Recommendations for use of retransformation methods in regression models used to estimate sediment loads ("The bias correction problem") In Reply Refer To: December 31, 1992 Mail Stop 415 OFFICE OF SURFACE WATER TECHNICAL MEMORANDUM NO. 93.08 Subject: Recommendations for use of retransformation methods in regression models used to estimate sediment loads ("The bias correction problem") Estimates of suspended-sediment loads are often derived from periodic data using regression models. Many of the regression models involve transformation into logarithmic space but final results are often required to be in the original engineering units; therefore, retransformation of load data is needed. This retransformation involves a "bias correction problem" that has received much attention. Systems Analysis Technical Report 91.01, "Estimating Loads from Periodic Records," by T. A. Cohn and E. J. Gilroy, identifies the problem of bias in computing sediment loads from transport curves and describes methods of handling the bias correction. The authors recommended the Minimum Variance Unbiased Estimator (MVUE) for use when the errors can be assumed to be normally distributed and they recommend the Smearing Estimator (SM) when a non-normal error distribution is identified. The Office of Surface Water endorses these recommendations and notes that they give considerable flexibility to the analyst to determine the most appropriate method for a given situation. Although the focus of this memorandum is on an appropriate bias correction factor, it is well worth emphasizing that mis- specification of the appropriate regression model in a particular situation can yield sizable errors and render any care taken in correcting for bias as a useless exercise. Attached to this memorandum is a short example calculation for loads showing the application of three methods of bias correction: 1. The Quasi-Maximum Likelihood Estimator (QMLE) [Ferguson method], 2. The Minimum Variance Unbiased Estimator (MVUE), and 3. The Smearing Estimator (SM). The Ferguson method is not recommended for use but is presented in the example because it has been used extensively in the past. The example also contains a FORTRAN program which is needed to implement the MVUE method. The report by T. A. Cohn and E. J. Gilroy also addresses issues such as transforming the response variable, form of the model to be used, and other covariates to consider (e.g., time trends, seasonality, flow dependence, and non-linear terms). Although not covered in depth in this report, attention is given to sampling questions such as; are data representative of target population, what are the dominant physical processes operating at the sites in question, and are there outliers in the data set? Some background in statistical analysis and terminology is needed to fully comprehend the report. In particular, the reader should be familiar with statistical notation and have an understanding of standard statistical analysis and simple linear regression. Charles W. Boning, Chief Office of Surface Water Attachment WRD DISTRIBUTION: A, B, FO, PO