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We perform a direct comparison of two state-of-the art single stellarpopulation (SSP) models that have been used to demonstrate the non-universalityof the low-mass end of the Initial Mass Function (IMF) slope. The two publicversions of the SSP models are restricted to either solar abundance patterns orsolar metallicity, too restrictive if one aims to disentangle elementalenhancements, metallicity changes and IMF variations in massive early-typegalaxies (ETGs) with star formation histories different from the solarneighborhood. We define response functions (to metallicity and\alpha-abundance) to extend the parameter space of each set of models. Wecompare these extended models with a sample of Sloan Digital Sky Survey (SDSS)ETGs spectra with varying velocity dispersions. We measure equivalent widths ofoptical IMF-sensitive stellar features to examine the effect of the underlyingmodel assumptions and ingredients, such as stellar libraries or isochrones, onthe inference of the IMF slope down to ~0.1 solar masses. We demonstrate thatthe steepening of the low-mass end of the Initial Mass Function (IMF) based ona non-degenerate set of spectroscopic optical indicators is robust against thechoice of the stellar population model. Although the models agree in a relativesense (i.e. both imply more bottom-heavy IMFs for more massive systems), wefind non-negligible differences on the absolute values of the IMF slopeinferred at each velocity dispersion by using the two different models. Inparticular, we find large inconsistency in the quantitative predictions of IMFslope variations and abundance patterns when sodium lines are used. Weinvestigate the possible reasons for these inconsistencies.

The non-universality of the low-mass end of the IMF is robust against the choice of SSP model