  We present an analysis of the effects of uncertainties in the atmosphere
models on the radius, mass, and other neutron star parameter constraints for
the NICER observations of rotation-powered millisecond pulsars. To date, NICER
has applied the X-ray pulse profile modeling technique to two
millisecond-period pulsars: PSR J0030+0451 and the high-mass pulsar PSR
J0740+6620. These studies have commonly assumed a deep-heated, fully ionized
hydrogen atmosphere model, although they have explored the effects of
partial-ionization and helium composition in some cases. Here, we extend that
exploration and also include new models with partially ionized carbon
composition, externally heated hydrogen, and an empirical atmospheric beaming
parameterization to explore deviations in the expected anisotropy of the
emitted radiation. None of the studied atmosphere cases have any significant
influence on the inferred radius of PSR J0740+6620, possibly due to its X-ray
faintness, tighter external constraints, and/or viewing geometry. In the case
of PSR J0030+0451, both the composition and ionization state could
significantly alter the inferred radius. However, based on the evidence (prior
predictive probability of the data), partially ionized hydrogen and carbon
atmospheres are disfavored. The difference in the evidence for ionized hydrogen
and helium atmospheres is too small to be decisive for most cases, but the
inferred radius for helium models trends to larger sizes around or above 14-15
km. External heating or deviations in the beaming that are less than $5\,\%$ at
emission angles smaller than 60 degrees, on the other hand, have no significant
effect on the inferred radius.
