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$_{4}$.
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