Segmented Bent-Cable Regression Model for Changepoint Data Analysis

Shahedul A. Khan () and Shakhawat Hossain ()
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Shahedul A. Khan: University of Saskatchewan
Shakhawat Hossain: University of Winnipeg

Sankhya B: The Indian Journal of Statistics, 2025, vol. 87, issue 2, No 13, 759-790

Abstract: Abstract Data showing a trend that characterizes a change are commonly observed in many areas of study including biological, medical and environmental applications. We consider here modeling time-series changepoint data, with the relationship between the response and time being non-linear, showing an incoming and an outgoing phase, both of which are linear or piecewise linear, joined by a curved transition. Bent-cable regression is an appealing statistical tool to characterize such trajectories, modeling the transition between the incoming and outgoing phases with a quadratic bend. The underlying assumption is that the slopes of both the incoming and outgoing phases are each constant, which may not be appropriate in many applications. For example, the incoming and/or the outgoing phase may exhibit a change in slope over time so that two slope parameters are necessary to adequately model each of these two phases. We propose a segmented bent-cable model to describe a changepoint trajectory using five phases: a piecewise linear model with one break-point in the incoming phase, followed by a quadratic transition and another piecewise linear relationship with one break-point to characterize the outgoing phase. The model has a simple structure with greatly interpretable regression coefficients. The properties of the proposed model are discussed and a Bayesian approach for inference is proposed. The application of the proposed methodology is demonstrated with applications to three data sets taken from environmental science and economics. This study suggests that the proposed model can be valuable in adequately describing changepoint data with a wide range of characteristics.

Keywords: Abrupt and gradual transition; Bayesian inference; Bent-cable regression; Changepoint data; Segmented regression model; Primary 62J02; Secondary 62M10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13571-025-00367-x

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