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In this paper, we compare two recent models [N. A. Yampolsky and N. J. Fisch, Phys. Plasmas 16, 072104 (2009); D. Bénisti, D. J. Strozzi, L. Gremillet, and O. Morice, Phys. Rev. Lett. 103, 155002 (2009)] introduced to predict the nonlinear growth of stimulated Raman scattering in the kinetic regime, and providing moreover a nonlinear description of the collisionless, Landau-like, damping rate of the driven electron plasma wave. We first recall the general theoretical framework common to these two models, based on the derivation of the imaginary part of the electron susceptibility, χi, and then discuss in detail why the two approaches differ. By comparing the theoretical predictions for χi to those derived from test particle or Vlasov simulations, we moreover discuss the range of validity of the two models. [ABSTRACT FROM AUTHOR]