Testing change-point in logistic models with covariate measurement error

We test the presence of a change of slope in a logistic regression model with covariate measured with errors. Under the null hypothesis of no change-point, estimation of a single intercept and slope can be carried out straightforwardly by various conditional score based methods. If the alternative hypothesis holds and indeed there exists a change-point, estimation becomes more challenging, nevertheless it can still be carried through via semiparametric procedures. However, this does not warrantee a score type of testing procedure due to a degeneration of the estimating equation for the change-point location under the null. The usual Wald type tests fail as well due to another degeneration caused by the singularity of the information matrix. We propose a Wald type test without requiring to estimate the change-point location. Numerical results show the satisfying performance of the proposed testing procedure in terms of both level precision and power.