Motivated by recent observations of galaxies dominated by emission lines, which show evidence of being metal poor with young stellar populations, we present calculations of multiple model grids with a range of abundances, ionization parameters, and stellar ages, finding that the predicted spectral line diagnostics are heavily dependent on all three parameters. These new model grids extend the ionization parameter to larger values than typically explored. We compare these model predictions with previous observations of such objects, including two new Lyman-$alpha$ emitting galaxies (LAE) that we have observed. Our models give improved constraints on the metallicity and ionization parameter of these previously studied objects, as we are now able to consider high ionization parameter models. However, similar to previous work, these models have difficulty predicting large line diagnostics for high ionization potential species, requiring future work refining the modelling of FUV photons. Our model grids are also able to constrain the metallicity and ionization parameter of our LAEs, and give constraints on their Ly$alpha$ escape fractions, all of which are consistent with recent lower redshift studies of LAEs.
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