Two-phase nonlinear regression with smooth transition

A method of estimating parameters of two-phase nonlinear regression with smooth transition between phases is described. It consists of two stages, both utilizing the least square fit. In the first one, each phase is fitted separately and, simultaneously, a transition point is determined. In the second stage, the two phases are joined smoothly by a proper transition function, which depends on the transition point chosen by the grid search. The practical aspects of the method proposed are demonstrated on the data concerning the soil bulk density in dependence on the soil water content.