The object of "data-based" quasi-likelihood analysis is to estimate the variance function from the data itself. Asymmetric power transformations, which are (possibly different) transformations applied to the mean sm; as well as to the observed variable y, are shown to be powerful diagnostic aids for checking first- and second-order model assumptions in the class of quasi-likelihood models. Asymmetric transformations to normality, coupled with the relation between transformation to normality and the variance function in the exponential family is a useful first step in an analysis leading to the optimum data-based variance function. © 1988.
Wixley, R. A. J. (1988). The use of asymmetric power transformation in data-based quasi-likelihood analysis. Computational Statistics and Data Analysis, 7(1), 1–21. https://doi.org/10.1016/0167-9473(88)90012-6