We study a relativistic anyon model with a spin-j matter field minimal
ly coupled to an abelian Chem-Simons gauge field with a statistical pa
rameter alpha. A spin and statistics transmutation is shown in terms o
f the continuum random walk method. An integer or odd-half-integer par
t of alpha can be reabsorbed by change of j. We discuss the equivalenc
e of a large class of Chem-Simons matter models for given j and alpha.