Criteria for estimating the variance function used in the asymptotic quasi-likelihood approach

The estimation of the variance function of a linear regression model used in the asymptotic quasi-likelihood approach is considered. It is shown that the variance function used in the determination of the asymptotic quasi-likelihood estimates encompasses the variance functions commonly found in the literature. Selection criteria of the most appropriate estimate of the variance function for given data are established. These criteria are based on a graphical technique and a chi-squared test.     

Analysis of experiments using the asymptotic quasi-likelihood approach

Comparison of treatment effects in an experiment is usually done through analysis of variance under the assumption that the errors are normally and independently distributed with zero mean and constant variance. The traditional approach in dealing with non-constant variance is to apply a variance stabilizing transformation and then run the analysis on the transformed data. In this approach, the conclusions of analysis of variance apply only to the transformed population. In this paper, the asymptotic quasi-likelihood method is introduced to the analysis of experimental designs. The weak assumptions of the asymptotic quasi-likelihood method make it possible to draw conclusions on heterogeneous populations without transforming them. This paper demonstrates how to apply the asymptotic quasi-likelihood technique to three commonly used models. This gives a possible way to analyse data given a complex experimental design.