Table 6.
Bias in Within-Class Mean Estimation and Mean Squared Error in Study 2.
| Bias | Mean squared error | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Variance | Sample size | Entropy | ML_E | ML_U | BCH | LTB | ML_E | ML_U | BCH | LTB |
| Equal | 100 | .5 | −0.427 | −0.433 | −0.436 | −0.331 | 0.333 | 0.356 | 0.329 | 0.328 |
| .6 | −0.295 | −0.299 | −0.317 | −0.224 | 0.204 | 0.235 | 0.218 | 0.206 | ||
| .7 | −0.212 | −0.221 | −0.236 | −0.157 | 0.139 | 0.172 | 0.154 | 0.140 | ||
| .8 | −0.138 | −0.155 | −0.172 | −0.107 | 0.097 | 0.125 | 0.108 | 0.100 | ||
| 200 | .5 | −0.341 | −0.371 | −0.361 | −0.191 | 0.230 | 0.287 | 0.244 | 0.215 | |
| .6 | −0.207 | −0.218 | −0.235 | −0.098 | 0.130 | 0.171 | 0.146 | 0.126 | ||
| .7 | −0.115 | −0.133 | −0.154 | −0.037 | 0.077 | 0.117 | 0.091 | 0.082 | ||
| .8 | −0.061 | −0.086 | −0.110 | −0.019 | 0.054 | 0.088 | 0.066 | 0.062 | ||
| 500 | .5 | −0.217 | −0.236 | −0.237 | −0.018 | 0.145 | 0.207 | 0.150 | 0.152 | |
| .6 | −0.106 | −0.105 | −0.136 | 0.029 | 0.065 | 0.118 | 0.072 | 0.078 | ||
| .7 | −0.040 | −0.061 | −0.080 | 0.032 | 0.037 | 0.083 | 0.042 | 0.054 | ||
| .8 | −0.016 | −0.026 | −0.063 | 0.020 | 0.030 | 0.064 | 0.034 | 0.042 | ||
| 1,000 | .5 | −0.142 | −0.143 | −0.153 | 0.051 | 0.104 | 0.221 | 0.091 | 0.122 | |
| .6 | −0.056 | −0.074 | −0.081 | 0.047 | 0.043 | 0.096 | 0.042 | 0.065 | ||
| .7 | −0.021 | −0.032 | −0.059 | 0.030 | 0.028 | 0.070 | 0.029 | 0.048 | ||
| .8 | −0.009 | −0.008 | −0.055 | 0.018 | 0.024 | 0.058 | 0.027 | 0.037 | ||
| Unequal | 100 | .5 | −0.027 | −0.407 | −0.269 | 0.009 | 25.634 | 21.224 | 13.298 | 42.274 |
| .6 | −0.102 | −0.425 | −0.251 | 0.221 | 16.216 | 16.737 | 12.057 | 40.826 | ||
| .7 | 0.266 | −0.240 | −0.052 | 0.347 | 16.047 | 15.133 | 11.417 | 36.397 | ||
| .8 | 0.434 | −0.196 | 0.024 | 0.623 | 16.269 | 11.923 | 10.166 | 25.876 | ||
| 200 | .5 | −0.020 | −0.727 | −0.193 | 0.462 | 10.916 | 19.402 | 8.209 | 72.673 | |
| .6 | 0.340 | −0.512 | −0.011 | 0.940 | 11.895 | 13.762 | 6.988 | 50.538 | ||
| .7 | 0.704 | −0.261 | 0.129 | 1.492 | 13.141 | 9.115 | 6.092 | 42.862 | ||
| .8 | 0.925 | −0.178 | 0.179 | 1.687 | 13.834 | 6.639 | 5.628 | 33.028 | ||
| 500 | .5 | 0.436 | −0.816 | 0.037 | 1.662 | 8.472 | 13.953 | 4.709 | 77.265 | |
| .6 | 0.770 | −0.491 | 0.160 | 2.721 | 10.388 | 6.816 | 3.570 | 64.227 | ||
| .7 | 1.174 | −0.329 | 0.219 | 3.293 | 10.987 | 3.813 | 2.805 | 47.579 | ||
| .8 | 1.253 | −0.275 | 0.255 | 2.898 | 10.773 | 2.869 | 2.528 | 39.944 | ||
| 1,000 | .5 | 0.758 | −0.916 | 0.205 | 2.841 | 8.341 | 12.149 | 2.728 | 88.742 | |
| .6 | 1.233 | −0.389 | 0.279 | 4.411 | 9.001 | 3.559 | 1.938 | 63.036 | ||
| .7 | 1.447 | −0.305 | 0.284 | 4.146 | 9.774 | 2.279 | 1.655 | 54.450 | ||
| .8 | 1.416 | −0.248 | 0.284 | 3.480 | 9.131 | 1.813 | 1.489 | 46.292 | ||
Note. ML = maximum likelihood–based approach (Vermunt, 2010); BCH = BCH approach, named after the developers Bock, Croon, and Hagennarrs (Bolck et al., 2004; Vermunt, 2010); LTB = LTB approach, named after the developers Lanza, Tan, and Bray (Lanza et al., 2013); ML_E = ML approach assuming equal variance among classes; ML_U = ML approach assuming unequal variance among classes.