Milliken and Graybill (1970) proposed a widely applicable test of a nonlinear specification in a regression model. In this note I show that their ad hoc procedure is equivalent to a score test and hence asymptotically equivalent to tests based on the maximum likelihood ratio.
St. Laurent, R. T., & St Laurent, R. T. (1990). The equivalence of the Milliken-Graybill procedure and the score test. The American Statistician, 44, 36-37. https://doi.org/10.1080/00031305.1990.10475689