  We investigate the physical cause of the great range in the ionization level
seen in the spectra of narrow lined active galactic nuclei (AGN). Mean field
independent component analysis identifies examples of individual SDSS galaxies
whose spectra are not dominated by emission due to star formation (SF), which
we designate as AGN. We assembled high S/N ratio composite spectra of a
sequence of these AGN defined by the ionization level of their narrow-line
regions (NLR), extending down to very low-ionization cases. We used a local
optimally emitting cloud (LOC) model to fit emission-line ratios in this AGN
sequence. These included the weak lines that can be measured only in the
co-added spectra, providing consistency checks on strong line diagnostics.
After integrating over a wide range of radii and densities our models indicate
that the radial extent of the NLR is the major parameter in determining the
position of high to moderate ionization AGN along our sequence, providing a
physical interpretation for their systematic variation. Higher ionization AGN
contain optimally emitting clouds that are more concentrated towards the
central continuum source than in lower ionization AGN. Our LOC models indicate
that for the objects that lie on our AGN sequence, the ionizing luminosity is
anticorrelated with the NLR ionization level, and hence anticorrelated with the
radial concentration and physical extent of the NLR. A possible interpretation
that deserves further exploration is that the ionization sequence might be an
age sequence where low ionization objects are older and have systematically
cleared out their central regions by radiation pressure. We consider that our
AGN sequence instead represents a mixing curve of SF and AGN spectra, but argue
that while many galaxies do have this type of composite spectra, our AGN
sequence appears to be a special set of objects with negligible SF excitation.
