Tests of transformation in nonlinear regression

This paper presents three versions of the Lagrange multiplier (LM) tests of transformation in nonlinear regression: (i) LM test based on expected information, (ii) LM test based on Hessian, and (iii) the LM test based on gradient. All three tests can be easily implemented through a nonlinear least squares procedure. Simulation results show that, in terms of finite sample performance, the LM test based on expected information is the best, followed by the LM test based on Hessian and then the LM test based on gradient. The LM test based on gradient can perform rather poorly. An example is given for illustration.