Analysis of Nonlinear Regression Models: A Cautionary Note. Dose Response 2005

Regression models are routinely used in many applied sciences for describing the rela-tionship between a response variable and an independent variable. Statistical inferences on the regression parameters are often performed using the maximum likelihood esti-mators (MLE). In the case of nonlinear models the standard errors of MLE are often obtained by linearizing the nonlinear function around the true parameter and by appeal-ing to large sample theory. In this article we demonstrate, through computer simulations, that the resulting asymptotic Wald confidence intervals cannot be trusted to achieve the desired confidence levels. Sometimes they could underestimate the true nominal level and are thus liberal. Hence one needs to be cautious in using the usual linearized stan-dard errors of MLE and the associated confidence intervals