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Mixed-effects ARX model identification of dynamical systems

Abstract : Objectives. With the advent of realtime biotechnologies, most of biological responses measured during in-vitro or in-vivo experiments exhibit non-linear behaviors and mixed effects models are often used to better characterize the responses. Parameter and confidence intervals estimation involve numerical integration, linearization or stochastic approximation algorithms. Instead of modeling the response we propose a method in which each biological process is regarded as a dynamical system with input-ouput variables and cofactors. We show that this approach allows to use classical linear methods. Methods. Firstly, we suppose that the response of each biological unit is the output of a linear time invariant system described by an autoregressive model structure with external input (ARX). The drug administration is considered as the input signal. To account for the variability within and between biological units, we introduce mixed effects in the ARX model. Data are assumed to be recorded at a constant sampling rate. The basic EM algorithm is implemented without approximation to estimate the model parameters under the likelihood function. Moreover, Fisher information matrix is determined by using Louis method. Results. We show how mixed-effects can be introduced in black-box modeling for the identification of a population of dynamic systems. We have determined parameter estimation and confidence intervals of an ARX model structure. We show relevance of the proposed solution in simulation and using real in-vitro data coming from realtime cell impedance measurements. Conclusion. New biotechnologies allow to use system identification models where the response of individuals is seen as the output of a system with unknown parameters. The proposed method suggests that, in some cases, it is possible to use linear mixed-effects estimation methods to characterize non-linear responses.
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Contributor : Thierry Bastogne <>
Submitted on : Tuesday, May 24, 2016 - 10:40:23 AM
Last modification on : Tuesday, March 2, 2021 - 5:12:05 PM


  • HAL Id : hal-01320594, version 1



Levy Batista, Thierry Bastogne, El-Hadi Djermoune. Mixed-effects ARX model identification of dynamical systems. 25th Meeting of the Population Approach Group in Europe, PAGE 2016, Jun 2016, Lisboa, Portugal. pp.PAGE 25 (2016) Abstr 5807. ⟨hal-01320594⟩



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