The ([Fe II] 1.644 mu m)/Br gamma and ([Fe II] 1.2567 mu m)/Pa beta ra
tios provide good separation of starburst and Seyfert galaxies; we sho
w that ([Fe II] 1.644 mu m)/Br gamma is nearly as good a discriminant
as the commonly used ([O I] lambda 6300)/H alpha ratio. The behavior o
f both the ([O I] lambda 6300)/H alpha and the ([Fe II] 1.644 mu m)/Br
gamma ratios is readily understood if there is a progression in the p
roportion of shock excitation going from H II region through starburst
and Seyfert galaxies to supernova remnants. We use the CLOUDY program
to show that the behavior is also explained if the dominant excitatio
n mechanism is photoionization. As a test of this technique for identi
fying excitation mechanisms, we have obtained infrared spectra of two
LINER galaxies. NGC 1052, which is thought to be excited by a nuclear
power-law UV source, is the prototype of LINERs, and NGC 3504 is class
ified as a weak-[O I] lambda 6300 LINER, better understood in terms of
photoionization by O stars than by a nonstellar source. The placement
of these galaxies on the ([Fe II] 1.644 mu m)/Br gamma versus ([O I]
lambda 6300)/H alpha diagram is in agreement with these previously det
ermined characteristics. The ([Fe II] 1.644 mu m)/Br gamma and ([Fe II
] 1.2567 mu m)/Pa beta ratios should be useful in classifying heavily
obscured galaxies because the ratios (1) are constructed at wavelength
s where extinction is relatively small and (2) involve lines over narr
ow spectral ranges.