018 (0.113) Level 2 0.812 0.812 0.812 0.812 0.479 0.479 0.479 0.479 (0.262) 0.445 0.445 0.445 0.445 (0.273) 0.166 0.166 0.166 0.166 (0.300) Level 3 0.026 0.026 0.026 0.026 0.106 0.106 0.106 0.106 (0.206) 0.143 0.143 0.143 0.143 (0.286) 0.816 0.816 0.816 0.816 (0.315)
item2
Level 1 0.085 0.085 0.085 0.085 0.217 0.217 0.217 0.217 (0.245) 0.206 0.206 0.206 0.206 (0.266) 0.010 0.010 0.010 0.010 (0.100) Level 2 0.607 0.607 0.607 0.607 0.487 0.487 0.487 0.487 (0.195) 0.468 0.468 0.468 0.468 (0.226) 0.050 0.050 0.050 0.050 (0.168) Level 3 0.308 0.308 0.308 0.308 0.296 0.296 0.296 0.296 (0.215) 0.325 0.325 0.325 0.325 (0.266) 0.940 0.940 0.940 0.940 (0.193)
item3
Level 1 0.331 0.331 0.331 0.331 0.272 0.272 0.272 0.272 (0.325) 0.206 0.206 0.206 0.206 (0.244) 0.054 0.054 0.054 0.054 (0.161) Level 2 0.465 0.465 0.465 0.465 0.310 0.310 0.310 0.310 (0.187) 0.350.350.350.352 2 2 2 (0.192) 0.280 0.280 0.280 0.280 (0.366) Level 3 0.205 0.205 0.205 0.205 0.418 0.418 0.418 0.418 (0.249) 0.442 0.442 0.442 0.442 (0.254) 0.666 0.666 0.666 0.666 (0.405)
item4
Level 1 0.577 0.577 0.577 0.577 0.478 0.478 0.478 0.478 (0.243) 0.463 0.463 0.463 0.463 (0.265) 0.043 0.043 0.043 0.043 (0.186) Level 2 0.418 0.418 0.418 0.418 0.378 0.378 0.378 0.378 (0.191) 0.376 0.376 0.376 0.376 (0.215) 0.123 0.123 0.123 0.123 (0.290) Level 3 0.005 0.005 0.005 0.005 0.144 0.144 0.144 0.144 (0.190) 0.161 0.161 0.161 0.161 (0.252) 0.833 0.833 0.833 0.833 (0.328)
item5
Level 1 0.359 0.359 0.359 0.359 0.440 0.440 0.440 0.440 (0.268) 0.423 0.423 0.423 0.423 (0.267) 0.078 0.078 0.078 0.078 (0.251) Level 2 0.343 0.343 0.343 0.343 0.274 0.274 0.274 0.274 (0.190) 0.285 0.285 0.285 0.285 (0.194) 0.217 0.217 0.217 0.217 (0.400) Level 3 0.298 0.298 0.298 0.298 0.286 0.286 0.286 0.286 (0.287) 0.291 0.291 0.291 0.291 (0.301) 0.704 0.704 0.704 0.704 (0.447)
Class 5 Class 5 Class 5 Class 5
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.009 0.009 0.009 0.009 0.035 0.035 0.035 0.035 (0.046) 0.018 0.018 0.018 0.018 (0.014) 0.011 0.011 0.011 0.011 (0.009) Level 2 0.019 0.019 0.019 0.019 0.134 0.134 0.134 0.134 (0.075) 0.093 0.093 0.093 0.093 (0.053) 0.055 0.055 0.055 0.055 (0.029) Level 3 0.972 0.972 0.972 0.972 0.831 0.831 0.831 0.831 (0.099) 0.889 0.889 0.889 0.889 (0.062) 0.934 0.934 0.934 0.934 (0.031)
item2
Level 1 0.000 0.000 0.000 0.000 0.008 0.008 0.008 0.008 (0.027) 0.003 0.003 0.003 0.003 (0.004) 0.0.0.0.001 001 001 001 (0.002) Level 2 0.009 0.009 0.009 0.009 0.087 0.087 0.087 0.087 (0.046) 0.067 0.067 0.067 0.067 (0.036) 0.015 0.015 0.015 0.015 (0.013) Level 3 0.991 0.991 0.991 0.991 0.905 0.905 0.905 0.905 (0.063) 0.931 0.931 0.931 0.931 (0.037) 0.984 0.984 0.984 0.984 (0.013)
Table 24 : (Continued)
item3
Level 1 0.018 0.018 0.018 0.018 0.013 0.013 0.013 0.013 (0.009) 0.014 0.014 0.014 0.014 (0.010) 0.007 0.007 0.007 0.007 (0.010) Level 2 0.156 0.156 0.156 0.156 0.130 0.130 0.130 0.130 (0.040) 0.135 0.135 0.135 0.135 (0.029) 0.065 0.065 0.065 0.065 (0.034) Level 3 0.826 0.826 0.826 0.826 0.858 0.858 0.858 0.858 (0.044) 0.851 0.851 0.851 0.851 (0.032) 0.929 0.929 0.929 0.929 (0.038)
item4
Level 1 0.018 0.018 0.018 0.018 0.051 0.051 0.051 0.051 (0.040) 0.036 0.036 0.036 0.036 (0.022) 0.013 0.013 0.013 0.013 (0.011) Level 2 0.074 0.074 0.074 0.074 0.111 0.111 0.111 0.111 (0.053) 0.087 0.087 0.087 0.087 (0.047) 0.033 0.033 0.033 0.033 (0.023) Level 3 0.908 0.908 0.908 0.908 0.838 0.838 0.838 0.838 (0.079) 0000.877 .877 .877 .877 (0.062) 0.955 0.955 0.955 0.955 (0.027)
item5
Level 1 0.070 0.070 0.070 0.070 0.092 0.092 0.092 0.092 (0.050) 0.086 0.086 0.086 0.086 (0.040) 0.056 0.056 0.056 0.056 (0.026) Level 2 0.247 0.247 0.247 0.247 0.235 0.235 0.235 0.235 (0.084) 0.221 0.221 0.221 0.221 (0.076) 0.170 0.170 0.170 0.170 (0.072) Level 3 0.683 0.683 0.683 0.683 0.673 0.673 0.673 0.673 (0.115) 0.694 0.694 0.694 0.694 (0.104) 0.773 0.773 0.773 0.773 (0.086)
Class 6 Class 6 Class 6 Class 6
