  A simplified theory of the diagonal Bianchi type I model coupled with a
massless scalar field in loop quantum cosmology is constructed according to the
$\bar{\mu}$ scheme. Kinematical and physical sectors of the theory are under
good analytical control as well as the scalar constraint operator. Although it
is possible to compute numerically the nonsingular evolution of the three
gravitational degrees of freedom, the naive implementation of the $\bar{\mu}$
scheme to the diagonal Bianchi type I model is problematic. The lack of the
full invariance of the theory with respect to the fiducial cell and fiducial
metric scaling causes serious problems in the semiclassical limit of the
theory. Because of this behavior it is very difficult to extract reasonable
physics from the model. The weaknesses of the implementation of the $\bar{\mu}$
scheme to the Bianchi I model do not imply limitations of the $\bar{\mu}$
scheme in the isotropic case.
