Haybach, G. and Küchenhoff, Helmut
Testing for a Breakpoint in Two-Phase Linear and Logistic Regression Models.
Collaborative Research Center 386, Discussion Paper 77
In many practical problems, it is of interest to check whether a functional relationship between an explanatory and a response variable remains unchanged over the whole domain of the explanatory variable or whether the functional form changes at certain unknown points, the so-called breakpoints. Thus, testing for the existence of a breakpoint is often an essential task. In this paper, we consider likelihood-ratio tests for different regression models such as broken line and threshold models. The problem related to the use of likelihood-ratio tests in this context concerns the determination of the null distribution of the likelihood-ratio statistic which has not been solved yet analytically. It is shown by means of Monte-Carlo experiments that the proposals of a limiting distribution discussed in the literature often yield unreliable results. It is therefore recommended to determine appropriate critical values by simulating the null distribution according to the data situation under investigation.