  The stellar velocity ellipsoid (SVE) in galaxies can provide important
information on the processes that participate in the dynamical heating of their
disc components (e.g. giant molecular clouds, mergers, spiral density waves,
bars). Earlier findings suggested a strong relation between the shape of the
disc SVE and Hubble type, with later-type galaxies displaying more anisotropic
ellipsoids and early-types being more isotropic. In this paper, we revisit the
strength of this relation using an exhaustive compilation of observational
results from the literature on this issue. We find no clear correlation between
the shape of the disc SVE and morphological type, and show that galaxies with
the same Hubble type display a wide range of vertical-to-radial velocity
dispersion ratios. The points are distributed around a mean value and scatter
of $\sigma_z/\sigma_R=0.7\pm 0.2$. With the aid of numerical simulations, we
argue that different mechanisms might influence the shape of the SVE in the
same manner and that the same process (e.g. mergers) does not have the same
impact in all the galaxies. The complexity of the observational picture is
confirmed by these simulations, which suggest that the vertical-to-radial axis
ratio of the SVE is not a good indicator of the main source of disc heating.
Our analysis of those simulations also indicates that the observed shape of the
disc SVE may be affected by several processes simultaneously and that the
signatures of some of them (e.g. mergers) fade over time.
