A Multivariate Mixed‐Effects Regression Framework for Ground Motion Modeling: Integrating Parametric and Machine Learning Approaches

Multivariate ground motion models (GMMs) that capture the correlation between different intensity measures (IMs) are essential for seismic risk assessment. Conventional GMMs are often developed using a two‐stage approach, where separate univariate models with predefined functional forms are fitted first, and correlation is addressed in a subsequent step. This study proposes a one‐stage multivariate mixed‐effects framework that jointly models multiple IMs while accounting for different sources of uncertainty through linear random effects. The fixed‐effects component can flexibly incorporate either parametric forms or nonparametric machine learning methods. We demonstrate the framework by developing three illustrative GMMs for the 5% damped orientation‐independent median spectral acceleration (RotD50) using a filtered subset of the NGA‐West2 dataset: one with a linear functional form and others based on nonparametric artificial neural networks (ANNs). Results show that the framework converges robustly across different fixed‐effect and random‐effect specifications. Importantly, the residual correlation structures emerging from the multivariate estimations are consistent with established empirical correlation models. A key contribution of this study is the unified, one‐stage estimation of median predictions, multiple uncertainty components, and correlation structures. Furthermore, the framework is compatible with standard resampling techniques, enabling uncertainty quantification for both model predictions and variance structures. The results, supported by an accompanying open‐source Python package, demonstrate the framework's potential to support the development of flexible GMMs.