A Computationally Efficient Correlated Mixed Probit Model for Credit Risk Inference

Abstract

Summary Mixed probit models are widely applied in many fields where prediction of a binary response is of interest. Typically, the random effects are assumed to be independent but this is seldom so for many real applications. In the credit risk application that is considered in the paper, random effects are present at the level of industrial sectors and they are expected to be correlated because of interfirm credit links inducing dependences in the firms’ risk to default. Unfortunately, existing inferential procedures for correlated mixed probit models are computationally very intensive already for a moderate number of effects. Borrowing from the literature on large network inference, we propose an efficient expectation–maximization algorithm for unconstrained and penalized likelihood estimation and derive the asymptotic standard errors of the estimates. An extensive simulation study shows that the approach proposed enjoys substantial computational gains relative to standard Monte Carlo approaches, while still providing accurate parameter estimates. Using data on nearly 64000 accounts for small and medium‐sized enterprises in the UK in 2013 across 13 industrial sectors, we find that accounting for network effects via a correlated mixed probit model increases significantly the default prediction power of the model compared with conventional default prediction models, making efficient inferential procedures for these models particularly useful in this field.

Reversing Transcriptome-Wide Association Studies to improve expression Quantitative Trait Loci associations

“…This allowed us to build EMBER from a linear regression model, although further improvements may be possible if more sophisticated multi-SNP models such as BLUP can be incorporated. These designs may present additional challenges: for example, a model combining EMBER and BLUP would require features from both the probit and linear mixed models, and while such algorithm have been proposed [27,28], these typically require performing operations on the full covariance matrix of random effects, which is increasingly impractical for large GWAS.…”