Inferences in Binary Dynamic Fixed Models in a Semi-parametric Setup

In a longitudinal setup, the so-called generalized estimating equations approach was a popular inference technique to obtain efficient regression estimates until it was discovered that this approach may in fact yield less efficient estimates than an independence assumption-based estimating equation approach. In this paper, we revisit this inference issue in a semi-parametric longitudinal setup for binary data and find that the semi-parametric generalized estimating equations also encounter similar efficiency drawbacks when compared with independence assumption-based approach. This makes the generalized estimating equations approach unacceptable for correlated data analysis. We analyze the repeated binary data by fitting a semi-parametric binary dynamic model. The non-parametric function and the regression parameters involved in the semi-parametric regression function are estimated by using a semi-parametric generalized quasi-likelihood and a semi-parametric quasi-likelihood approach, respectively, whereas the dynamic dependence, that is, the correlation index parameter of the model is estimated by a semi-parametric method of moments. Asymptotic and finite sample properties of the estimators are discussed. The proposed model and the estimation methodology are also illustrated by reanalyzing the well-known respiratory disease data.