  We investigate the ability of state-of-the-art redshift-space distortions
models for the galaxy anisotropic two-point correlation function \xi(r_p, \pi),
to recover precise and unbiased estimates of the linear growth rate of
structure f, when applied to catalogues of galaxies characterised by a
realistic bias relation. To this aim, we make use of a set of simulated
catalogues at z = 0.1 and z = 1 with different luminosity thresholds, obtained
by populating dark-matter haloes from a large N-body simulation using halo
occupation prescriptions. We examine the most recent developments in
redshift-space distortions modelling, which account for non-linearities on both
small and intermediate scales produced respectively by randomised motions in
virialised structures and non-linear coupling between the density and velocity
fields. We consider the possibility of including the linear component of galaxy
bias as a free parameter and directly estimate the growth rate of structure f.
Results are compared to those obtained using the standard dispersion model,
over different ranges of scales.We find that the model of Taruya et al. (2010),
the most sophisticated one considered in this analysis, provides in general the
most unbiased estimates of the growth rate of structure, with systematic errors
within 4% over a wide range of galaxy populations spanning luminosities between
L > L* and L > 3L*. The scale-dependence of galaxy bias plays a role on
recovering unbiased estimates of f when fitting quasi non-linear scales. Its
effect is particularly severe for most luminous galaxies, for which systematic
effects in the modelling might be more difficult to mitigate and have to be
further investigated. [...]
