A comparison of the variance estimation methods for heteroscedastic nonlinear models

Heteroscedasticity is commonly encountered when fitting nonlinear regression models in practice. We discuss eight different variance estimation methods for nonlinear regression models with heterogeneous response variances, and present a simulation study to compare the performance of the eight methods in terms of estimating the standard errors of the fitted model parameters. The simulation study suggests that when the true variance is a function of the mean model, the power of the mean variance function estimation method and the transform-both-sides method are the best choices for estimating the standard errors of the estimated model parameters. In general, the wild bootstrap estimator and two modified versions of the standard sandwich variance estimator are reasonably accurate with relatively small bias, especially when the heterogeneity is nonsystematic across values of the covariate. Furthermore, we note that the two modified sandwich estimators are appealing choices in practice, considering the computational advantage of these two estimation methods relative to the variance function estimation method and the transform-both-sides approach. Copyright © 2016 John Wiley & Sons, Ltd.