Hierarchical Bayesian inference for concurrent model fitting and comparison for group studies
Fig 6
Performance of the HBI as a function of the number of subjects.
In this analysis, simulations were repeated 1000 times, in which in half of the simulations, the ratio of the RL model was three times more than the dual-α RL, and vice versa in the other half. A) Protected exceedance probabilities (PXP) of the most frequent model estimated by the HBI and NHI; B) Model frequency of the most frequent model across all simulations. The black line indicates the true frequency (0.75). C-D) Model selection performance by the HBI and NHI at PXP>0.5 and PXP>0.95, respectively. The NHI almost never selects the most frequent model at PXP>0.95. E) Model selection performance using area under the ROC curve. Higher values indicate better performance (one corresponds to perfect model selection). The HBI performance improves by increasing the number of subjects. F) Error in estimating individual parameters across both models and parameters. Estimation errors are computed on the normally distributed parameters. The estimation error is defined as the absolute difference between estimated parameters and the true parameters. In A, B, and F, median across 1000 simulations is plotted and error-bars represent the first and third quantile.