Ordinal Neural Network Transformation Models: Deep and interpretable regression models for ordinal outcomes

Outcomes with a natural order commonly occur in prediction tasks and oftentimes the available input data are a mixture of complex data, like images, and tabular predictors. Deep Learning (DL) methods are state-of-the-art for image classification tasks but frequently treat ordinal outcomes as unordered and lack interpretability. In contrast, classical ordinal regression models consider the outcome's order and yield interpretable predictor effects but are limited to tabular data. We present ordinal neural network transformation models (ONTRAMs), which unite DL with classical ordinal regression methods. ONTRAMs are a special case of transformation models and trade off flexibility and interpretability by additively decomposing the transformation function into terms for image and tabular data using jointly trained neural networks. We discuss how to interpret model components for both tabular and image data. The proposed ONTRAMs achieve on-par performance with common DL models while being directly interpretable and more efficient in training.