  Over three decades of reverberation mapping (RM) studies on local broad-line
active galactic nuclei (AGNs) have measured reliable black-hole (BH) masses for
$> 100$ AGNs. These RM measurements reveal a significant correlation between
the Balmer broad-line region size and the AGN optical luminosity (the $R-L$
relation). Recent RM studies for AGN samples with more diverse BH accretion
parameters (e.g., mass and Eddington ratio) reveal a substantial intrinsic
dispersion around the average $R-L$ relation, suggesting variations in the
overall spectral energy distribution shape as functions of accretion
parameters. Here we perform a detailed photoionization investigation of
expected broad-line properties as functions of accretion parameters, using the
latest models for the AGN continuum implemented in {\tt qsosed}. We compare
theoretical predictions with observations of a sample of 67 $z\lesssim0.5$
reverberation-mapped AGNs with both rest-frame optical and UV spectra in the
moderate-accretion regime (Eddington ratio $\lambda_{\rm Edd}\equiv L/L_{\rm
Edd}<0.5$). The UV/optical line strengths and their dependences on accretion
parameters can be reasonably well reproduced by the locally-optimally-emitting
cloud (LOC) photoionization models. We provide quantitative recipes that use
optical/UV line flux ratios to infer the ionizing continuum, which is not
directly observable. In addition, photoionization models with universal values
of ionization parameter ($\log U_{\rm H}=-2$) and hydrogen density ($\log
n({\rm H})=12$) can qualitatively reproduce the observed global $R-L$ relation
for the current AGN sample. However, such models fail to reproduce the observed
trend of decreasing BLR size with $L/L_{\rm Edd}$ at fixed optical luminosity,
which may imply that the gas density increases with the accretion rate.
