Abstract
A modified ANOVA setting is used to develop a one degree of freedom test for intrinsic curvature effect. The approach provides clear cutoffs for the measurement of intrinsic curvature effect. It is shown that the significance of the correction factor itself and its usefulness in correcting a global test based on linear approximation are distinct elements. They depend on the local frame of reference provided by the model-data combination and null hypothesis considered.
Highlights
Nonlinear models are applied in many areas of science, often reflecting scientific theory, for example in toxicology, cancer research and econometrics
Procedures for statistical inference are typically described in terms of Wald statistics, corresponding to the use of a local linear approximation of the regression surface, or likelihood based regions corresponding to use of the likelihood function and likelihood ratio (Seber and Wild, 1989)
It is only in this direction that the curvature of the regression surface is relevant to modification of the relevant sums of squares and the determination of the Wald statistic value based on the assumed null value η(x; β0) and the m.l.e. η(x; β).The linear approximation here is taken at β = β0 not at the maximum likelihood value, giving the analysis a focused local aspect
Summary
Nonlinear models are applied in many areas of science, often reflecting scientific theory, for example in toxicology, cancer research and econometrics. The presence of significant nonlinearity or local curvature in the regression surface when a linear approximation is used creates a type of model mis-specification and can affect the accuracy of p-values and confidence regions (Donaldson and Schnabel, 1987). This requires some correction to the relevant test statistics, typically based on squared lengths and related sums of squares. Note that nonlinear models often represent discipline specific theories or solutions to differential equations and have a specified structure and parameterization.
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