In this paper, we present the results of the calculated and experimental dependence of photoluminescence on the excitation power density for GaN:Si layers grown by molecular beam epitaxy. A model was constructed for transitions  in a compensated semiconductor upon interband generation of electron-hole pairs. It is shown that the dependence of the photoluminescence intensity on the excitation power density can be used to determine the recombination mechanism and concentrations of donors and acceptors in semiconductor.