Nonlinear mixed-effects model Nonlinear mixed-effects models constitute a class of statistical models generalizing linear mixed-effects models. Like linear mixed-effects models, they are particularly useful in settings where there are multiple measurements within the same sta ...

s are a special case of regression analysis for which a range of different

software Software consists of computer programs that instruct the Execution (computing), execution of a computer. Software also includes design documents and specifications. The history of software is closely tied to the development of digital comput ...

solutions are available. The statistical properties of nonlinear mixed-effects models make direct estimation by a BLUE estimator impossible. Nonlinear mixed effects models are therefore estimated according to

Maximum Likelihood In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed stati ...

principles. Specific estimation methods are applied, such as linearization methods as first-order (FO), first-order conditional (FOCE) or the laplacian (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 Thomas Bayes ( ; c. 1701 – 1761) was an English statistician, philosopher, and Presbyterian minister. Bayesian ( or ) may be either any of a range of concepts and approaches that relate to statistical methods based on Bayes' theorem Bayes ...

frameworks is performed using the Metropolis-Hastings or the

NUTS Nut often refers to: * Nut (fruit), fruit composed of a hard shell and a seed * Nut (food), a dry and edible fruit or seed, including but not limited to true nuts * Nut (hardware), fastener used with a bolt Nut, NUT or Nuts may also refer to: A ...

algorithms. 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 open source software system, such as nlme. *

MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementat ...

provides multiple estimation methods in their nlmefit system.

SPSS SPSS Statistics is a statistical software suite developed by IBM for data management, advanced analytics, multivariate analysis, business intelligence, and criminal investigation. Long produced by SPSS Inc., it was acquired by IBM in 2009. Versi ...

at the moment does not support non-linear mixed effects methods.

Software dedicated to a single estimation method

WinBUGS WinBUGS is statistical software for Bayesian analysis using Markov chain Monte Carlo (MCMC) methods. It is based on the BUGS ( Bayesian inference Using Gibbs Sampling) project started in 1989. It runs under Microsoft Windows, though it can also ...

is an implementation of the Metropolis-Hastings method for Bayesian analysis. * Stan is open source software that implements the NUTS algorithm.

Software dedicated to pharmacometrics

The field of

pharmacometrics Pharmacometrics is a field of study of the methodology and application of models for disease and pharmacological measurement. It uses mathematical models of biology, pharmacology, disease, and physiology to describe and quantify interactions between ...

relies heavily on nonlinear mixed effects approaches and therefore uses specialized software approaches. As with general-purpose software, implementations of both single or multiple estimation methods are available. This type of software relies heavily on ODE solvers.

Software with multiple estimation methods

* NONMEM is the most widely used software in the field of pharmacometics. * Phoenix implements multiple estimation methods in a graphical user interface. * Pumas implements multiple estimation methods in the

julia Julia may refer to: People *Julia (given name), including a list of people with the name *Julia (surname), including a list of people with the name *Julia gens, a patrician family of Ancient Rome *Julia (clairvoyant) (fl. 1689), lady's maid of Qu ...

language. * nlmixr/nlmixr2 is a suite interfaced in R that implements FOCE and SAEM. * ADAPT and S-ADAPT implement multiple estimation methods in a graphical or scripting interface, respectively.

Software dedicated to a single estimation method

* Monolix is a powerful implementation of SAEM which also can parse NMTRAN. * NPEM implements non-parametric mixed effects.

Related software

* Efficiency of ODE solvers impacts quality of estimation. Popular solvers are Runge-

Kutta Kutta is a small village in Ponnampet taluk of Kodagu, in Karnataka state of India. Location code number of Kutta is 618078. Location Kutta is the southern tip of Kodagu district. It is located at a distance of 86 km from district headquarter ...

based methods, various stiff solvers and switching solvers such as LSODA of the

LAPACK LAPACK ("Linear Algebra Package") is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It als ...

suite. * A specialized form of pharmacokinetics modeling, physiology-based pharmacokinetic (

PBPK Physiologically based pharmacokinetic (PBPK) modeling is a mathematical modeling technique for predicting the absorption, distribution, metabolism and excretion (ADME) of synthetic or natural chemical substances in humans and other animal species. ...

) modeling can in some cases also be seen as a nonlinear mixed-effects implementation, see also the

section of that lemma. *

Optimal design In the design of experiments, optimal experimental designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to D ...

software such as PopED can be used in conjunction with estimation.

References

{{Reflist Regression analysis Numerical software