A posteriori bias correction of three models used for environmental reporting

A plethora of forest models were developed by transforming the dependent variable, which introduces bias if appropriate corrections are not applied when back-transformed. Many recognized models are still biased and the original data sets are no longer available, which suggests ad hoc bias corrections. The present research presents a procedure for bias correction in the absence of needed information from summary statistics. Additionally, we developed a realistic correction of the square root transformation based on a truncated normal distribution. The transformations considered in this study are the logarithm, the square root and arcsine square root. Using simulated data we found that uncorrected back-transformation created biases by as much as 100 percent. The generated data revealed that depending on available information, that bias can still be present after correction. In addition to generated data we corrected the site index of Douglas-fir and ponderosa pine in Oregon USA, tree volume of 27 species from Romania, stand merchantable volume for longleaf pine in Louisiana and East Texas USA, and canopy fuel weight in Washington USA. Using only the available information, the unbiased back-transformed estimates can change from ≤1 percent (i.e. the site index and canopy fuel weight) to ≥⅓ (tree and stand volume).