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.002 0.002 0.002 0.002 0.248 0.248 0.248 0.248 (0.231) 0.236 0.236 0.236 0.236 (0.220) 0.024 0.024 0.024 0.024 (0.068) Level 2 0.709 0.709 0.709 0.709 0.465 0.465 0.465 0.465 (0.205) 0.508 0.508 0.508 0.508 (0.232) 0.406 0.406 0.406 0.406 (0.345) Level 3 0.289 0.289 0.289 0.289 0.288 0.288 0.288 0.288 (0.253) 0.256 0.256 0.256 0.256 (0.269) 0.569 0.569 0.569 0.569 (0.351)
item2
Level 1 0.009 0.009 0.009 0.009 0.109 0.109 0.109 0.109 (0.225) 0.098 0.098 0.098 0.098 (0.181) 0.001 0.001 0.001 0.001 (0.014) Level 2 0.528 0.528 0.528 0.528 0.405 0.405 0.405 0.405 (0.206) 0.437 0.437 0.437 0.437 (0.189) 0.069 0.069 0.069 0.069 (0.165) Level 3 0.463 0.463 0.463 0.463 0.487 0.487 0.487 0.487 (0.250) 0.465 0.465 0.465 0.465 (0.240) 0.929 0.929 0.929 0.929 (0.166)
item3
Level 1 0.001 0.001 0.001 0.001 0.098 0.098 0.098 0.098 (0.232) 0.071 0.071 0.071 0.071 (0.185) 0.010 0.010 0.010 0.010 (0.061) Level 2 0.079 0.079 0.079 0.079 0.209 0.209 0.209 0.209 (0.158) 0.206 0.206 0.206 0.206 (0.164) 0.055 0.055 0.055 0.055 (0.183) Level 3 0.920 0.920 0.920 0.920 0.692 0.692 0.692 0.692 (0.244) 0.723 0.723 0.723 0.723 (0.239) 0.936 0.936 0.936 0.936 (0.209)
item4
Level 1 0.001 0.001 0.001 0.001 0.245 0.245 0.245 0.245 (0.218) 0.221 0.221 0.221 0.221 (0.213) 0.013 0.013 0.013 0.013 (0.071) Level 2 0.397 0.397 0.397 0.397 0.390 0.390 0.390 0.390 (0.191) 0.403 0.403 0.403 0.403 (0.224) 0.129 0.129 0.129 0.129 (0.318) Level 3 0.6020.6020.6020.602 0.364 0.364 0.364 0.364 (0.249) 0.376 0.376 0.376 0.376 (0.281) 0.858 0.858 0.858 0.858 (0.336)
item5
Level 1 0.271 0.271 0.271 0.271 0.322 0.322 0.322 0.322 (0.194) 0.306 0.306 0.306 0.306 (0.185) 0.094 0.094 0.094 0.094 (0.242) Level 2 0.403 0.403 0.403 0.403 0.386 0.386 0.386 0.386 (0.198) 0.423 0.423 0.423 0.423 (0.200) 0.484 0.484 0.484 0.484 (0.468) Level 3 0.326 0.326 0.326 0.326 0.292 0.292 0.292 0.292 (0.244) 0.271 0.271 0.271 0.271 (0.236) 0.422 0.422 0.422 0.422 (0.462)
Table 25: Average Latent Prevalences for 100 replication in 6-class model, N=1000 (sample standard deviance in parentheses)
TRUE K_Corr K_Cova H_Cova
class1 0.269 0.269 0.269 0.269 0.253 0.253 0.253 0.253 (0.074) 0.237 0.237 0.237 0.237 (0.080) 0.791 0.791 0.791 0.791 (0.205) class2 0.137 0.137 0.137 0.137 0.114 0.114 0.114 0.114 (0.046) 0.128 0.128 0.128 0.128 (0.064) 0.007 0.007 0.007 0.007 (0.007) class3 0.196 0.196 0.196 0.196 0.208 0.208 0.208 0.208 (0.064) 0.220 0.220 0.220 0.220 (0.080) 0.061 0.061 0.061 0.061 (0.201) class4 0.118 0.118 0.118 0.118 0.117 0.117 0.117 0.117 (0.060) 0.121 0.121 0.121 0.121 (0.073) 0.00.00.00.004 04 04 04 (0.003) class5 0.158 0.158 0.158 0.158 0.189 0.189 0.189 0.189 (0.054) 0.174 0.174 0.174 0.174 (0.046) 0.129 0.129 0.129 0.129 (0.023) class6 0.123 0.123 0.123 0.123 0.120 0.120 0.120 0.120 (0.046) 0.120 0.120 0.120 0.120 (0.056) 0.008 0.008 0.008 0.008 (0.006)
Table 26: Average Correlation Coefficients for 100 replication in 6-class model, N=1000 (total number of not NA values in parentheses)
K_Corr K_Cova H_Cova
class1 0.098 0.098 0.098 0.098 (100) 0.114 0.114 0.114 0.114 (100) 0.201 0.201 0.201 0.201 (99) class2 0.124 0.124 0.124 0.124 (100) 0.123 0.123 0.123 0.123 (100) 0.806 0.806 0.806 0.806 (75) class3 0.096 0.096 0.096 0.096 (100) 0.097 0.097 0.097 0.097 (100) 0.770 0.770 0.770 0.770 (59) class4 0.119 0.119 0.119 0.119 (100) 0.121 0.121 0.121 0.121 (100) 0.909 0.909 0.909 0.909 (41) class5 0.194 0.194 0.194 0.194 (100) 0.170 0.170 0.170 0.170 (100) 0.203 0.203 0.203 0.203 (100) class6 0.148 0.148 0.148 0.148 (100) 0.130 0.130 0.130 0.130 (100) 0.733 0.733 0.733 0.733 (72)
Table 27: Average parameters estimations for 100 replication in 2-class model, N=150 (standard error in multinomial regression / sample standard error for 100 replication)
item 1 item 1item 1 item 1
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----3.743 3.743 3.743 ----2.311 3.743 2.311 2.311 2.311 (1.31 / 1.699) ----3.144 3.144 3.144 3.144 (1.56 / 2.493) ----8.656 8.656 8.656 8.656 (1.518 / 3.18) class 1 6.790 6.790 6.790 6.790 5.153 5.153 5.153 5.153 (1.123 / 3.005) 6.753 6.753 6.753 6.753 (1.119 / 3.854) 9.142 9.142 9.142 9.142 (1.471 / 2.639)
