  The unknown cause of the correlation between Type Ia supernova (SN Ia) Hubble
residuals and their host-galaxy masses (the "mass step") may bias cosmological
parameter measurements. To better understand the mass step, we develop a SALT3
light-curve model for SN cosmology that uses the host-galaxy masses of 296
low-redshift SNe Ia to derive a spectral-energy distribution--host-galaxy mass
relationship. The resulting model has larger Ca II H&K, Ca II near-infrared
triplet, and Si II equivalent widths for SNe in low-mass host galaxies at
2.2-2.7$\sigma$ significance; this indicates higher explosion energies per unit
mass in low-mass-hosted SNe. The model has phase-dependent changes in SN Ia
colors as a function of host mass, indicating intrinsic differences in mean
broadband light curves. Although the model provides a better fit to the SN data
overall, it does not substantially reduce data--model residuals for a typical
light curve in our sample nor does it significantly reduce Hubble residual
dispersion. This is because we find that previous SALT models parameterized
most host-galaxy dependencies with their first principal component, although
they failed to model some significant spectral variations. Our new model is
luminosity and cosmology independent, and applying it to data reduces the mass
step by $0.021\pm0.002$ mag (uncertainty accounts for correlated data sets);
these results indicate that $\sim$35% of the mass step can be attributed to
luminosity-independent effects. This SALT model version could be trained using
alternative host-galaxy properties and at different redshifts, and therefore
will be a tool for understanding redshift-dependent correlations between SNe Ia
and their host properties as well as their impact on cosmological parameter
measurements.
