Simultaneous Diagnostic Methods for the Double Power-Normal Transformation Model

We describe simultaneous diagnostic methods for assessing the influence of an individual case on the estimates of the two transformation parameters in the double power-normal transformation model proposed by Goto, Inoue and Tsuchiya (1987), which attempts simultaneously to achieve the two assumptions of at least approximate normality of the additive errors and linearity or additivity of structure for the expected value of the response in regression analysis. We also consider a simple analogy of the methods discussed by Hinkley and Wang (1988) and Tsai and Wu (1990). Furthermore, we provide a graphical presentation for assessing the degree to which individual cases influence the estimates of the two transformation parameters. Two examples are used to illustrate the proposed method.