Feasible computation of the generalized linear mixed models with application to credit risk modelling

Sammanfattning: This thesis deals with developing and testing feasible computational procedures to facilitate the estimation of and carry out the prediction with the generalized linear mixed model (GLMM) with a scope of applying them to large data sets. The work of this thesis is motivated from an issue arising in credit risk modelling. We have access to a huge data set, consisting of about one million observations, on credit history obtained from two major Swedish banks. The principal research interest involved with the data analysis is to model the probability of credit defaults by incorporating the systematic dependencies among the default events. In order to model the dependent credit defaults we adopt the framework of GLMM which is a popular approach to model correlated binary data. However, existing computational procedures for GLMM did not offer us the flexibility to incorporate the desired correlation structure of defaults events. For the feasible estimation of the GLMM we propose two estimation techniques being the fixed effects (FE) approach and the two-step pseudo likelihood approach (2PL). The preciseness of the estimation techniques and their computational advantages are studied by Monte-Carlo simulations and by applying them to the credit risk modelling. Regarding the prediction issue, we show how to apply the likelihood principle to carry out prediction with GLMM. We also provide an R add-in package to facilitate the predictive inference for GLMM.