  This is the fourth paper in a series that reports on our investigation of the
clustering properties of active galactic nuclei (AGN) identified in the ROSAT
All-Sky Survey (RASS) and Sloan Digital Sky Survey (SDSS). In this paper we
investigate the cause of the X-ray luminosity dependence of the clustering of
broad-line, luminous AGN at 0.16<z<0.36. We fit the H-alpha line profile in the
SDSS spectra for all X-ray and optically-selected broad-line AGN, determine the
mass of the super-massive black hole (SMBH), M_BH, and infer the accretion rate
relative to Eddington (L/L_EDD). Since M_BH and L/L_EDD are correlated, we
create AGN subsamples in one parameter while maintaining the same distribution
in the other parameter. In both the X-ray and optically-selected AGN samples we
detect a weak clustering dependence with M_BH and no statistically significant
dependence on L/L_EDD. We find a difference of up to 2.7sigma when comparing
the objects that belong to the 30% least and 30% most massive M_BH subsamples,
in that luminous broad-line AGN with more massive black holes reside in more
massive parent dark matter halos at these redshifts. These results provide
evidence that higher accretion rates in AGN do not necessarily require dense
galaxy environments in which more galaxy mergers and interactions are expected
to channel large amounts of gas onto the SMBH. We also present semi-analytic
models which predict a positive M_DMH dependence on M_BH, which is most
prominent at M_BH ~ 10^{8-9} M_SUN.
