A multilevel nonlinearity study design

A nonlinear multilevel approach to investigate nonlinearity in relations is presented, based on nonlinear feedforward networks, and indicates strong obscuring of non linearity due to noise.

Abstract

Multilevel models are designed to deal with studies on data that contain hierarchical structures and are becoming increasingly important in many fields of research. Since they are limited to parametric models, in practice only linear multilevel models are used. We present a nonlinear multilevel approach to investigate nonlinearity in relations. This model is based on nonlinear feedforward networks. Furthermore, the proposed multilevel model enables one to study how errors in measurements may obscure nonlinear relations. An imaginary dataset was generated as an example, based on an epidemiological model; and with this dataset the effect of noise on nonlinear relations was studied, using the proposed multilevel model. This simulation confirms the applicability of the multilevel nonlinearity study and indicates strong obscuring of nonlinearity due to noise.