  High-spin rotational bands in rare-earth Er ($Z=68$), Tm ($Z=69$) and Yb
($Z=70$) isotopes are investigated by three different nuclear models. These are
(i) the cranked relativistic Hartree-Bogoliubov (CRHB) approach with
approximate particle number projection by means of the Lipkin-Nogami (LN)
method, (ii) the cranking covariant density functional theory (CDFT) with
pairing correlations treated by a shell-model-like approach (SLAP) or the so
called particle-number conserving (PNC) method, and (iii) cranked shell model
(CSM) based on the Nilsson potential with pairing correlations treated by the
PNC method. A detailed comparison between these three models in the description
of the ground state rotational bands of even-even Er and Yb isotopes is
performed. The similarities and differences between these models in the
description of the moments of inertia, the features of band crossings,
equilibrium deformations and pairing energies of even-even nuclei under study
are discussed. These quantities are considered as a function of rotational
frequency and proton and neutron numbers. The changes in the properties of the
first band crossings with increasing neutron number in this mass region are
investigated. On average, a comparable accuracy of the description of available
experimental data is achieved in these models. However, the differences between
model predictions become larger above the first band crossings. Because of
time-consuming nature of numerical calculations in the CDFT-based models, a
systematic study of the rotational properties of both ground state and excited
state bands in odd-mass Tm nuclei is carried out only by the PNC-SCM. With few
exceptions, the rotational properties of experimental 1-quasiparticle and
3-quasiparticle bands in $^{165,167,169,171}$Tm are reproduced reasonably well.
