Choosing the Composition of Multivariate Relationships in the Nonlinear Regression Problem
D. K. Tyumikov
Keywords: nonlinear regression, multivariate models, variance ratios, additive and multiplicative composition
Pages: 53-61
Abstract
An approach to choosing the composition of a multivariate nonlinear relationship based on pair functions is considered. The approach is based on an analysis of the elements of decomposition of a multiple variance ratio (MVR) into pair variance ratios (PVRs), variance-correlation ratios of coupling effects (VCRCE), and variance ratios of interaction effects (VRIE). It is shown that if such a decomposition contains only PVDR, an additive composition of pair nonlinear functions is recommended. In a decomposition dominated by VRIE, a multiplicative combination is proposed. In a mixed set of variance ratios, mixed combinations are preferred. VCRCE participate in the selection of dominant variables. The identity of the models is determined by MVR. An example illustrating the various combinations of multivariate relationships is given, and variance ratios are analyzed.
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