Analyzing derived metallicities and ionization parameters from
  model-based determinations in ionized gaseous nebulae
  We analyze the reliability of oxygen abundances and ionization parameters
obtained from different diagnostic diagrams. For this, we compiled from the
literature observational emission line intensities and oxygen abundance of 446
star-forming regions whose O/H abundance was determined by direct estimation of
electron temperature. The abundances compiled were compared with the values
calculated in this work using different diagnostic diagrams in combination with
results from a grid of photoionization models. We found that the
[\ion{O}{iii}]/[\ion{O}{ii}] vs. [\ion{N}{ii}]/[\ion{O}{ii}],
[\ion{O}{iii}]/H$\beta$ vs. [\ion{N}{ii}]/[\ion{O}{ii}], and
([\ion{O}{iii}]/H$\beta$)/([\ion{N}{ii}]/H$\alpha$) vs.
[\ion{S}{ii}]/[\ion{S}{iii}] diagnostic diagrams give O/H values close to the
$T_{\rm e}$-method, with differences of about 0.04 dex and dispersion of about
0.3 dex. Similar results were obtained by detailed models but with a dispersion
of 0.08 dex. The origin of the dispersion found in the use of diagnostic
diagrams is probably due to differences between the real N/O-O/H relation of
the sample and the one assumed in the models. This is confirmed by the use of
detailed models that do not have a fixed N/O-O/H relation. We found no
correlation between ionization parameter and the metallicity for the objects of
our sample. We conclude that the combination of two line ratio predicted by
photoionization models, one sensitive to the metallicity and another sensitive
to the ionization parameter, which takes into account the physical conditions
of star-forming regions, gives O/H estimates close to the values derived using
direct detections of electron temperatures.