sex 0.391 0.391 0.391 0.391 0.347 0.347 0.347 0.347 (0.557 / 0.607) 0.438 0.438 0.438 0.438 (0.59 / 0.587) 0.318 0.318 0.318 0.318 (0.462 / 0.501) age 0.051 0.051 0.051 0.051 0.025 0.025 0.025 0.025 (0.034 / 0.034) 0.025 0.025 0.025 0.025 (0.036 / 0.037) 0.012 0.012 0.012 0.012 (0.027 / 0.029)
level 2 v.s. level 3
intercept ----0.866 0.866 0.866 ----0.477 0.866 0.477 0.477 0.477 (1.126 / 1.117) ----0.915 0.915 0.915 0.915 (1.18 / 1.819) ----6.543 6.543 6.543 6.543 (1.795 / 3.919) class 1 3.962 3.962 3.962 3.962 2.879 2.879 2.879 2.879 (1.063 / 2.845) 4.161 4.161 4.161 4.161 (0.847 / 3.717) 6.875 6.875 6.875 6.875 (1.682 / 3.868) sex 0.501 0.501 0.501 0.501 0.465 0.465 0.465 0.465 (0.499 / 0.491) 0.535 0.535 0.535 0.535 (0.525 / 0.508) 0.475 0.475 0.475 0.475 (0.495 / 0.537) age 0.012 0.012 0.012 0.012 0.003 0.003 0.003 0.003 (0.031 / 0.028) 0.005 0.005 0.005 0.005 (0.032 / 0.031) ----0.003 0.003 0.003 0.003 (0.029 / 0.026)
item 2 item 2item 2 item 2
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----3.986 3.986 3.986 ----3.624 3.986 3.624 3.624 3.624 (1.853 / 4.279) ----5.861 5.861 5.861 5.861 (3.782 / 4.607) ----7.697 7.697 7.697 7.697 (2.202 / 2.056) class 1 6.047 6.047 6.047 6.047 5.916 5.916 5.916 5.916 (1.601 / 4.183) 8.354 8.354 8.354 8.354 (3.688 / 4.391) 8.314 8.314 8.314 8.314 (2.184 / 1.597)
sex 0.311 0.311 0.311 0.311 0.325 0.325 0.325 0.325 (0.548 / 0.584) 0.358 0.358 0.358 0.358 (0.571 / 0.625) 0.234 0.234 0.234 0.234 (0.45 / 0.49) age ----0.014 0.014 0.014 ----0.029 0.014 0.029 0.029 0.029 (0.033 / 0.036) ----0.033 0.033 0.033 0.033 (0.034 / 0.035) ----0.024 0.024 0.024 0.024 (0.027 / 0.028)
level 2 v.s. level 3
intercept ----0.923 0.923 0.923 ----0.706 0.923 0.706 0.706 0.706 (1.001 / 1.628) ----0.758 0.758 0.758 0.758 (1.047 / 1.113) ----7.976 7.976 7.976 7.976 (0.961 / 3.775) class 1 2.586 2.586 2.586 2.586 2.332 2.332 2.332 2.332 (0.602 / 1.479) 2.655 2.655 2.655 2.655 (0.713 / 1.141) 8.251 8.251 8.251 8.251 (0.913 / 3.689) sex 0.312 0.312 0.312 0.312 0.333 0.333 0.333 0.333 (0.45 / 0.5) 0.375 0.375 0.375 0.375 (0.468 / 0.553) 0.287 0.287 0.287 0.287 (0.404 / 0.46) age ----0.002 0.002 0.002 ----0.009 0.002 0.009 0.009 0.009 (0.027 / 0.028) ----0.012 0.012 0.012 0.012 (0.028 / 0.027) ----0.006 0.006 0.006 0.006 (0.024 / 0.025)
item 3 item 3item 3 item 3
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----4.839 4.839 4.839 ----5.092 4.839 5.092 5.092 5.092 (3.648 / 3.836) ----7.544 7.544 7.544 7.544 (5.633 / 4.615) ----9.040 9.040 9.040 9.040 (5.332 / 1.977) class 1 4.373 4.373 4.373 4.373 5.380 5.380 5.380 5.380 (3.15 / 4.303) 7.505 7.505 7.505 7.505 (5.33 / 4.309) 7.959 7.959 7.959 7.959 (5.706 / 1.355)
sex ----0.053 0.053 0.053 ----0.145 0.053 0.145 0.145 0.145 (0.554 / 0.538) ----0.088 0.088 0.088 0.088 (0.541 / 0.543) 0.009 0.009 0.009 0.009 (0.47 / 0.45) age 0.024 0.024 0.024 0.024 0.013 0.013 0.013 0.013 (0.033 / 0.036) 0.014 0.014 0.014 0.014 (0.032 / 0.037) 0.009 0.009 0.009 0.009 (0.028 / 0.031)
Table 27: (Continued)
level 2 v.s. level 3
intercept ----1.780 1.780 1.780 ----1.701 1.780 1.701 1.701 1.701 (0.963 / 1.892) ----1.752 1.752 1.752 1.752 (0.989 / 1.022) ----8.078 8.078 8.078 8.078 (5.289 / 2.635) class 1 1.990 1.990 1.990 1.990 1.880 1.880 1.880 1.880 (0.44 / 1.922) 1.963 1.963 1.963 1.963 (0.462 / 0.977) 7.638 7.638 7.638 7.638 (5.262 / 2.769) sex ----0.442 0.442 0.442 ----0.432 0.442 0.432 0.432 0.432 (0.421 / 0.426) ----0.419 0.419 0.419 0.419 (0.424 / 0.447) ----0.353 0.353 0.353 0.353 (0.384 / 0.371) age 0.019 0.019 0.019 0.019 0.013 0.013 0.013 0.013 (0.025 / 0.025) 0.013 0.013 0.013 0.013 (0.025 / 0.025) 0.009 0.009 0.009 0.009 (0.023 / 0.022)
item itemitem item 4 4 4 4
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----2.893 2.893 2.893 ----1.920 2.893 1.920 1.920 1.920 (1.265 / 2.065) ----2.417 2.417 2.417 2.417 (1.358 / 2.062) ----7.992 7.992 7.992 7.992 (1.16 / 3.369) class 1 5.733 5.733 5.733 5.733 5.273 5.273 5.273 5.273 (1.285 / 3.45) 6.018 6.018 6.018 6.018 (1.278 / 3.56) 8.597 8.597 8.597 8.597 (1.111 / 3.245)
