Joint models of multivariate longitudinal outcomes and discrete survival data with INLA: An application to credit repayment behaviour

Survival models with time-varying covariates (TVCs) are widely used in the literature on credit risk pre-diction. However, when these covariates are endogenous, the inclusion procedure has been limited to practices such as lagging these variables or treating them as exogenous. That leads to possible biased estimators (depending on the strength of the exogeneity assumption) and a lack of prediction frame-work that consolidates the joint evolution of the survival process and the endogenous TVCs. The use of joint models is a suitable approach for handling endogeneity, however, it comes at a high computational cost. We propose a joint model for bivariate endogenous TVCs and discrete survival data using integrated nested Laplace approximation (INLA). We illustrate the implementation via simulations and build a model for full-prepayment consumer loans. We also propose a methodology for individual survival prediction using the Laplace method that leads to more accurate approximations than comparable approaches. We evidence the superiority of joint models over the traditional survival approach for an out-of-sample and out-of-time analysis.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Automated summary

Survival models with time-varying covariates (TVCs) are commonly used in credit risk prediction, but the handling of endogeneity in these models is limited. This study proposes a joint model for bivariate endogenous TVCs and discrete survival data using integrated nested Laplace approximation (INLA). The implementation is illustrated through simulations and a model for full-prepayment consumer loans, and a methodology for individual survival prediction is also proposed. The superiority of joint models over traditional survival approaches is demonstrated in an out-of-sample and out-of-time analysis.