Joint models of multivariate longitudinal outcomes and discrete survival data with INLA: An application to credit repayment behaviour
针对信用风险预测中时变协变量内生性问题，提出基于INLA的联合模型，处理双变量内生协变量与离散生存数据，并通过模拟和消费贷款数据验证其预测优势。
Survival models with time-varying covariates (TVCs) are widely used in the literature on credit risk prediction. 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 framework 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.