sex ----0.462 0.462 0.462 ----0.391 0.462 0.391 0.391 0.391 (0.545 / 0.602) ----0.375 0.375 0.375 0.375 (0.569 / 0.649) ----0.180 0.180 0.180 0.180 (0.448 / 0.518) age 0.042 0.042 0.042 0.042 0.019 0.019 0.019 0.019 (0.033 / 0.036) 0.022 0.022 0.022 0.022 (0.035 / 0.041) 0.009 0.009 0.009 0.009 (0.027 / 0.03)
level 2 v.s. level 3
intercept ----0.727 0.727 0.727 ----0.260 0.727 0.260 0.260 0.260 (1.104 / 1.783) ----0.549 0.549 0.549 0.549 (1.163 / 1.778) ----6.510 6.510 6.510 6.510 (2.002 / 4.212) class 1 3.3.3.3.630 630 630 3.431 630 3.431 3.431 3.431 (1.257 / 3.34) 4.134 4.134 4.134 4.134 (1.174 / 3.586) 7.282 7.282 7.282 7.282 (1.924 / 4.165) sex 0.105 0.105 0.105 0.105 0.206 0.206 0.206 0.206 (0.494 / 0.52) 0.207 0.207 0.207 0.207 (0.513 / 0.537) 0.320 0.320 0.320 0.320 (0.471 / 0.548) age 0.007 0.007 0.007 0.007 ----0.009 0.009 0.009 0.009 (0.03 / 0.033) ----0.006 0.006 0.006 0.006 (0.032 / 0.037) ----0.015 0.015 0.015 0.015 (0.028 / 0.031)
item 5 item 5item 5 item 5
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----1.218 1.218 1.218 ----1.255 1.218 1.255 1.255 1.255 (1.158 / 2.374) ----1.211 1.211 1.211 1.211 (1.125 / 1.698) ----7.060 7.060 7.060 7.060 (1.495 / 4.058) class 1 2.900 2.900 2.900 2.900 3.006 3.006 3.006 3.006 (0.633 / 1.89) 3.051 3.051 3.051 3.051 (0.555 / 1.591) 7.925 7.925 7.925 7.925 (1.417 / 3.832) sex ----0.268 0.268 0.268 ----0.307 0.268 0.307 0.307 0.307 (0.488 / 0.5) ----0.301 0.301 0.301 0.301 (0.484 / 0.487) ----0.238 0.238 0.238 0.238 (0.437 / 0.485) age 0.011 0.011 0.011 0.011 0.007 0.007 0.007 0.007 (0.03 / 0.033) 0.006 0.006 0.006 0.006 (0.029 / 0.03) 0.001 0.001 0.001 0.001 (0.026 / 0.024)
level 2 v.s. level 3
intercept 0.373 0.373 0.373 0.373 0.291 0.291 0.291 0.291 (1.217 / 2.464) 0.332 0.332 0.332 0.332 (1.072 / 1.102) ----5.144 5.144 5.144 5.144 (2.757 / 4.114) class 1 1.223 1.223 1.223 1.223 1.311 1.311 1.311 1.311 (0.73 / 2.243) 1.455 1.455 1.455 1.455 (0.518 / 1.245) 6.207 6.207 6.207 6.207 (2.639 / 4.317) sex ----0.292 0.292 0.292 ----0.308 0.292 0.308 0.308 0.308 (0.475 / 0.523) ----0.309 0.309 0.309 0.309 (0.472 / 0.517) ----0.289 0.289 0.289 0.289 (0.468 / 0.57) age ----0.013 0.013 0.013 ----0.014 0.013 0.014 0.014 0.014 (0.029 / 0.032) ----0.015 0.015 0.015 0.015 (0.029 / 0.03) ----0.019 0.019 0.019 0.019 (0.028 / 0.027)
Table 28: Average parameters estimations for 100 replication in 2-class model, N=150 (standard error in multinomial regression / sample standard error for 100 replication)
Class 1 vs. Class 2 Class 1 vs. Class 2 Class 1 vs. Class 2 Class 1 vs. Class 2
TRUE K_Corr K_Cova H_Cova
intercept ----0.935 0.935 0.935 0.935 ----0.596 0.596 0.596 0.596 (0.345 / 0.749) ----0.439 0.439 0.439 0.439 (0.337 / 0.635) 5.091 5.091 5.091 5.091 (4.067 / 12.64) occup 0.441 0.441 0.294 0.441 0.441 0.294 0.294 0.294 (0.399 / 0.452) 0.306 0.306 0.306 0.306 (0.407 / 0.438) 2.366 2.366 2.366 2.366 (22.899 / 4.745) dprime 0.414 0.414 0.414 0.282 0.414 0.282 0.282 0.282 (0.109 / 0.13) 0.309 0.309 0.309 0.309 (0.108 / 0.12) 0.648 0.648 0.648 0.648 (1.301 / 6.422)
Table 29: Average conditional Probability for 100 replication in 2-class model, N=150
(sample standard deviance in parentheses)
Class 1 Class 1 Class 1 Class 1
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.765 0.765 0.765 0.765 0.706 0.706 0.706 0.706 (0.086) 0.696 0.696 0.696 0.696 (0.087) 0.489 0.489 0.489 0.489 (0.066) Level 2 0.229 0.229 0.229 0.229 0.245 0.245 0.245 0.245 (0.060) 0.266 0.266 0.266 0.266 (0.070) 0.314 0.314 0.314 0.314 (0.051) Level 3 0.005 0.005 0.005 0.005 0.049 0.049 0.049 0.049 (0.052) 0.038 0.038 0.038 0.038 (0.038) 0.197 0.197 0.197 0.197 (0.043)
item2
Level 1 0.457 0.457 0.457 0.457 0.421 0.421 0.421 0.421 (0.094) 0.418 0.418 0.418 0.418 (0.075) 0.278 0.278 0.278 0.278 (0.082) Level 2 0.464 0.464 0.464 0.464 0.457 0.457 0.457 0.457 (0.072) 0.465 0.465 0.465 0.465 (0.053) 0.405 0.405 0.405 0.405 (0.057) Level 3 0.079 0.079 0.079 0.079 0.122 0.122 0.122 0.122 (0.073) 0.117 0.117 0.117 0.117 (0.065) 0.317 0.317 0.317 0.317 (0.053)
item3
