# Semi-structured multi-state delinquency model for mortgage default

arXiv: https://arxiv.org/abs/2603.26309 · HTML: https://mlsanity.com/paper/2603.26309/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 42 references that are in the map.
- First posted on arXiv 27 Mar 2026.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Semi-Structured Distributional Regression -- Extending Structured Additive Models by Arbitrary Deep Neural Networks and Data Modalities](https://mlsanity.com/paper/2002.05777/) (2020)
- [deepregression: a Flexible Neural Network Framework for Semi-Structured Deep Distributional Regression](https://mlsanity.com/paper/2104.02705/) (2021)
- [DeepPAMM: Deep Piecewise Exponential Additive Mixed Models for Complex Hazard Structures in Survival Analysis](https://mlsanity.com/paper/2202.07423/) (2022)
- [The Deep Promotion Time Cure Model](https://mlsanity.com/paper/2305.11575/) (2023)
- [Joint model for longitudinal and spatio-temporal survival data](https://mlsanity.com/paper/2311.04008/) (2023)

## Built on by (most cited first, 1 of 1)

- [textttfindr: Transparent and Fair Credit Risk Decisions through Semi-Structured Regressions](https://mlsanity.com/paper/2608.24582/) (2026)

## Abstract (arXiv)

We propose a semi-structured discrete-time multi-state model to analyse mortgage delinquency transitions. This model combines an easy-to-understand structured additive predictor, which includes linear effects and smooth functions of time and covariates, with a flexible neural network component that captures complex nonlinearities and higher-order interactions. To ensure identifiability when covariates are present in both components, we orthogonalise the unstructured part relative to the structured design. For discrete-time competing transitions, we derive exact transformations that map binary logistic models to valid competing transition probabilities, avoiding the need for continuous-time approximations. In simulations, our framework effectively recovers structured baseline and covariate effects while using the neural component to detect interaction patterns. We demonstrate the method using the Freddie Mac Single-Family Loan-Level Dataset, employing an out-of-time test design. Compared with a structured generalised additive benchmark, the semi-structured model provides modest but consistent gains in discrimination across the earliest prediction spans, while maintaining similar Brier scores. Adding macroeconomic indicators provides limited incremental benefit in this out-of-time evaluation and does not materially change the estimated borrower-, loan-, or duration-driven effects. Overall, semi-structured multi-state modelling offers a practical compromise between transparent effect estimates and flexible pattern learning, with potential applications beyond credit-transition forecasting.