Neutron spectroscopy has become a standard technique for remotely measuring planetary surface compositions from orbital spacecraft around various planets. Measurements have successfully been carried out at the Moon, Mars, Mercury, and the asteroids Vesta and Ceres. The NASA Psyche mission is planning to make neutron measurements to characterize the composition of the M-class asteroid (16) Psyche. Earth-based remote sensing measurements allow for a wide range of Fe concentrations, ranging from ~25 wt.% to 90 wt.%, and geochemically plausible Ni concentrations range from 0 wt.% to 10 wt.% or higher. To prepare for the analysis of Psyche neutron data, we have developed a new principal component analysis framework using four neutron energy ranges of thermal, low-energy epithermal, high-energy epithermal, and fast neutrons. With this analysis framework, we have demonstrated that the neutron measurements can uniquely distinguish variations of metal-to-silicate fraction, Ni, and hydrogen compositions. The strongest principal component is that of metal-to-silicate; the second strongest is Ni variations; the third is hydrogen variations. The validity of this framework can be first tested during a Mars gravity assist prior to arrival at Psyche.