Estimating the transition between two intersecting straight lines

doi:10.1093/biomet/58.3.525

Biometrika 1971 58(3):525-534; doi:10.1093/biomet/58.3.525
© 1971 by Biometrika Trust

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Estimating the transition between two intersecting straight lines

DAVID W. BACON¹ and DONALD G. WATTS²

¹Queen's University Kingston, Ontario
²University of Wisconsin

For experimental data which appear to behave according to twodifferent distinct linear relationships, a general model isproposed which allows for a smooth transition from one linearrégime to the other. The transition is accomplished bya curve incorporating a transition parameter. The special caseof two intersecting straight lines is included in this model.A Bayesian estimation procedure is used to determine the plausibilityof different parameter values. The analysis procedure may beextended to any number of join points and for any linear intersectingfunctions.

Key Words: Discontinuous regression relations • Bayesian estimation of change-point in regression • Two-phase regressions

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