Hyperbolic regression - a model based on two-phase piecewise linear regression with a smooth transition between regimes

An hyperbolic regression model is proposed for two-phase piecawise linear regression with a smooth transition between regines and compared with an altarnative model proposed by Bacon and Watts . The modal may be generalised to a situation in which there are several possible points of transition between the linear regines, each representing some 'critical level' for a particular data set. In particular this way apply when the secon linear regine corresponds to an asymptotic level of the dependent variable