One of the objectives in performance-based earthquake engineering is to quantify the seismic reliability of a structure at a site. For that purpose, probabilistic seismic demand analysis (PSDA) is used as a tool to estimate the mean annual frequency of exceeding a specified value of a structural demand parameter (e.g. interstorey drift). This paper compares and contrasts the use, in PSDA, of certain advanced scalar versus vector and conventional scalar ground motion intensity measures (IMs). One of the benefits of using a well-chosen IM is that more accurate evaluations of seismic performance are achieved without the need to perform detailed ground motion record selection for the nonlinear dynamic structural analyses involved in PSDA (e.g. record selection with respect to seismic parameters such as earthquake magnitude, source-to-site distance, and ground motion epsilon). For structural demands that are dominated by a first mode of vibration, using inelastic spectral displacement (Sdi) can be advantageous relative to the conventionally used elastic spectral acceleration (Sa) and the vector IM consisting of Sa and epsilon (??). This paper demonstrates that this is true for ordinary and for near-source pulse-like earthquake records. The latter ground motions cannot be adequately characterized by either Sa alone or the vector of Sa and ??. For structural demands with significant higher-mode contributions (under either of the two types of ground motions), even Sdi (alone) is not sufficient, so an advanced scalar IM that additionally incorporates higher modes is used.