Transition Regression for Continuous Data

Reto Stauffer, University of Innsbruck

Co-authors: Reto Stauffer, University of Innsbruck; Nikolaus Umlauf, University of Innsbruck

Abstract: Transition models are widely recognized for their flexibility in count data regression and are commonly applied in ordinal regression, where they are also known as continuation ratio models. The core concept involves modeling transition probabilities–specifically, the conditional probability of observing counts exceeding a given threshold. These probabilities can be estimated using standard binary regression methods with an augmented dataset, enabling the use of any software designed for binary response models.

In this paper, we extend the application of transition models to continuous data by employing a slicing technique that transforms continuous observations into count-like data. This approach facilitates the estimation of full probabilistic models, including distributional and quantile regression, using simple binary regression methods. The proposed method is highly adaptable and can seamlessly accommodate complex data structures, such as excess zeros and non-standard distributions. We illustrate the robustness and utility of this approach through an application to precipitation climatologies in Ireland, demonstrating its potential for broader applications in probabilistic modeling.