Level 1 0.325 0.325 0.325 0.325 0.324 0.324 0.324 0.324 (0.156) 0.311 0.311 0.311 0.311 (0.114) 0.203 0.203 0.203 0.203 (0.087) Level 2 0.441 0.441 0.441 0.441 0.418 0.418 0.418 0.418 (0.112) 0.420.420.420.423 3 3 3 (0.084) 0.349 0.349 0.349 0.349 (0.054) Level 3 0.234 0.234 0.234 0.234 0.258 0.258 0.258 0.258 (0.094) 0.266 0.266 0.266 0.266 (0.082) 0.448 0.448 0.448 0.448 (0.063)
item4
Level 1 0.683 0.683 0.683 0.683 0.626 0.626 0.626 0.626 (0.105) 0.620 0.620 0.620 0.620 (0.077) 0.443 0.443 0.443 0.443 (0.068) Level 2 0.304 0.304 0.304 0.304 0.321 0.321 0.321 0.321 (0.094) 0.331 0.331 0.331 0.331 (0.057) 0.339 0.339 0.339 0.339 (0.050) Level 3 0.012 0.012 0.012 0.012 0.053 0.053 0.053 0.053 (0.055) 0.049 0.049 0.049 0.049 (0.050) 0.218 0.218 0.218 0.218 (0.041)
item5
Level 1 0.647 0.647 0.647 0.647 0.617 0.617 0.617 0.617 (0.069) 0.601 0.601 0.601 0.601 (0.074) 0.454 0.454 0.454 0.454 (0.067) Level 2 0.258 0.258 0.258 0.258 0.269 0.269 0.269 0.269 (0.064) 0.282 0.282 0.282 0.282 (0.057) 0.312 0.312 0.312 0.312 (0.051) Level 3 0.095 0.095 0.095 0.095 0.114 0.114 0.114 0.114 (0.051) 0.118 0.118 0.118 0.118 (0.052) 0.234 0.234 0.234 0.234 (0.045)
Table 29: (Continued)
Class 2 Class 2 Class 2 Class 2
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.082 0.082 0.082 0.082 0.156 0.156 0.156 0.156 (0.116) 0.114 0.114 0.114 0.114 (0.086) 0.021 0.021 0.021 0.021 (0.070) Level 2 0.415 0.415 0.415 0.415 0.390 0.390 0.390 0.390 (0.090) 0.362 0.362 0.362 0.362 (0.093) 0.094 0.094 0.094 0.094 (0.193) Level 3 0.504 0.504 0.504 0.504 0.455 0.455 0.455 0.455 (0.110) 0.524 0.524 0.524 0.524 (0.126) 0.885 0.885 0.885 0.885 (0.224)
item2
Level 1 0.009 0.009 0.009 0.009 0.057 0.057 0.057 0.057 (0.070) 0000.026 .026 .026 .026 (0.051) 0.006 0.006 0.006 0.006 (0.038) Level 2 0.304 0.304 0.304 0.304 0.312 0.312 0.312 0.312 (0.080) 0.282 0.282 0.282 0.282 (0.076) 0.056 0.056 0.056 0.056 (0.167) Level 3 0.687 0.687 0.687 0.687 0.631 0.631 0.631 0.631 (0.120) 0.692 0.692 0.692 0.692 (0.107) 0.937 0.937 0.937 0.937 (0.177)
item3
Level 1 0.014 0.014 0.014 0.014 0.041 0.041 0.041 0.041 (0.047) 0.018 0.018 0.018 0.018 (0.024) 0.001 0.001 0.001 0.001 (0.010) Level 2 0.202 0.202 0.202 0.202 0.214 0.214 0.214 0.214 (0.086) 0.196 0.196 0.196 0.196 (0.080) 0.028 0.028 0.028 0.028 (0.099) Level 3 0.784 0.784 0.784 0.784 0.745 0.745 0.745 0.745 (0.109) 0.786 0.786 0.786 0.786 (0.091) 0.971 0.971 0.971 0.971 (0.102)
item4
Level 1 0.098 0.098 0.098 0.098 0.156 0.156 0.156 0.156 (0.102) 0.117 0.117 0.117 0.117 (0.076) 0.030 0.030 0.030 0.030 (0.116) Level 2 0.356 0.356 0.356 0.356 0.350 0.350 0.350 0.350 (0.073) 0.326 0.326 0.326 0.326 (0.087) 0.082 0.082 0.082 0.082 (0.204) Level 3 0.547 0.547 0.547 0.547 0.494 0.494 0.494 0.494 (0.116) 0.557 0.557 0.557 0.557 (0.124) 0.888 0.888 0.888 0.888 (0.250)
item5
Level 1 0.173 0.173 0.173 0.173 0.187 0.187 0.187 0.187 (0.097) 0.178 0.178 0.178 0.178 (0.081) 0.051 0.051 0.051 0.051 (0.118) Level 2 0.368 0.368 0.368 0.368 0.361 0.361 0.361 0.361 (0.103) 0.345 0.345 0.345 0.345 (0.073) 0.112 0.112 0.112 0.112 (0.216) Level 3 0.459 0.459 0.459 0.459 0.451 0.451 0.451 0.451 (0.127) 0.477 0.477 0.477 0.477 (0.101) 0.837 0.837 0.837 0.837 (0.283)
Table 30: Average Latent Prevalences for 100 replication in 2-class model, N=150 (sample standard deviance in parentheses)
TRUE K_Corr K_Cova H_Cova
class1 0.560.56 0.560.56 0.5520.5520.5520.552 (0.139) 0.60.60.60.6 (0.114) 0.9510.951 0.9510.951(0.100) class2 0.440.44 0.440.44 0.4480.4480.4480.448 (0.139) 0.40.40.40.4 (0.114) 0.04910.0491 0.04910.0491(0.100)
Table 31: Average Correlation Coefficients for 100 replication in 2-class model, N=150 (total number of not NA values in parentheses)
K_Corr K_Cova H_Cova
class1 0.143 0.143 0.143 0.143 (100) 0.148 0.148 0.148 0.148 (100) 0.289 0.289 0.289 0.289 (100) class2 0.234 0.234 0.234 0.234 (100) 0.190 0.190 0.190 0.190 (100) 0.790 0.790 0.790 0.790 (77)
Table 32: Average parameters estimations for 100 replication in 2-class model, N=700 (standard error in multinomial regression / sample standard error for 100 replication)
item 1 item 1item 1 item 1
