Nonlinear Mixed Effects Modeling of Deterministic and Stochastic Dynamical Systems in Wolfram Mathematica

J. Leander, J. Almquist, A. Johnning, J. Larsson, M. Jirstrand. IFAC-PapersOnLine Vol. 54, Issue 7, 2021, Pages 409-414. Online 15 September, 2021.


Nonlinear mixed effects (NLME) modeling is a powerful tool to analyze timeseries 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 eff ects modeling of dynamical systems where the underlying dynamics are described by either ordinary or stochastic diff erential 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.

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