Goodness of fit in nonlinear dynamics: misspecified rates or misspecified states? (English) Zbl 1397.62269

Hooker, Giles; Ellner, Stephen P.

Ann. Appl. Stat. 9, No. 2, 754-776 (2015).

Summary: This paper introduces diagnostic tests for the nature of lack of fit in ordinary differential equation models (ODEs) proposed for data. We present a hierarchy of three possible sources of lack of fit: unaccounted-for stochastic variation, misspecification of functional forms in rate equations, and omission of dynamic variables in the description of the system. We represent lack of fit by allowing a parameter vector to vary over time, and propose generic testing procedures that do not rely on specific alternative models. Instead, different sources for lack of fit are characterized in terms of nonparametric relationships among latent variables. The tests are carried out through a combination of residual bootstrap and permutation methods. We demonstrate the effectiveness of these tests on simulated data and on real data from laboratory ecological experiments and electro-cardiogram data.

MSC:

62J20	Diagnostics, and linear inference and regression
62G09	Nonparametric statistical resampling methods
62P10	Applications of statistics to biology and medical sciences; meta analysis

Keywords:

differential equation; diagnostics; goodness of fit; attractor reconstruction; bootstrap; nonparametric relationships

Software:

mgcv; PhysioToolkit

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