The relative curvature measures of nonlinearity proposed by Bates and Watts (1980) are extended to an arbitrary subset of the parameters in a normal, nonlinear regression model. In particular, the subset curvatures proposed indicate the validity of linearization-based approximate confidence intervals for single parameters. The derivation produces the original Bates-Watts measures directly from the likelihood function. When the intrinsic curvature is negligible, the Bates-Watts parameter-effects curvature array contains all information necessary to construct curvature measures for parameter subsets.
"Curvatures for Parameter Subsets in Nonlinear Regression." Ann. Statist. 14 (4) 1399 - 1418, December, 1986. https://doi.org/10.1214/aos/1176350166