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. 2011 Feb;141(2):1059-1068.
doi: 10.1016/j.jspi.2010.09.011.

Simultaneous Confidence Band for the Difference of Segmented Linear Models

Greg Yothers  1 , Allan R Sampson  2
Affiliations

Simultaneous Confidence Band for the Difference of Segmented Linear Models

Greg Yothers et al. J Stat Plan Inference. 2011 Feb.

Abstract

Consider comparing between two treatments a response variable, whose expectation depends on the value of a continuous covariate in some nonlinear fashion. We fit separate segmented linear models to each treatment to approximate the nonlinear relationship. For this setting, we provide a simultaneous confidence band for the difference between treatments of the expected value functions. The treatments are said to differ significantly on intervals of the covariate where the simultaneous confidence band does not contain zero. We consider segmented linear models where the locations of the changepoints are both known and unknown. The band is obtained from asymptotic results.

Keywords: Segmented linear model; asymptotic simultaneous confidence band; subset selection; treatment comparison.

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Figures

Figure 1
Figure 1
2-segment linear models fit to data from surfactant 1 (circles with solid fit) and surfactant 2 (squares with dashed fit)
Figure 2
Figure 2
Difference in mean response of the 2 models with 95% simultaneous confidence band
See this image and copyright information in PMC

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