  We examine the redshift evolution of standard strong emission-line
diagnostics for Hbeta-selected star-forming galaxies using the local SDSS
sample and a new z = 0.2 - 2.3 sample obtained from HST WFC3 grism and Keck
DEIMOS and MOSFIRE data. We use the SDSS galaxies to show that there is a
systematic dependence of the strong emission-line properties on Balmer-line
luminosity, which we interpret as showing that both the N/O abundance and the
ionization parameter increase with increasing line luminosity. Allowing for the
luminosity dependence tightens the diagnostic diagrams and the metallicity
calibrations. The combined SDSS and high-redshift samples show that there is no
redshift evolution in the line properties once the luminosity correction is
applied, i.e., all galaxies with a given L(Hbeta) have similar strong
emission-line distributions at all the observed redshifts. We argue that the
best metal diagnostic for the high-redshift galaxies may be a
luminosity-adjusted version of the [NII]6584/Halpha metallicity relation.
