Fast Estimation of Regression Parameters in a Broken-Stick Model for Longitudinal Data

Estimation of change-point locations in the broken-stick model has significant applications in modeling important biological phenomena. In this article, we present a computationally economical likelihood-based approach for estimating change-point(s) efficiently in both cross-sectional and longitudinal settings. Our method, based on local smoothing in a shrinking neighborhood of each change-point, is shown via simulations to be computationally more viable than existing methods that rely on search procedures, with dramatic gains in the multiple change-point case. The proposed estimates are shown to have n$\sqrt{n}$-consistency and asymptotic normality—in particular, they are asymptotically efficient in the cross-sectional setting—allowing us to provide meaningful statistical inference. As our primary and motivating (longitudinal) application, we study the Michigan Bone Health and Metabolism Study cohort data to describe patterns of change in log estradiol levels, before and after the final menstrual period, for which a two change-point broken-stick model appears to be a good fit. We also illustrate our method on a plant growth dataset in the cross-sectional setting. Supplementary materials for this article are available online.