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Abstract:
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Likelihood ratio tests are used to check a proposed nonlinear regression model for lack of fit. In particular, cluster-based lack-of-fit tests for nonreplicated linear models, as presented by Christensen (1989,1991), have been generalized for nonlinear models with additive error. In addition, cluster selection is based on a maximin power clustering criterion given by Miller, Neill and Sherfey (1998,1999) adapted to the nonlinear case. Simulation results for a two parameter exponential model with one predictor and normal errors indicate that the testing procedure has good power for detecting between-cluster lack-of-fit. Notably, the simulation study shows that for such good power, cluster selection varies according to different points along the expectation surface. The constructed full model uses the convexity of a class of fuzzy clusterings to form a continuous alternative model.
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