Inferences in median regression models for asymmetric longitudinal data: A quasi-likelihood approach

Abstract

In the independence setup, when the responses exhibit high degree of asymmetry, the median regression model is preferred to the mean regression model to obtain consistent and efficient regression estimates. However, when this type of asymmetric data are collected repeatedly over time, developing median regression model for such correlated asymmetric data may not be easy. As a remedy, there exist some studies where the longitudinal correlations of this type of asymmetric data have been computed using the moment estimates for all pairwise correlations and these correlations of repeated (multi-dimensional) data used to develop a median based quasi-likelihood approach for estimation of the regression effects. By considering an autoregressive order 1 (AR(1)) model for longitudinal exponential responses, in this paper, it is however, demonstrated that the existing pairwise estimates of correlations under median regression model may yield inefficient estimates as compared to the simpler independence assumption based estimates. We illustrate the inference techniques discussed in the paper by reanalyzing the well-known labor pain data.