  Mass loss rate formulae are derived from observations or from suites of
models. For theoretical models, the following have all been identified as
factors greatly influencing the atmospheric structure and mass loss rates:
Pulsation with piston amplitude scaling appropriately with stellar L; dust
nucleation and growth, with radiation pressure and grain-gas interactions and
appropriate dependence on temperature and density; non-grey opacity with at
least 51 frequency samples; non-LTE and departures from radiative equilibrium
in the compressed and expanding flows; and non-equilibrium processes affecting
the composition (grain formation; molecular chemistry). No one set of models
yet includes all the factors known to be important. In fact, it is very
difficult to construct a model that can simultaneously include these factors
and be useful for computing spectra. Therefore, although theoretical model
grids are needed to separate the effects of M,L,R and/or $T_{\mathrm{eff}}$ or
Z on the mass loss rates, these models must be carefully checked against
observations. Getting the right order of magnitude for the mass loss rate is
only the first step in such a comparison, and is not sufficient to determine
whether the mass loss formula is correct. However, there are observables that
do test the validity of mass loss formulae as they depend directly on $d\log
\dot M/d\log L$, $d\log \dot M/d\log R$, or $d\log \dot M/d\log P$.
