  We investigate the fraction of starbursts, starburst-AGN composites,
Seyferts, and LINERs as a function of infrared luminosity (L_IR) and merger
progress for ~500 infrared-selected galaxies. Using the new optical
classifications afforded by the extremely large data set of the Sloan Digital
Sky Survey, we find that the fraction of LINERs in IR-selected samples is rare
(< 5%) compared with other spectral types. The lack of strong infrared emission
in LINERs is consistent with recent optical studies suggesting that LINERs
contain AGN with lower accretion rates than in Seyfert galaxies. Most
previously classified infrared-luminous LINERs are classified as starburst-AGN
composite galaxies in the new scheme. Starburst-AGN composites appear to
"bridge" the spectral evolution from starburst to AGN in ULIRGs. The relative
strength of the AGN versus starburst activity shows a significant increase at
high infrared luminosity. In ULIRGs (L_IR >10^12 L_odot), starburst-AGN
composite galaxies dominate at early--intermediate stages of the merger, and
AGN galaxies dominate during the final merger stages. Our results are
consistent with models for IR-luminous galaxies where mergers of gas-rich
spirals fuel both starburst and AGN, and where the AGN becomes increasingly
dominant during the final merger stages of the most luminous infrared objects.
