The Overlooked Importance of Constants Added in Log Transformation of Independent Variables with Zero Values: A Proposed Approach for Determining an Optimal Constant

Abstract

ABSTRACTTransformation of variables has been recommended for addressing deviations from regression assumptions of normality, constant variance, and linearity. Though the log transformation has become the most commonly used transformation in biomedical, public health, and psychosocial research, challenges arise when the variable to be transformed has zero values. One suggested solution is adding constants. The constants added are usually chosen based on what is commonly used in a given field and have been shown to affect statistical inference. In this article, we examine the effect of the added constants in log transformation of independent variables and propose an approach to improve the choice of the added constant by considering it as a parameter to be estimated simultaneously with other model parameters. We reveal that the constants that are added to deal with zero values when log-transforming independent variables have profound effects on the goodness-of-fit of regression models. Arbitrary chosen values for constants may therefore result in poor fitting models. In contrast, considering the added constant as a model parameter optimizes the model fit.