After applying the lack-of-fit p-value threshold, there may be several statistical models that fit the data well. From these remaining models, the one with the lowest AIC (Akaike information criterion) is selected as the best fit.
The AIC is a measure of prediction error that penalizes models with more parameters. This means that if there are two models that do an equally good job of explaining the data, the model with fewer parameters will be selected.
The AIC is not displayed in the results table on the curve fitting page, but it is included in the “bmd.txt” file that can be downloaded from the Analysis Pipeline on the left page (see a screenshot below).