POWER-TRANSFORMATION MODEL TO ADDITIVITY IN REGRESSION

概要

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We study the properties of the power-transformation model to improve the non-additivity in regression, proposed by Goto (1992). This power additive transformation (PAT) model is an extension of the Box and Cox power transformation (BCPT) model and then includes the Bleasdale's simplified model and the one-compartment model as special cases. We describe the procedure to obtain the maximum likelihood estimates of the PAT model and discuss some issues in the maximum likelihood estimation, especially the consistency of the estimates and the effect of the error variance on the parameter estimation. We also provide two examples to illustrate the aspect of the PAT model, compared with the BCPT model. The results suggest that the PAT model provides reasonable transformations for improving the non-additivity in the data and is useful for identifying the nonlinear function form even when there is no strong knowledge on the data-generating process.