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----3.743 3.743 3.743 ----2.596 3.743 2.596 2.596 2.596 (0.62 / 1.675) ----2.905 2.905 2.905 2.905 (0.653 / 0.648) ----6.079 6.079 6.079 6.079 (0.808 / 3.425) class 1 6.790 6.790 6.790 6.790 5.113 5.113 5.113 5.113 (0.64 / 1.702) 5.576 5.576 5.576 5.576 (0.463 / 1.361) 6.356 6.356 6.356 6.356 (0.748 / 3.424) sex 0.391 0.391 0.391 0.391 0.483 0.483 0.483 0.483 (0.261 / 0.272) 0.483 0.483 0.483 0.483 (0.272 / 0.278) 0.397 0.397 0.397 0.397 (0.203 / 0.221) age 0.051 0.051 0.051 0.051 0.023 0.023 0.023 0.023 (0.017 / 0.017) 0.027 0.027 0.027 0.027 (0.017 / 0.017) 0.010 0.010 0.010 0.010 (0.013 / 0.014)
level 2 v.s. level 3
intercept ----0.866 0.866 0.866 ----0.518 0.866 0.518 0.518 0.518 (0.507 / 1.579) ----0.537 0.537 0.537 0.537 (0.519 / 0.56) ----4.249 4.249 4.249 4.249 (0.53 / 4.284) class 1 3.962 3.962 3.962 3.962 2.780 2.780 2.780 2.780 (0.609 / 1.659) 3.015 3.015 3.015 3.015 (0.43 / 1.273) 4.695 4.695 4.695 4.695 (0.425 / 4.273)
sex 0.501 0.501 0.501 0.501 0.568 0.568 0.568 0.568 (0.226 / 0.217) 0.572 0.572 0.572 0.572 (0.23 / 0.229) 0.542 0.542 0.542 0.542 (0.216 / 0.22) age 0.012 0.012 0.012 0.012 ----0.002 0.002 0.002 0.002 (0.014 / 0.016) 0.000 0.000 0.000 0.000 (0.015 / 0.017) ----0.009 0.009 0.009 0.009 (0.014 / 0.016)
item 2 item 2item 2 item 2
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----3.986 3.986 3.986 ----3.193 3.986 3.193 3.193 3.193 (0.784 / 2.404) ----4.007 4.007 4.007 4.007 (0.853 / 2.45) ----9.006 9.006 9.006 9.006 (0.526 / 0.993) class 1 6.047 6.047 6.047 6.047 5.347 5.347 5.347 5.347 (0.607 / 2.411) 6.260 6.260 6.260 6.260 (0.664 / 2.353) 9.243 9.243 9.243 9.243 (0.525 / 1.003) sex 0.311 0.311 0.311 0.311 0.361 0.361 0.361 0.361 (0.253 / 0.262) 0.364 0.364 0.364 0.364 (0.265 / 0.275) 0.283 0.283 0.283 0.283 (0.203 / 0.209) age ----0.014 0.014 0.014 ----0.027 0.014 0.027 0.027 0.027 (0.016 / 0.017) ----0.027 0.027 0.027 0.027 (0.017 / 0.018) ----0.018 0.018 0.018 0.018 (0.013 / 0.015)
level 2 v.s. level 3
intercept ----0.923 0.923 0.923 ----0.789 0.923 0.789 0.789 0.789 (0.46 / 1.709) ----0.768 0.768 0.768 0.768 (0.477 / 0.456) ----7.517 7.517 7.517 7.517 (0.659 / 2.993) class 1 2.586 2.586 2.586 2.586 2.503 2.503 2.503 2.503 (0.252 / 1.801) 2.578 2.578 2.578 2.578 (0.229 / 0.404) 7.731 7.731 7.731 7.731 (0.632 / 2.964) sex 0.312 0.312 0.312 0.312 0.353 0.353 0.353 0.353 (0.205 / 0.206) 0.358 0.358 0.358 0.358 (0.212 / 0.225) 0.313 0.313 0.313 0.313 (0.182 / 0.197) age ----0.002 0.002 0.002 ----0.010 0.002 0.010 0.010 0.010 (0.013 / 0.012) ----0.010 0.010 0.010 0.010 (0.013 / 0.012) ----0.005 0.005 0.005 0.005 (0.012 / 0.011)
item 3 item 3item 3 item 3
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----4.839 4.839 4.839 ----4.617 4.839 4.617 4.617 4.617 (0.882 / 2.337) ----5.492 5.492 5.492 5.492 (0.895 / 2.712) ----9.030 9.030 9.030 9.030 (1.53 / 1.304) class 1 4.373 4.373 4.373 4.373 5.510 5.510 5.510 5.510 (0.605 / 4.204) 5.178 5.178 5.178 5.178 (0.706 / 2.65) 7.760 7.760 7.760 7.760 (1.526 / 1.208)
sex ----0.053 0.053 0.053 0.053 0.009 0.009 0.009 0.009 (0.263 / 0.263) ----0.010 0.010 0.010 0.010 (0.246 / 0.251) 0.122 0.122 0.122 0.122 (0.213 / 0.203) age 0.024 0.024 0.024 0.024 0.011 0.011 0.011 0.011 (0.017 / 0.021) 0.015 0.015 0.015 0.015 (0.016 / 0.015) 0.009 0.009 0.009 0.009 (0.013 / 0.013)
Table 32: (Continued)
level 2 v.s. level 3
intercept ----1.780 1.780 1.780 ----1.714 1.780 1.714 1.714 1.714 (0.441 / 1.885) ----1.707 1.707 1.707 1.707 (0.45 / 0.443) ----7.492 7.492 7.492 7.492 (1.833 / 2.753) class 1 1.990 1.990 1.990 1.990 1.791 1.791 1.791 1.791 (0.188 / 2.159) 2.018 2.018 2.018 2.018 (0.199 / 0.267) 7.038 7.038 7.038 7.038 (1.812 / 2.699) sex ----0.442 0.442 0.442 ----0.380 0.442 0.380 0.380 0.380 (0.19 / 0.189) ----0.405 0.405 0.405 0.405 (0.193 / 0.192) ----0.312 0.312 0.312 0.312 (0.175 / 0.184) age 0.019 0.019 0.019 0.019 0.012 0.012 0.012 0.012 (0.012 / 0.012) 0.013 0.013 0.013 0.013 (0.012 / 0.012) 0.009 0.009 0.009 0.009 (0.011 / 0.012)
item 4 item 4item 4 item 4
