Most change-point models assume that the response is continuous or cross sectional binary. However, in many public health problems, the data is longitudinal binary. There are few studies of change-point problems for longitudinal outcomes. This paper describes a flexible change-point model which includes random-effects and takes into account the difference between various individuals in longitudinal binary data. A transition function is used to make the linear-linear logistic model differentiable at the change-point. The location of the change-point is estimated using the maximum likelihood method. Adjustment of the transition parameter from zero to one controls the sharpness of the transition. The performance of this estimation procedure is illustrated with simulations using SAS/proc nlmixed and a detailed analysis of data relating hormone levels and ovary functions based on data from the Obstetrics and Gynecology Hospital, Medical Center of Fudan University.
For partial linear model Y = X τ β 0 + g 0(T) + ∈ with unknown β 0 ∈ ? d and an unknown smooth function g 0, this paper considers the Huber-Dutter estimators of β 0, scale σ for the errors and the function g 0 approximated by the smoothing B-spline functions, respectively. Under some regularity conditions, the Huber-Dutter estimators of β 0 and σ are shown to be asymptotically normal with the rate of convergence n ?1/2 and the B-spline Huber-Dutter estimator of g 0 achieves the optimal rate of convergence in nonparametric regression. A simulation study and two examples demonstrate that the Huber-Dutter estimator of β 0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator.
