  We apply the self-interaction corrected local spin density %(SIC-LSD)
approximation to study the electronic structure and magnetic properties of the
spinel ferrites MnFe$_{2}$O$_{4}$, Fe$_{3}$O$_{4}$, CoFe$_{2}$O$_{4}$, and
NiFe$_{2}$O$_{4}$. We concentrate on establishing the nominal valence of the
transition metal elements and the ground state structure, based on the study of
various valence scenarios for both the inverse and normal spinel structures for
all the systems. For both structures we find all the studied compounds to be
insulating, but with smaller gaps in the normal spinel scenario. On the
contrary, the calculated spin magnetic moments and the exchange splitting of
the conduction bands are seen to increase dramatically when moving from the
inverse spinel structure to the normal spinel kind. We find substantial orbital
moments for NiFe$_{2}$O$_{4}$ and CoFe$_{2}$O$_{4}$.
