  We study a relativistic anyon model with a spin-$j$ matter field minimally
coupled to a statistical gauge potential governed by the Chern-Simons dynamics
with a statistical parameter $\alpha$. A spin and statistics transmutation is
shown in terms of a continuous random walk method. An integer or
odd-half-integer part of $\alpha$ can be reabsorbed by change of $j$. We
discuss the equivalence of a large class of (infinite number) Chern-Simons
matter models for given $j$ and $\alpha$.
