Inference on Segmented Polynomial Models

Abstract

Segmented polynomial regression models with unknown change-points are used in a wide variety of biological settings. The application that stimulated this work uses a segmented polynomial model to examine the optimal hematocrit hypothesis. We discuss problems in the fitting of these models and compare, by simulation, two methods of inference in these models: that based on the chi-squared approximation to the distribution of the likelihood ratio statistic and that based on the asymptotic normality of the least-squares estimates. The results show that, of the two, only the likelihood ratio statistic produces reliable inference concerning the change-point.