supersymmetry - Do the Grassmann coordinates in the superfield formalism have any physical meaning?

In the superfield formalism we consider fields in a space who has four so called bosonic coordinates $x^{\nu}$ and four so called fermionic coordinates $\theta_1$,$\theta_2$,$\bar{\theta_1}$,$\bar{\theta_2}$.

$x^{\mu}$ are of course the physical space-time coordinates, but, do the Grassmannian coordinates have an analog interpretation like some kind of extra dimension or should I view them as a mere formal artifact?