We investigate the relationship between 8.44 GHz brightness temperatures and 1.4 to 8.44 GHz radio spectral indices with 6.2 mu m polycyclic aromatic hydrocarbon (PAH) emission and 9.7 mu m silicate absorption features for a sample of 36 local luminous and ultra-luminous infrared galaxies. The three active galactic nuclei (AGN) identified through their excessively large 8.44 GHz brightness temperatures are also identified as AGN via their small 6.2 mu m PAH EQWs. Finally, we investigate the location of these infrared-bright systems relative to the main sequence of star-forming galaxies in the local universe. We find that the radio spectral indices of galaxies flatten with increasing distance above the main sequence, or in other words, with increasing specific star formation rate. This indicates that galaxies located above the main sequence, having high specific star formation rates, are typically compact star-bursts hosting deeply embedded star formation that becomes more optically thick in the radio and infrared with increased distance above the main sequence.