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Non-linear mixed-effects modeling software

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Nonlinear mixed effects models are a special case of regression analysis and a range of different software solutions are available. The statistical properties of nonlinear mixed-effects models make direct estimation by a Gauss–Markov theorem impossible. Nonlinear mixed effects models are therefore estimated according to Maximum Likelihood principles.[1]. Specific estimation methods are applied, such as linearization methods as first-order (FO), first-order conditional (FOCE) or the lapplacian (LAPL), approximation methods such as iterative-two stage (ITS), importance sampling (IMP), stochastic approximation estimation (SAEM) or direct sampling. A special case is use of non-parametric approaches. Furthermore, estimation in limited or full Bayesian frameworks is performed using the Metropolic-Hastings or the NUTS algorithms.[2] Some software solutions focus on a single estimation method, others cover a range of estimation methods and/or with interfaces for specific use cases.

General-purpose software

General (use case agnostic) nonlinear mixed effects estimation software can be covering multiple estimation methods or focus on a single.

Software with multiple estimation methods

  • SAS is a package that is used in the wide statistical community and supports multiple estimation methods from PROC NLMIX
  • Multiple estimation methods are available in the R software system
  • MATLAB provides multiple estimation methods in their nlmefit system[3]

SPSS at the moment does not support non-linear mixed effects methods.[4]

References

  1. ^ Davidian, Marie; Giltinan, David M. (1995-06-01). Nonlinear Models for Repeated Measurement Data. CRC Press. ISBN 978-0-412-98341-2.
  2. ^ Tsiros, Periklis; Bois, Frederic Y.; Dokoumetzidis, Aristides; Tsiliki, Georgia; Sarimveis, Haralambos (2019-04-01). "Population pharmacokinetic reanalysis of a Diazepam PBPK model: a comparison of Stan and GNU MCSim". Journal of Pharmacokinetics and Pharmacodynamics. 46 (2): 173–192. doi:10.1007/s10928-019-09630-x. ISSN 1573-8744.
  3. ^ "Nonlinear mixed-effects estimation - MATLAB nlmefit - MathWorks Benelux". nl.mathworks.com. Retrieved 2022-05-09.
  4. ^ "Does IBM SPSS Statistics offer nonlinear mixed models?". www.ibm.com. 2020-04-16. Retrieved 2022-05-09.
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