In this paper, we present high-resolution optical spectra and optical classifications from our large sample of 285 warm infrared galaxies 10 8< L IR< 10 12.5 L☉. We have classified these galaxies using new theoretical lines on the standard optical diagnostic diagrams. We use a theoretical extreme mixing line between the starburst and AGN regions to classify LINER galaxies and we define a theoretical boundary separating AGNs from starbursts. We find that many galaxies previously classified as LINERs appear to lie on a mixing sequence between starburst and AGN type galaxies. These are likely to be of a composite nature with their excitation being a combination of photoionization due to hot stars plus either ionization by a power-law radiation field associated with an AGN or shock excitation where the shock may result from such processes as cooling flows, superwind activity, or an accretion disk around an AGN. We compare our theory-based classification scheme with the previous semiempirical scheme of Veilleux & Osterbrock. We find that our classification method results in 6% ambiguity in classifications between the different diagnostic diagrams compared with 16% ambiguity using the traditional Veilleux & Osterbrock method. We find that 70% of the galaxies in our sample are classified optically as starburst, 17% are Seyfert 2, 4% are Seyfert 1, and 0.4% are LINERs. A further 2% of our sample are certainly composite galaxies. A fraction (20%) of the Seyfert galaxies, 3% of the starburst galaxies, and 71% of the ambiguous galaxies are possibly composite in nature (11% of the total sample).