Median regression models for longitudinal exponential data

Nagarajah, Varathan (2012) Median regression models for longitudinal exponential data. Masters thesis, Memorial University of Newfoundland.

[English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (2MB)

Abstract

In independence setup, the quasi-likelihood estimation of the regression parameters involved in the mean function requires only the specification of the mean and variance function of the responses. In the longitudinal setup, one also has to accommodate the underlying correlation structure in order to obtain consistent and efficient regression estimates. Under the independence setup, when the responses follow an asymmetric distribution with a heavy tail, it has been argued in the literature that the regression estimates using mean regression model can be inefficient as compared to those obtained using a median regression model. Subsequently, the median regression models have been extended to study the asymmetric longitudinal data, but the longitudinal correlation of this type of asymmetric data have been computed using the moment estimates for all pairwise correlations. By considering an autoregressive order 1 (AR(l)) model for longitudinal exponential responses, in this thesis, it is 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. It is also argued in the thesis that the quasi-likelihood approach for median regression models may perform the same or worse than the mean regression models unless the data are highly asymmetric such as involving outliers. We illustrate the inference techniques discussed in the thesis by re-analysing the well-known labor pain data.

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