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----2.893 2.893 2.893 ----2.240 2.893 2.240 2.240 2.240 (0.584 / 2.094) ----2.381 2.381 2.381 2.381 (0.618 / 0.615) ----8.290 8.290 8.290 8.290 (0.847 / 2.815) class 1 5.733 5.733 5.733 5.733 4.886 4.886 4.886 4.886 (0.497 / 2.155) 5.050 5.050 5.050 5.050 (0.406 / 0.766) 8.598 8.598 8.598 8.598 (0.829 / 2.847) sex ----0.462 0.462 0.462 ----0.331 0.462 0.331 0.331 0.331 (0.251 / 0.25) ----0.396 0.396 0.396 0.396 (0.262 / 0.26) ----0.108 0.108 0.108 0.108 (0.202 / 0.227) age 0.0.0.0.042 042 042 0.020 042 0.020 0.020 0.020 (0.016 / 0.016) 0.024 0.024 0.024 0.024 (0.017 / 0.016) 0.012 0.012 0.012 0.012 (0.013 / 0.012)
level 2 v.s. level 3
intercept ----0.727 0.727 0.727 ----0.575 0.727 0.575 0.575 0.575 (0.5 / 1.92) ----0.481 0.481 0.481 0.481 (0.514 / 0.495) ----7.349 7.349 7.349 7.349 (0.499 / 3.442) class 1 3.630 3.630 3.630 3.630 3.138 3.138 3.138 3.138 (0.469 / 1.94) 3.071 3.071 3.071 3.071 (0.372 / 0.575) 7.935 7.935 7.935 7.935 (0.469 / 3.451) sex 0.105 0.105 0.105 0.105 0.158 0.158 0.158 0.158 (0.224 / 0.216) 0.118 0.118 0.118 0.118 (0.228 / 0.217) 0.304 0.304 0.304 0.304 (0.21 / 0.232) age 0.007 0.007 0.007 0.007 ----0.005 0.005 0.005 0.005 (0.014 / 0.014) ----0.002 0.002 0.002 0.002 (0.015 / 0.014) ----0.010 0.010 0.010 0.010 (0.013 / 0.013)
item 5 item 5item 5 item 5
TRUE K_Corr K_Cova H_Cova
level 1 v.s. level 3
intercept ----1.218 1.218 1.218 ----1.278 1.218 1.278 1.278 1.278 (0.499 / 2.513) ----1.048 1.048 1.048 1.048 (0.512 / 0.57) ----6.118 6.118 6.118 6.118 (0.734 / 3.634) class 1 2.900 2.900 2.900 2.900 3.091 3.091 3.091 3.091 (0.303 / 2.388) 2.757 2.757 2.757 2.757 (0.237 / 0.713) 6.772 6.772 6.772 6.772 (0.69 / 3.536)
sex ----0.268 0.268 0.268 ----0.223 0.268 0.223 0.223 0.223 (0.217 / 0.218) ----0.239 0.239 0.239 0.239 (0.219 / 0.225) ----0.134 0.134 0.134 0.134 (0.197 / 0.227) age 0.011 0.011 0.011 0.011 0.004 0.004 0.004 0.004 (0.014 / 0.013) 0.005 0.005 0.005 0.005 (0.014 / 0.014) 0.001 0.001 0.001 0.001 (0.012 / 0.012)
level 2 v.s. level 3
intercept 0.373 0.373 0.373 0.373 0.081 0.081 0.081 0.081 (0.469 / 2.414) 0.413 0.413 0.413 0.413 (0.476 / 0.46) ----5.206 5.206 5.206 5.206 (0.462 / 4.279) class 1 1.223 1.223 1.223 1.223 1.668 1.668 1.668 1.668 (0.297 / 2.615) 1.286 1.286 1.286 1.286 (0.223 / 0.965) 6.171 6.171 6.171 6.171 (0.403 / 4.188) sex ----0.292 0.292 0.292 ----0.254 0.292 0.254 0.254 0.254 (0.211 / 0.216) ----0.257 0.257 0.257 0.257 (0.21 / 0.203) ----0.207 0.207 0.207 0.207 (0.209 / 0.232) age ----0.013 0.013 0.013 ----0.016 0.013 0.016 0.016 0.016 (0.013 / 0.013) ----0.016 0.016 0.016 0.016 (0.013 / 0.013) ----0.017 0.017 0.017 0.017 (0.013 / 0.013)
Table 33: Average parameters estimations for 100 replication in 2-class model, N=700 (standard error in multinomial regression / sample standard error for 100 replication)
Class 1 vs. Class 2 Class 1 vs. Class 2 Class 1 vs. Class 2 Class 1 vs. Class 2
TRUE K_Corr K_Cova H_Cova
intercept ----0.935 0.935 0.935 ----0.679 0.935 0.679 0.679 0.679 (0.158 / 0.749) ----0.640 0.640 0.640 0.640 (0.149 / 0.266) 3.201 3.201 3.201 3.201 (0.412 / 0.903) occup 0.441 0.441 0.441 0.441 0.319 0.319 0.319 0.319 (0.193 / 0.221) 0.362 0.362 0.362 0.362 (0.184 / 0.185) 0.861 0.861 0.861 0.861 (4.131 / 2.246) dprime 0.414 0.414 0.414 0.414 0.309 0.309 0.309 0.309 (0.05 / 0.087) 0.338 0.338 0.338 0.338 (0.048 / 0.061) 0.174 0.174 0.174 0.174 (0.144 / 0.172)
Table 34: Average conditional Probability for 100 replication in 2-class model, N=700
(sample standard deviance in parentheses)
Class 1 Class 1 Class 1 Class 1
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.758 0.758 0.758 0.758 0.707 0.707 0.707 0.707 (0.080) 0.717 0.717 0.717 0.717 (0.036) 0.0.467 0.0.467 467 467 (0.021) Level 2 0.237 0.237 0.237 0.237 0.256 0.256 0.256 0.256 (0.044) 0.259 0.259 0.259 0.259 (0.028) 0.322 0.322 0.322 0.322 (0.021) Level 3 0.006 0.006 0.006 0.006 0.037 0.037 0.037 0.037 (0.047) 0.023 0.023 0.023 0.023 (0.018) 0.212 0.212 0.212 0.212 (0.020)
item2
Level 1 0.460 0.460 0.460 0.460 0.425 0.425 0.425 0.425 (0.061) 0.434 0.434 0.434 0.434 (0.038) 0.266 0.266 0.266 0.266 (0.019) Level 2 0.461 0.461 0.461 0.461 0.462 0.462 0.462 0.462 (0.037) 0.471 0.471 0.471 0.471 (0.027) 0.405 0.405 0.405 0.405 (0.023) Level 3 0.078 0.078 0.078 0.078 0.113 0.113 0.113 0.113 (0.070) 0.096 0.096 0.096 0.096 (0.031) 0.330 0.330 0.330 0.330 (0.025)
