Abstract In practice it is common to estimate site effects using a single proxy, or single variable such as 30 m shear wave velocity (VS30) or site period. Many studies have investigated merits of proposed proxies with contradicting recommendations. Yet, most studies indicate the single proxy approach is less than ideal, resulting in large uncertainty. To provide a better understanding of components that drive site response, we performed a parameterized study on 19 shallow soil profiles with VS ranging from 150 m/s to 400 m/s. We propagated 74 input motions through each soil column using one-dimensional equivalent-linear method to produce 1406 site response analyses. The resulting amplification factors (the ratio of surface to base motion) were then analyzed statistically to identify trends. The mean amplification factor, averaged from 74 records, was used to isolate and quantify the effects of VS on site response. Based on analysis of record-to-record trends, we identified two separate mechanisms through which nonlinearity affects site response including “damping increase” and “site period shift”. The interaction of these two mechanisms makes amplification-shaking intensity models highly depth-dependent. The residual standard deviation of amplification factor based on depth-independent models was found to be up to three times larger than the corresponding standard deviation based on depth-specific models. We found strain compatible site period a promising site parameter that complements the predictive information obtained from VS. Finally, a simplified procedure providing a five-point estimate of site transfer function is outlined. The proposed procedure can fill the gap in current practice for an intermediate solution between the numerically rigorous solution and the single proxy approach. Implementation of this procedure is demonstrated in an example.