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This work aims at identifying and modelling statistical dependencies between empirical amplification functions of sites in central Italy and the main geological and geophysical characteristics of the region, within a geostatistical analysis framework. The empirical functions, named δS2S, are estimated by decomposing the residuals of the median predictions of a non-ergodic ground motion model of elastic acceleration response spectra developed for the reference region. To select the model that best describes the spatial variability of the data, the performance of stationary and non-stationary spatial models is compared, the latter being able to constrain the prediction of the empirical functions to physical quantities available in the region and descriptive of the geology, topography and geographical location of the site. Finally, we obtain optimal models of δS2S, for each spectral ordinate, parameterised as a function of geographical coordinates and an input map of shear wave velocity in the upper 30 m (Vs30) constructed ad hoc by combining information gathered from two high-resolution maps available for the region. The methodology allows the development of a new practice-oriented framework for the empirical estimation of site amplification, which can be adopted for the generation of shaking scenarios in the context of regional hazard and seismic risk assessment. • We map the empirical site-to-site response δS2S derived from a nonergodic ground motion model for central Italy. • Predictions of δS2S are obtained by means of a geostatistical approach that allows dealing with spatial non-stationarity. • The best spatial model is obtained as a function of geographic coordinates and Vs30. • Lithologic maps do not show significant improvements in predictions compared with the corresponding stationary models. [ABSTRACT FROM AUTHOR]