Joint model for longitudinal and spatio-temporal survival data
Victor Medina-Olivares Finn Lindgren Raffaella Calabrese Jonathan Crook
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.