We derive a set of regional ground‐motion prediction equations (GMPEs) in the Fourier amplitude spectra (FAS‐GMPE) and in the spectral acceleration (SA‐GMPE) domains for the purpose of interpreting the between‐event residuals in terms of source parameter variability. We analyze a dataset of about 65,000 recordings generated by 1400 earthquakes (moment magnitude , hypocentral distance ) that occurred in central Italy between January 2008 and October 2017. In a companion article (Bindi, Spallarossa, et al., 2018), the nonparametric acceleration source spectra were interpreted in terms of ‐square models modified to account for deviations from a high‐frequency flat plateau through a parameter named . Here, the GMPEs are derived considering the moment (), the local (), and the energy () magnitude scales, and the between‐event residuals are computed as random effects. We show that the between‐event residuals for the FAS‐GMPE implementing are correlated with stress drop, with correlation coefficients increasing with increasing frequency up to about 10 Hz. Contrariwise, the correlation is weak for the FAS‐GMPEs implementing and , in particular between 2 and 5 Hz, where most of the corner frequencies lie. At higher frequencies, all models show a strong correlation with . The correlation with the source parameters reflects in a different behavior of the standard deviation of the between‐event residuals with frequency. Although is smaller for the FAS‐GMPE using below 1.5 Hz, at higher frequencies, the model implementing either or shows smaller values, with a reduction of about 30% at 3 Hz (i.e., from 0.3 for to 0.1 for ). We conclude that considering magnitude scales informative for the stress‐drop variability allows to reduce the between‐event variability with a significant impact on the hazard assessment, in particular for studies in which the ergodic assumption on site is removed.