  It is difficult to accurately identify galaxy mergers and it is an even
larger challenge to classify them by their mass ratio or merger stage. In
previous work we used a suite of simulated mergers to create a classification
technique that uses linear discriminant analysis (LDA) to identify major and
minor mergers. Here, we apply this technique to 1.3 million galaxies from the
SDSS DR16 photometric catalog and present the probability that each galaxy is a
major or minor merger, splitting the classifications by merger stages (early,
late, post-coalescence). We present publicly-available imaging predictor values
and all of the above classifications for one of the largest-yet samples of
galaxies. We measure the major and minor merger fraction ($f_{\mathrm{merg}}$)
and build a mass-complete sample of galaxies, which we bin as a function of
stellar mass and redshift. For the major mergers, we find a positive slope of
$f_{\mathrm{merg}}$ with stellar mass and negative slope of $f_{\mathrm{merg}}$
with redshift between stellar masses of $10.5 < M_* (log\ M_{\odot}) < 11.6$
and redshifts of $0.03 < z < 0.19$. We are able to reproduce an artificial
positive slope of the major merger fraction with redshift when we do not bin
for mass or craft a complete sample, demonstrating the importance of mass
completeness and mass binning. We determine that the positive trend of the
major merger fraction with stellar mass is consistent with a hierarchical
assembly scenario. The negative trend with redshift requires that an additional
assembly mechanism, such as baryonic feedback, dominates in the local Universe.

Astrophysics of Galaxies