  We present an improved and expanded simply parameterized phenomenological
model of the broad line region (BLR) in active galactic nuclei (AGN) for
modeling reverberation mapping data. By modeling reverberation mapping data
directly, we can constrain the geometry and dynamics of the BLR and measure the
black hole mass without relying on the normalization factor needed in the
traditional analysis. For realistic simulated reverberation mapping datasets of
high-quality, we can recover the black hole mass to $0.05-0.25$ dex uncertainty
and distinguish between dynamics dominated by elliptical orbits and inflowing
gas. While direct modeling of the integrated emission line light curve allows
for measurement of the mean time lag, other details of the geometry of the BLR
are better constrained by the full spectroscopic dataset of emission line
profiles. We use this improved model of the BLR to explore possible sources of
uncertainty in measurements of the time lag using cross-correlation function
(CCF) analysis and in measurements of the black hole mass using the virial
product. Sampling the range of geometries and dynamics in our model of the BLR
suggests that the theoretical uncertainty in black hole masses measured using
the virial product is on the order of 0.25 dex. These results support the use
of the CCF to measure time lags and the virial product to measure black hole
masses when direct modeling techniques cannot be applied, provided the
uncertainties associated with the interpretation of the results are taken into
account.
