On the Selection of Power Transformation Parameters in Regression Analysis

Abstract

In multiple linear regression, there are several classical methods used to estimate the parameters of power transformation models that are used to transform the response variable. Traditionally, these parameters can be estimated using either Maximum Likelihood Estimation or Bayesian methods in conjunction with the other model parameters. In this chapter, attention has been paid to four indicators of the efficiency and reliability of the regressive modeling, and study the possibility of considering them as decision rules through which the optimal power parameter can be chosen. The indicators are the coefficient of determination and p-value of the general linear F-test statistic. Also, the p-value of Shapiro-Wilk test (SWT) statistic for the residual’s normality of the estimated linear regression of the transformed response vector and the estimated nonlinear regression of the original response vector resulting from the back transform of the power Transformation model. Real data were used and a computational algorithm was proposed to estimate the optimal power parameter. The authors concluded that the multiplicity of indicators does not lead to obtaining an optimal single value for the power parameter, but this multiplicity may be useful in fortifying the decision-making ability.