  Type Ia supernovae (SNe Ia) are standardizable candles, but for over a
decade, there has been a debate on how to properly account for their
correlations with host galaxy properties. Using the Bayesian hierarchical model
UNITY, we simultaneously fit for the SN Ia light curve and host galaxy
standardization parameters on a set of 103 Sloan Digital Sky Survey II SNe Ia.
We investigate the influences of host stellar mass, along with both localized
($r<3$ kpc) and host-integrated average stellar ages, derived from stellar
population synthesis modeling. We find that the standardization for the
light-curve shape ($\alpha$) is correlated with host galaxy standardization
terms ($\gamma_i$) requiring simultaneous fitting. In addition, we find that
these correlations themselves are dependent on host galaxy stellar mass that
includes a shift in the color term ($\beta$) of $0.8 \mathrm{mag}$, only
significant at $1.2\sigma$ due to the small sample. We find a linear host mass
standardization term at the $3.7\sigma$ level, that by itself does not
significantly improve the precision of an individual SN Ia distance. However, a
standardization that uses both stellar mass and average local stellar age is
found to be significant at $>3\sigma$ in the two-dimensional posterior space.
In addition, the unexplained scatter of SNe Ia absolute magnitude post
standardization, is reduced from $0.122^{+0.019}_{-0.018}$ to $0.109\pm0.017$
mag, or $\sim10\%$. We do not see similar improvements when using global ages.
This combination is consistent with either metallicity or line-of-sight dust
affecting the observed luminosity of SNe Ia.
