The piecewise linear model, sometimes called a broken stick, is commonly fitted to data that arise from natural phenomena viewed as containing a threshold or change point. For example, consider the relationship of abundance versus time for a declining fish population. A fisheries manager would often estimate the date of onset by the location of the kink in a broken-stick fit, and use it as a clue to the actual cause of the decline. However, researchers in this and other fields are often tempted to conclude abruptness even when there is seldom solid theory to justify such claims. To address this issue, we use what we call the bent-cable model whose quadratic bend of non-negative width generalizes the kink of a broken stick.
Part 1 of this talk features worked examples of bent-cable regression for assessing abruptness of change in natural phenomena. They demonstrate that data for typical biological phenomena are far too imprecise to support the abruptness notion associated with the broken-stick model. Part 2 discusses the irregularity intrinsic to bent-cable regression, and the practical design conditions that yield regular asymptotics for the estimation problem.