Journal of Data Science

Summary: Longitudinal binary data often arise in clinical trials when repeated measurements, positive or negative to certain tests, are made on the same subject over time. To account for the serial corre lation within subjects, we propose a marginal logistic model which is implemented using the Generalized Estimating Equation (GEE) ap proach with working correlation matrices adopting some widely used forms. The aim of this paper is to seek some robust working correla tion matrices that give consistently good fit to the data. Model-fit is assessed using the modified expected utility of Walker & Guti´errez Pe˜na (1999). To evaluate the effect of the length of time series and the strength of serial correlation on the robustness of various working correlation matrices, the models are demonstrated using three data sets containing respectively all short time series, all long time series and time series of varying length. We identify factors that affect the choice of robust working correlation matrices and give suggestions under different situations.

The shape parameter of a symmetric probability distribution is often more difficult to estimate accurately than the location and scale parameters. In this paper, we suggest an intuitive but innovative matching quantile estimation method for this parameter. The proposed shape parameter estimate is obtained by setting its value to a level such that the central 1-1/n portion of the distribution will just cover all n observations, while the location and scale parameters are estimated using existing methods such as maximum likelihood (ML). This hybrid estimator is proved to be consistent and is illustrated by two distributions, namely Student-t and Exponential Power. Simulation studies show that the hybrid method provides reasonably accurate estimates. In the presence of extreme observations, this method provides thicker tails than the full ML method and protect inference on the location and scale parameters. This feature offered by the hybrid method is also demonstrated in the empirical study using two real data sets.