Threshold regression models are also called two-phase regression, broken-stick regression, split-point regression, structural change models, and regression kink models, with and without interaction terms. Methods for both continuous and discontinuous threshold models are included, but the support for the former is much greater. This package is described in Fong, Huang, Gilbert and Permar (2017)
This package is also hosted on CRAN. The github repository is alway up to date, while the CRAN repository may be several releases behind.