Estimating the transition between two intersecting straight lines

Abstract

For experimental data which appear to behave according to two different distinct linear relationships, a general model is proposed which allows for a smooth transition from one linear régime to the other. The transition is accomplished by a curve incorporating a transition parameter. The special case of two intersecting straight lines is included in this model. A Bayesian estimation procedure is used to determine the plausibility of different parameter values. The analysis procedure may be extended to any number of join points and for any linear intersecting functions.