We investigate the propagation of uncertainty in site-response analyses from the soil model parameters to the ground surface motion at three downhole array sites in the Los Angeles (LA) Basin. For this purpose, we develop realistic stochastic models of elastic and nonlinear dynamic soil properties using extensive site-specific and generic geotechnical data on the variability of soil properties. We also generate synthetic ground motions using a finite source dynamic rupture model over a wide range of magnitudes and distances and use this statistically significant number of ground motions in the analysis. For each of the three sites, we evaluate the effects of soil parameter uncertainty as a function of the seismic input intensity and frequency content. We show that the frequency range, where the ground-motion variability due to soil parameter uncertainty is maximized, is a function of both the site and the seismogram characteristics. We compare our results with previously published studies and show that different soil models, statistical descriptions of soil parameters, or ground-motion scenarios may yield substantial differences in the estimated site-response scatter. We conclude that the effects of nonlinear soil property uncertainties on the ground-motion variability strongly depend on the seismic motion intensity, and this dependency is more pronounced for soft soil profiles. By contrast, the effects of velocity profile uncertainties are less intensity dependent and more sensitive to the velocity impedance in the near surface that governs the maximum site amplification.