A ratio estimator for bias correction in logarithmic regressions

Abstract

It is recommended that the proportional bias in logarithmic regressions be estimated from the ratio of the arithmetic sample mean and the mean of the back-transformed predicted values from the regression. Under the assumption of a lognormal distribution of errors, the conditions for application of this ratio estimator are optimal. A simulated sampling study has shown that this method gives more reliable results than the methods recommended by Baskerville (G.L. Baskerville. 1972. Can. J. For. Res. 2: 49–53) or that derived by Finney (D.J. Finney. 1941. J. R. Stat. Soc. 7(Suppl): 55–61). The new method is also less sensitive to departures from the assumption of a lognormal distribution than the other two methods.