The Sun has been found to be depleted in refractory (rock-forming) elements relative to nearby solar analogs, suggesting a potential indicator of planet formation. Given the small amplitude of the depletion (~0.05 dex), previous analyses have primarily relied on high signal-to-noise stellar spectra and a strictly differential approach to determine elemental abundances of nearby solar analogs relative to the Sun. In this work, we develop an alternative hierarchical Bayesian modeling approach that can be applied to larger samples of stars with lower precision abundance measurements. Using chemical abundance determinations from the Apache Point Observatory Galactic Evolution Experiment (APOGEE-2) and the stellar parameter and chemical abundance pipeline (ASPCAP DR16), we place constraints on the statistical properties of the elemental abundances, including correlations with condensation temperature and the fraction of stars with refractory element depletions. We find evidence for two distinct populations: a depleted population of stars that make up the majority of solar analogs including the Sun, and a comparatively not-depleted population of stars that make up between 10-30% of our solar neighborhood sample. We find chemical abundance correlations with condensation temperature generally in agreement with higher precision surveys of a smaller sample of stars. Such trends, if robustly linked to the formation of planetary systems, provide a means to connect stellar chemical abundance patterns to planetary systems over large samples of Milky Way stars.