Regression - hockey sticks, broken sticks, piecewise, change points

Abstract

A simple regression analysis assumes that the change in response is the same across the range of X values. In some cases, a model where the slope changes in different parts of the X space may be biologically more realistic. This chapter examines two cases of fitting regression lines with breaks in the slope. In the first case, the location of the change in slope is known in advance; the second cases also estimates the location of the change, also known as the change point problem. The examples in this chapter look at cases with a single change point – the extension to multiple change points (both known and unknown) is straightforward. Similarly, the change from linear to quadratic lines is also straightforward. A related method, a spline fit to the data, where a flexible curve is fit between (evenly) spaced knot points that is a like a non-parametric curve fit is explored in a different chapter.