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

ABSTRACT

Transformation 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.

KEYWORDS:

• Goodness of fit
• Linearity assumption
• Regression
• Started logarithm

Acknowledgments

The authors thank the Pure North S'Energy Foundation for allowing their data to be analyzed for the purpose of this article. They specifically thank Peter Tran and Ken Fyle for management and validation of the Foundation's data. P.J.V. holds a Canada Research Chair in Population Health, an Alberta Research Chair in Nutrition and Disease Prevention, and an Alberta Innovates Health Scholarship. The funding for the Canada Research Chair is provided through the Canadian Institutes for Health Research to the University of Alberta. The Alberta Research Chair is awarded by the School of Public Health at the University of Alberta through a thematic research contract with the Pure North S'Energy Foundation. The Alberta Innovates Health Scholarship is funded by the Alberta provincial government through Alberta Innovates Health Solutions to the University of Alberta.

Ethical approval

The Human Research Ethics Board of the University of Alberta approved the present research.

Additional information

Funding

School of Public Health at the University of Alberta.