item3
Level 1 0.322 0.322 0.322 0.322 0.356 0.356 0.356 0.356 (0.195) 0.307 0.307 0.307 0.307 (0.027) 0.190 0.190 0.190 0.190 (0.014) Level 2 0.439 0.439 0.439 0.439 0.392 0.392 0.392 0.392 (0.124) 0.436 0.436 0.436 0.436 (0.027) 0.342 0.342 0.342 0.342 (0.021) Level 3 0.239 0.239 0.239 0.239 0.252 0.252 0.252 0.252 (0.101) 0.257 0.257 0.257 0.257 (0.030) 0.469 0.469 0.469 0.469 (0.023)
item4
Level 1 0.675 0.675 0.675 0.675 0.625 0.625 0.625 0.625 (0.082) 0.639 0.639 0.639 0.639 (0.042) 0.427 0.427 0.427 0.427 (0.020) Level 2 0.313 0.313 0.313 0.313 0.332 0.332 0.332 0.332 (0.050) 0.331 0.331 0.331 0.331 (0.029) 0.346 0.346 0.346 0.346 (0.018) Level 3 0.013 0.013 0.013 0.013 0.043 0.043 0.043 0.043 (0.055) 0.030 0.030 0.030 0.030 (0.019) 0.228 0.228 0.228 0.228 (0.022)
item5
Level 1 0.642 0.642 0.642 0.642 0.613 0.613 0.613 0.613 (0.092) 0.614 0.614 0.614 0.614 (0.070) 0.443 0.443 0.443 0.443 (0.023) Level 2 0.263 0.263 0.263 0.263 0.279 0.279 0.279 0.279 (0.083) 0.280 0.280 0.280 0.280 (0.076) 0.319 0.319 0.319 0.319 (0.018) Level 3 0.095 0.095 0.095 0.095 0.108 0.108 0.108 0.108 (0.044) 0.106 0.106 0.106 0.106 (0.023) 0.238 0.238 0.238 0.238 (0.020)
Table 34: (Continued)
Class 2 Class 2 Class 2 Class 2
TRUE K_Corr K_Cova H_Cova
item 1
Level 1 0.078 0.078 0.078 0.078 0.130 0.130 0.130 0.130 (0.109) 0.093 0.093 0.093 0.093 (0.044) 0.049 0.049 0.049 0.049 (0.070) Level 2 0.414 0.414 0.414 0.414 0.391 0.391 0.391 0.391 (0.058) 0.397 0.397 0.397 0.397 (0.031) 0.189 0.189 0.189 0.189 (0.201) Level 3 0.508 0.508 0.508 0.508 0.480 0.480 0.480 0.480 (0.102) 0.510 0.510 0.510 0.510 (0.043) 0.763 0.763 0.763 0.763 (0.240)
item2
Level 1 0.010 0.010 0.010 0.010 0.042 0.042 0.042 0.042 (0.070) 0.015 0.015 0.015 0.015 (0.024) 0.000 0.000 0.000 0.000 (0.004) Level 2 0.304 0.304 0.304 0.304 0.301 0.301 0.301 0.301 (0.055) 0.284 0.284 0.284 0.284 (0.033) 0.032 0.032 0.032 0.032 (0.090) Level 3 0.686 0.686 0.686 0.686 0.657 0.657 0.657 0.657 (0.110) 0.701 0.701 0.701 0.701 (0.048) 0.967 0.967 0.967 0.967 (0.090)
item3
Level 1 0.013 0.013 0.013 0.013 0.024 0.024 0.024 0.024 (0.032) 0.014 0.014 0.014 0.014 (0.020) 0.001 0.001 0.001 0.001 (0.007) Level 2 0.198 0.198 0.198 0.198 0.210 0.210 0.210 0.210 (0.069) 0.180.180.180.188 8 8 8 (0.027) 0.027 0.027 0.027 0.027 (0.087) Level 3 0.788 0.788 0.788 0.788 0.766 0.766 0.766 0.766 (0.088) 0.797 0.797 0.797 0.797 (0.040) 0.972 0.972 0.972 0.972 (0.089)
item4
Level 1 0.094 0.094 0.094 0.094 0.137 0.137 0.137 0.137 (0.096) 0.102 0.102 0.102 0.102 (0.039) 0.013 0.013 0.013 0.013 (0.038) Level 2 0.356 0.356 0.356 0.356 0.339 0.339 0.339 0.339 (0.060) 0.341 0.341 0.341 0.341 (0.029) 0.049 0.049 0.049 0.049 (0.118) Level 3 0.551 0.551 0.551 0.551 0.524 0.524 0.524 0.524 (0.116) 0.557 0.557 0.557 0.557 (0.044) 0.938 0.938 0.938 0.938 (0.142)
item5
Level 1 0.170 0.170 0.170 0.170 0.188 0.188 0.188 0.188 (0.085) 0.172 0.172 0.172 0.172 (0.042) 0.057 0.057 0.057 0.057 (0.104) Level 2 0.372 0.372 0.372 0.372 0.357 0.357 0.357 0.357 (0.077) 0.367 0.367 0.367 0.367 (0.034) 0.110 0.110 0.110 0.110 (0.171) Level 3 0.458 0.458 0.458 0.458 0.454 0.454 0.454 0.454 (0.115) 0.462 0.462 0.462 0.462 (0.039) 0.833 0.833 0.833 0.833 (0.227)
Table 35: Average Latent Prevalences for 100 replication in 2-class model, N=700 (sample standard deviance in parentheses)
TRUE K_Corr K_Cova H_Cova
class1 0.5540.5540.5540.554 0.5450.5450.5450.545 (0.159) 0.5730.573 0.5730.573(0.058) 0.966 0.966 0.966 0.966 (0.027) class2 0.4460.4460.4460.446 0.4550.4550.4550.455 (0.159) 0.4270.427 0.4270.427(0.058) 0.034 0.034 0.034 0.034 (0.027)
Table 36: Average Correlation Coefficients for 100 replication in 2-class model, N=700 (total number of not NA values in parentheses)
K_Corr K_Cova H_Cova
class1 0.098 0.098 0.098 0.098 (100) 0.089 0.089 0.089 0.089 (100) 0.288 0.288 0.288 0.288 (100) class2 0.179 0.179 0.179 0.179 (100) 0.143 0.143 0.143 0.143 (100) 0.610 0.610 0.610 0.610 (99)