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Keywords:

  • Piecewise regression;
  • Spline;
  • Two-phase regression;
  • Broken stick model;
  • Broken line model;
  • Hockey stick model;
  • Profile likelihood;
  • Change point;
  • Mixed model

Abstract

This paper considers inference for the break point in the segmented regression or piece-wise regression model. Standard likelihood theory does not apply because the break point is absent under the null hypothesis. We use results by Davies for this type of non-standard set-up [Biometrika64 (1977), 247–254 and 74 (1987), 33–43] to obtain a test for the null hypothesis of no break point. A confidence interval can be constructed provided replicate data are available. The methods are exemplified using two longitudinal datasets, the one from ecology, the other from pharmacology.