A Profile-Based Approach to Parametric Sensitivity Analysis of Nonlinear Regression Models

Predictions from a nonlinear regression model are subject to uncertainties propagated from the estimated parameters in the model. Parameters exerting the strongest influence on model predictions can be identified by a sensitivity analysis. In this article, a new parametric sensitivity measure is introduced, based on the profiling algorithm developed by Bates and Watts for constructing likelihood intervals for the individual parameters in nonlinear regression models. In contrast with traditional sensitivity coefficients, this profile-based sensitivity measure accounts for both correlation structure among the parameters and model nonlinearity. It also provides sensitivity information over wide ranges of parameter uncertainties. Application of the proposed approach is illustrated with three examples.

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