Inference for the break point in segmented regression with application to longitudinal data

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 [Biometrika 64 (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.