Non-linear regression analysis with errors in both variables: Estimation of co-operative binding parameters

Four different parameter estimation criteria, the geometric mean functional relationship (GMFR), the maximum likelihood (ML), the perpendicular least- squares (PLS) and the non-linear weighted least squares (WLS), were used to fit a model to the observed data when both regression variables were subje ct to error. Performances of these criteria were evaluated by fitting the c o-operative drug-protein binding Hill model on simulated data containing er rors in both variables. Six types of data were simulated with known varianc es. Comparison of the criteria was done by evaluating the bias, the relativ e standard deviation (S.D.) and the root-mean-squared error (RMSE), between estimated and true parameter values. Results show that (1) for data with c orrelated errors, all criteria perform poorly; in particular, the GMFR and ML criteria. For data with uncorrelated errors, all criteria perform equall y well with regard to the RMSE. (2) Use of GMFR and ML lead to lower values far S.D. but higher biases compared with WLS and PLS. (3) WLS performs les s well when equal dispersion is applied to the two observed variables. Copy right (C) 2000 John Wiley & Sons, Ltd.