The corrected chi-square was robust for all tested sample sizes and numbers of parameters, whatever the nature of the factors (scenarios i, ii, iii) and the method used to calculate the P-value (P-value1, P-value2, see File S1 and Fig. S3 for more details). The type I error of this method remained indeed very close to 5% (Fig. 1) . On the contrary, the robustness of the logistic regression approach decreased with the N F /n ratio (number of factors/sample size). In scenarios i (only qualitative factors) and ii (only quantitative factors), the type I error was around 5% for a ratio of 0.005, around 8% for a ratio of 0.15 and around 20% for a ratio of 0.35. It became significantly different from 5% for ratios larger than 0.12 (type I error = 6.7%, z = 2.47, p = 0.019) and 0.08 (type I error = 7.9%, z = 4.21, p = 5.7610 25 ) for scenarios i and ii, respectively. In the mixed scenario (iii), the type I error became significantly different to 5% for all N F /n ratio larger than 0.075 (type I error = 7.1%, z = 3.047, p = 0.0038). More details are available in File S1 and Fig. S2 . Taken together, these results show that, as a rule of thumb, the logistic regression approach is robust for N F /n ratios below 0.1 for all types of factors.