Atmospheric gravity waves (GWs) perturb minor species involved in the chemical reactions of airglow emissions in the upper mesosphere and lower thermosphere. In order to determine gravity wave fluxes and the forcing effects of gravity waves on the mean state (which are proportional to the square of the wave amplitude), it is essential that the amplitude of airglow brightness fluctuation be related to the amplitude of major gas density fluctuation in a deterministic way. This has been achieved through detailed modeling combining gravity wave dynamics described using a full-wave model with the chemistry relevant to the airglow emission of interest. Alternatively, others have employed approximations allowing them to derive analytic expressions relating airglow brightness fluctuations to major gas density fluctuations through a so-called cancellation factor (CF). The effects of these approximations on the derived CF are investigated here using a full-wave model describing gravity wave propagation in a nonisothermal, windy, and viscous atmosphere. This numerical model combined with the chemical reaction scheme for the OH (8, 3) Meinel airglow emission is used to derive fluctuations in the OH* nightglow from which an equivalent CF is calculated. Comparisons are made between the analytically derived CF's and the numerically derived CF's based on using different approximations in the latter model. Differences exist at most wave periods, but they also depend on the horizontal wavelengths of the gravity waves considered. In addition to these different model comparisons, the sensitivity of the numerically derived CF to specific physical processes is examined exclusively using the full-wave model. These sensitivity tests show that the effect of eddy diffusion marginally influences the calculated CF's only for the very slowest gravity waves. Accounting for the effects of a nonisothermal mean state has a significant influence on the calculated CF's, and the CF's calculated assuming an isothermal mean state can be as much as a factor of 2 smaller than those calculated assuming a nonisothermal mean state. The effects of background mean winds also influence the derived CF's, which then become dependent on the azimuth of propagation. In this case the calculated CF's can vary by a factor of ~2 from their windless values for gravity waves of short horizontal wavelength with phase speeds less than 100 m s-1. Finally, reflection from the lower and middle thermosphere in the full-wave model leads to undulations in the calculated CF's as a function of phase speed for gravity waves with horizontal wavelengths of 100 km and phase speeds greater than about 100 m s-1. These effects that are not reproduced in the analytic model lead to large differences between the CF's calculated with and without winds, but they only occur for fast gravity waves that are not usually observed in the airglow.