Although the best AIC just shows that the more complex model approximates the data better, it does not represent an unequivocal proof of the selection hypothesis; however, the results point to the possibility that the data could be better described by this hypothesis.
To identify DE genes, our method fits three quantile regression models (constant, linear and piecewise linear models) to the expression profile of each gene, and selects the least complex model that best fits the available data.
Since it may be desirable to find the least complex model that best fits to the data, the AIC combines a measure of complexity and a measure of fit to identify the model that describes the data in the most efficient way.
The reason why the best performed model came from the most complex model maybe becaue of our insufficient training data.
The calc_ftest command computes the significance using the F test with the degrees of freedom of the simple model (dof_1) and its best-fit statistic (stat_1), along with the degrees of freedom of the complex model (dof_2) and its best-fit statistic (stat_2).
Calculate the F statistic for where the simple model has 2 degrees of freedom and a best-fit statistic of 20.28 and the complex model has 34 degrees of freedom and a best-fit statistic of 33.63.
The results show that the most complex model, which allows for both branch-specific and family-specific rate variation, achieves the best fit, without overfitting.
