Mixed Posterior Predictive checks for the HFD example. The upper plots present the distribution of the p-values for the two conditions (HFD and NFD) after fitting the calibration model presented in (3) which assumes a polynomial function of the level of expression. They show a uniform behavior for both conditions, indicating good model fit. The values for λ1jk, λ2jkand λ3jkare presented in Table 7 of Additional file 1. The bottom plots present the distribution of the p-values for the two conditions (HFD and NFD) fitting the simpler calibration model assuming λ2jk= 0 and λ3jk= 0. The histograms indicate the presence of two peaks corresponding to very small and very large p-values, suggesting a poor fit.