  We combine spectroscopic measurements of H$\alpha$ and H$\beta$ and UV
continuum photometry for a sample of 673 galaxies from the MOSFIRE Deep
Evolution Field survey to constrain hydrogen ionizing photon production
efficiencies ($\xi_{\rm ion}$, xi_ion) at z=1.4-2.6. We find average
log(xi_ion/[Hz erg$^{-1}$])=25.06 (25.34), assuming the Calzetti (SMC) curve
for the UV dust correction and a scatter of 0.28 dex in xi_ion distribution.
After accounting for observational uncertainties and variations in dust
attenuation, we conclude that the remaining scatter in xi_ion is likely
dominated by galaxy-to-galaxy variations in stellar populations, including the
slope and upper-mass cutoff of the initial mass function, stellar metallicity,
star-formation burstiness, and stellar evolution (e.g., single/binary star
evolution). Moreover, xi_ion is elevated in galaxies with high ionization
states (high [OIII]/[OII]) and low oxygen abundances (low [NII]/H$\alpha$ and
high [OIII]/H$\beta$) in the ionized ISM. However, xi_ion does not correlate
with the offset from the z~0 star-forming locus in the BPT diagram, suggesting
no change in the hardness of ionizing radiation accompanying the offset from
the z~0 sequence. We also find that galaxies with blue UV spectral slopes
($\langle\beta\rangle$=-2.1) have elevated xi_ion by a factor of ~2 relative to
the average xi_ion of the sample ($\langle\beta\rangle$=-1.4). If these blue
galaxies are similar to those at z > 6, our results suggest that a lower Lyman
continuum escape fraction is required for galaxies to maintain reionization,
compared to the canonical xi_ion predictions from stellar population models.
Furthermore, we demonstrate that even with robustly dust-corrected H$\alpha$,
the UV dust attenuation can cause on average a ~0.3dex systematic uncertainty
in xi_ion calculations.
