An Alternative Approach to Fitting Models When Re-Expression of the Response is Useful

Abstract

It is common practice to mathematically transform or re-express data (e.g., logs, reciprocals, square roots) to ensure that the assumptions of normal distribution statistics are more closely satisfied. Re-expression is a problem in some instances because the original scale of measurement is not used and the relationship between the response and predictor variables is often not simplified. It is shown that these limitations can be avoided by applying the re-expression function to both the response and the proposed model form and estimating the model parameters by nonlinear least squares techniques. The model form is not altered, the units of the predicted values and uncertainty are those of the original measurement scale, and the modeling assumptions of homogeneous variance and normal distribution of observation errors are satisfied. Several examples are included to illustrate the variety of circumstances in which this procedure can be useful.

• Box-Cox Estimation
• Nonlinear Least Squares
• Nonnormality
• Power-normal Model
• Regression Analysis
• Transformations

Additional information

Notes on contributors

Ronald D. Snee

Dr. Snee is Consultant Supervisor in the Gulf Regional Office of the Engineering Department. He is a Fellow of ASQC.