Correction for bias of models with lognormal distributed variables in absence of original data

Abstract

The logarithmic transformation of the dependent variables for models developed using regression analysis induces bias that should be corrected, regardless its magnitude. The simplest correction for bias was proposed by Sprugel (1983), which basically multiplies the back-transformed estimates with the constant value of exponential of half the variance of the errors of the logarithmically transformed variable. While this correction is fast and easy to implement does not supplies estimates of the variability existing in the original data. Consequently, a procedure based on generated data was developed to provide unbiased estimates for both attribute of interest and variability existing along the model. The procedure reveals that valid estimates can be obtained if large number of values is generated (e.g., 5000 values/x). The procedures supplies accurate estimates for the attribute of interest and its variability, but encounters significant data processing difficulties for models with more than one predictor variable. Nevertheless, irrespective the number of predictor of variables and magnitude of the correction factor computed by Sprugel, the estimates determined using logarithmic transformations should be corrected for bias, to avoid cumulated errors or chaotic effects associated with nonlinear models.