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.
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