A simple computational procedure is developed for performing a wide variety of model specification tests which are either explicit Lagrange multiplier tests or asymptotically equivalent variants, and thus require estimates under the null hypothesis only. They may be used to test for many types of misspecification in the context of rather general nonlinear models. Our procedure is based on an artificial linear regression, so that the test statistics can easily be calculated using any regression package. This artificial regression can also be used to compute covariance matrix estimates or as part of a nonlinear maximization algorithm. (From the introduction)