Measuring the Physical Conditions in High-redshift Star-forming Galaxies: Insights from KBSS-MOSFIRE

XWe use photoionization models that are designed to reconcile the joint rest-UV-optical spectra of high-z star-forming galaxies to self-consistently infer the gas chemistry and nebular ionization and excitation conditions for similar to 150 galaxies from the Keck Baryonic Structure Survey (KBSS), using only observations of their rest-optical nebular spectra. We find that the majority of z similar to 2-3 KBSS galaxies are moderately O-rich, with an interquartile range in 12 + log(O/H) = 8.29-8.56, and have significantly sub-solar Fe enrichment, with an interquartile range of [Fe/H] = [-0.79, -0.53], which contributes additional evidence in favor of super-solar O/Fe in high-z galaxies. The model-inferred ionization parameters and N/O are strongly correlated with common strong-line indices (such as O32 and N2O2), with the latter exhibiting similar behavior to local extragalactic H II regions. In contrast, diagnostics commonly used for measuring gas-phase O/H (such as N2 and O3N2) show relatively large scatter with the overall amount of oxygen present in the gas and behave differently than observed at z similar to 0. We provide a new calibration for using R23 to measure O/H in typical high-z galaxies, although it is most useful for relatively O-rich galaxies; combining O32 and R23 does not yield a more effective calibration. Finally, we consider the implications for the intrinsic correlations between physical conditions across the galaxy sample and find that N/O varies with O/H in high-z galaxies in a manner that is almost identical to local H II regions. However, we do not find a strong anti-correlation between ionization parameter and metallicity (O/H or Fe/H) in high-z galaxies, which is one of the principal bases for using strong-line ratios to infer oxygen abundance.