Table 1.

Likelihood ratios for deviance differences using PBCM model comparisons

Likelihood Ratios	S1	S2	S3	S4
$\frac{\mathcal{L}(D_{H1}-D_{H3}|H_3)}{\mathcal{L}(D_{H1}-D_{H3}|H_1)}$	6 × 1043	2 × 10165	3 × 1064	1.03
$\frac{\mathcal{L}(D_{H2}-D_{H3}|H_3)}{\mathcal{L}(D_{H2}-D_{H3}|H_2)}$	1 × 1012	1 × 1022	6 × 1021	0.17

Ratios greater than 1 indicate a preferable model fit for hypothesis 3 (H3) than either hypothesis 1 (H1; row 1), or hypothesis 2 (H2; row 2); ratios greater than 100 indicate a “decisively” better fit while less than 0.01 corresponds to a significantly worse fit (Jeffreys 1998). The fits for each subject (S1–S4) from experiment 1 are shown. S1–S3 are fit decisively better by the H3 model while there are not enough uncertain responses for subject S4 to determine the best fit. PBCM, parametric bootstrap cross-fitting method.