Joint model for longitudinal and spatio-temporal survival data

Abstract: In credit risk analysis, survival models with fixed and time-varying covariates are widely used to predict a borrower's time-to-event. When the time-varying drivers are endogenous, modelling jointly the evolution of the survival time and the endogenous covariates is the most appropriate approach, also known as the joint model for longitudinal and survival data. In addition to the temporal component, credit risk models can be enhanced when including borrowers' geographical information by considering spatial clustering and its variation over time. We propose the Spatio-Temporal Joint Model (STJM) to capture spatial and temporal effects and their interaction. This Bayesian hierarchical joint model reckons the survival effect of unobserved heterogeneity among borrowers located in the same region at a particular time. To estimate the STJM model for large datasets, we consider the Integrated Nested Laplace Approximation (INLA) methodology. We apply the STJM to predict the time to full prepayment on a large dataset of 57,258 US mortgage borrowers with more than 2.5 million observations. Empirical results indicate that including spatial effects consistently improves the performance of the joint model. However, the gains are less definitive when we additionally include spatio-temporal interactions.