Based on our previous study, we developed ground motion prediction equations (GMPEs) with two site proxies, that is, with one GMPE using the site period (, four times the travel time of shear waves down to the bedrock) and the other one using a pseudosite period (, four times the travel time of shear waves down to 30 m depth). We used two reasonably simple site‐effect models based on or , and each site model has four parameters with each parameter having a physical meaning and miming the theoretical process in site amplification calculations. We found that only the linear magnitude terms in the site class (SC) model from our previous study need to be modified to accommodate the change in the site response parameters, suggesting that the source effect interacts with the site effect. At short periods up to about 0.3 s, the performances of these site models are largely similar. However, at spectral periods over 0.3 s, the performances of these site models are strikingly different, and the rank of the three models in the site model performance is (from the best to the worst) , SC, and site models. It is a surprise that the SC model with four classes can be better than the site model, which does not account for the effect of the soil or rock layers between the 30 m and the bedrock depth. These results may mean that the inclusion of these deep soil layers is more important than the limitations of using a simple step function for the SC model. The GMPE using presented in this study improved the prediction accuracy significantly, especially for sites with over 0.3 s at spectral periods over 0.3 s. The GMPE using in this study can be used whenever is available.