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. Author manuscript; available in PMC: 2018 Jan 1.
Published in final edited form as: Struct Equ Modeling. 2016 Dec 5;24(2):230–245. doi: 10.1080/10705511.2016.1252265

Table 4. Minimum and maximum bootstrap selection model selection rates of the 3 fitted 2-group models in relation to BIC differences observed in samples drawn from the population.

Δ BIC Model 1 Model 2 Model 3
N=200
min max #samp min max #samp min max #samp
0-2 0.183 0.636 158 0.532 0.73 10 0.221 0.795 196
2-4 0.195 0.714 72 0.471 0.732 12 0.304 0.784 156
4-6 0.311 0.79 43 0.696 0.696 1 0.211 0.823 128
6-8 0.358 0.789 18 0.693 0.78 3 0.425 0.89 74
8-10 0.501 0.91 10 0.537 0.722 2 0.528 0.888 44
10-15 0.602 0.884 5 NA NA 0 0.552 0.947 55
15-25 NA NA 0 0.889 0.889 1 0.778 0.948 12
>25 NA NA 0 NA NA 0 NA NA 0
N=350
0-2 0.204 0.654 171 0.582 0.712 20 0.2 0.693 206
2-4 0.272 0.728 96 0.674 0.762 11 0.251 0.752 156
4-6 0.333 0.774 54 0.668 0.786 12 0.338 0.792 85
6-8 0.49 0.867 16 0.6 0.829 10 0.403 0.85 62
8-10 0.586 0.916 14 0.662 0.845 4 0.496 0.88 33
10-15 0.722 0.936 8 0.808 0.876 4 0.528 0.944 29
15-25 NA NA 0 0.918 0.962 4 0.702 0.935 5
>25 NA NA 0 NA NA 0 NA NA 0
N=700
0-2 0.198 0.552 73 0.614 0.752 53 0.178 0.59 96
2-4 0.328 0.680 42 0.668 0.773 47 0.236 0.644 96
4-6 0.374 0.804 14 0.704 0.82 54 0.32 0.77 59
6-8 0.459 0.836 15 0.738 0.84 52 0.39 0.797 39
8-10 0.494 0.891 8 0.766 0.868 39 0.498 0.846 19
10-15 0.558 0.92 4 0.808 0.924 89 0.54 0.904 21
15-25 NA NA 0 0.868 0.982 117 0.698 0.94 3
>25 NA NA 0 0.957 0.998 60 NA NA 0

Note: ΔBIC is the BIC difference between the best and second-best fitting model in samples drawn from the population. Min and max are the minimum and maximum bootstrap selection rates for samples within a given range of ΔBIC presented for each winning model, and #samp is the number of samples within that range favoring that model. For instance, for N=700, there were 42 samples (out of P=1000) with a BIC difference between 0 and 2 favoring model 1, and the minimum and maximum bootstrap selection rates for model 1 in this bin were 0.328 and 0.680, respectively.