Using the S-band radar at Arecibo Observatory, we observed 16 Psyche, the largest M-class asteroid in the main belt. We obtained 18 radar imaging and 6 continuous wave runs in November and December 2015, and combined these with 16 continuous wave runs from 2005 and 6 recent adaptive-optics (AO) images (Drummond et al., 2016) to generate a three-dimensional shape model of Psyche. Our model is consistent with a previously published AO image (Hanus et al., 2013) and three multi-chord occultations. Our shape model has dimensions 279 × 232 × 189 km (± 10%), Deff = 226 ± 23 km, and is 6% larger than, but within the uncertainties of, the most recently published size and shape model generated from the inversion of lightcurves (Hanus et al., 2013). Psyche is roughly ellipsoidal but displays a mass-deficit over a region spanning 90° of longitude. There is also evidence for two ˜50-70 km wide depressions near its south pole. Our size and published masses lead to an overall bulk density estimate of 4500 ± 1400 kgm-3. Psyche's mean radar albedo of 0.37 ± 0.09 is consistent with a near-surface regolith composed largely of iron-nickel and ˜40% porosity. Its radar reflectivity varies by a factor of 1.6 as the asteroid rotates, suggesting global variations in metal abundance or bulk density in the near surface. The variations in radar albedo appear to correlate with large and small-scale shape features. Our size and Psyche's published absolute magnitude lead to an optical albedo of pv = 0.15 ± 0.03, and there is evidence for albedo variegations that correlate with shape features.