Nonlinear Mixed Effects Modeling of Deterministic and Stochastic Dynamical Systems in Wolfram Mathematica⁎This work has been partly founded by the Swedish Foundation for Strategic Research by the project Hierarchical Mixed Effects Modeling of Dynamical Systems (Grant no. AM13-0046). Issue 7 (2021)

• Record Type: Journal Article
• Authors: Leander, Jacob; Almquist, Joachim; Johnning, Anna; Larsson, Julia; Jirstrand, Mats
• Is Part Of: IFAC-PapersOnLine. Volume 54:Issue 7(2021)
• Page Start: 409
• Page End: 414
• Publication Date: 2021
• Subjects: Nonlinear mixed effects -- Dynamical system models -- Ordinary differential equations -- Stochastic differential equations -- Wolfram Mathematica -- First-order conditional estimation (FOCE) -- Modeling software; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2021.08.394
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: Nonlinear mixed effects (NLME) modeling is a powerful tool to analyze time-series data from several individual entities in an experiment. In this paper, we give a brief overview of a package for NLME modeling in Wolfram Mathematica entitled NLMEModeling, implementing the first-order conditional estimation method with sensitivity equation-based gradients for parameter estimation. NLMEModeling supports mixed effects modeling of dynamical systems where the underlying dynamics are described by either ordinary or stochastic differential equations combined with observation equations with flexible observation error models. Moreover, NLMEModeling is a user-friendly package with functionality for parameter estimation, model diagnostics (such as goodness-of-fit analysis and visual predictive checks), and model simulation. The package is freely available and provides an extensible add-on to Wolfram Mathematica.