Testing for a Breakpoint in Two-Phase Linear and Logistic Regression Models

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.