Nonlinear Mixed Effects Modeling of Deterministic and Stochastic Dynamical Systems in Wolfram Mathematica
Paper i proceeding, 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 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.

Wolfram Mathematica

Stochastic differential equations

First-order conditional estimation (FOCE)

Dynamical system models

Nonlinear mixed effects

Ordinary differential equations

Modeling software


Jacob Leander

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Joachim Almquist

AstraZeneca R&D

Anna Johnning

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Julia Larsson

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Mats Jirstrand

Chalmers, Elektroteknik, System- och reglerteknik


2405-8963 (ISSN)

Vol. 54 7 409-414

19th IFAC Symposium on System Identification (SYSID)
Padova, Italy,


Teknisk mekanik

Sannolikhetsteori och statistik




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