  Accurately accounting for spectral structure in spectrometer data induced by
instrumental chromaticity on scales relevant for detection of the 21-cm signal
is among the most significant challenges in global 21-cm signal analysis. In
the publicly available EDGES low-band data set, this complicating structure is
suppressed using beam-factor based chromaticity correction (BFCC), which works
by dividing the data by a sky-map-weighted model of the spectral structure of
the instrument beam. Several analyses of this data have employed models that
start with the assumption that this correction is complete. However, while BFCC
mitigates the impact of instrumental chromaticity on the data, given realistic
assumptions regarding the spectral structure of the foregrounds, the correction
is only partial. This complicates the interpretation of fits to the data with
intrinsic sky models (models that assume no instrumental contribution to the
spectral structure of the data). In this paper, we derive a BFCC data model
from an analytic treatment of BFCC and demonstrate using simulated observations
that, in contrast to using an intrinsic sky model for the data, the BFCC data
model enables unbiased recovery of a simulated global 21-cm signal from
beam-factor chromaticity corrected data in the limit that the data is corrected
with an error-free beam-factor model.
