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.