We conducted multi-epoch Very Long Baseline Array (VLBA) phase-referenced observations of LS I +61°303 in order to study its precessing radio jet. Compared to similar observations in 2006, we find that the observed elliptical trajectory of emission at 8.4 GHz repeats after the 9 yr gap. The accurate alignment of the emission patterns yields a precession period of 26.926 ± 0.005 d, which is consistent with that determined by Lomb-Scargle analysis of the radio light curve. We analytically model the projection on the sky plane of the peak position of a precessing, synchrotron-emitting jet, which traces an elliptical trajectory on the sky. Comparing the simulation with the VLBA astrometry we improve our knowledge of the geometry of the system. We measure the LS I +61°303 absolute proper motion to be -0.150 ± 0.006 mas yr-1 eastward and -0.264 ± 0.006 mas yr-1 northward. Removing Galactic rotation, this reveals a small, northward. Removing Galactic rotation, this reveals a small, -1, non-circular motion, which indicates a very low kick velocity when the black hole was formed.