  Ionization sources other than HII regions give rise to the right-hand branch
in the standard ([NII]) BPT diagram, populated by Seyfert 2s and LINERs.
However, because the majority of Seyfert/LINER hosts are star forming (SF), HII
regions contaminate the observed lines to some extent, making it unclear if the
position along the branch is merely due to various degrees of mixing between
pure Seyfert/LINER and SF, or whether it reflects the intrinsic diversity of
Seyfert/LINER ionizing sources. In this study, we empirically remove SF
contributions in ~100,000 Seyfert/LINERs from SDSS using the doppelganger
method. We find that mixing is not the principal cause of the extended
morphology of the observed branch. Rather, Seyferts/LINERs intrinsically have a
wide range of line ratios. Variations in ionization parameter and metallicity
can account for much of the diversity of Seyfert/LINER line ratios, but the
hardness of ionization field also varies significantly. Furthermore, our
k-means classification on seven decontaminated emission lines reveals that
LINERs are made up of two populations, which we call soft and hard LINERs. The
Seyfert 2s differ from both types of LINERs primarily by higher ionization
parameter, whereas the two LINER types mainly differ from each other (and from
star-forming regions) in the hardness of the radiation field. We confirm that
the [NII] BPT diagram more efficiently identifies LINERs than [SII] and [OI]
diagnostics, because in the latter many LINERs, especially soft ones, occupy
the same location as pure star-formers, even after the SF has been removed from
LINER emission.
