computer science

Non-linear mixed-effects modeling software

Non-linear mixed-effects modeling software is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Non-linear mixed-effects modeling software rather than just read about it. In short: Nonlinear mixed-effects models are a special case of regression analysis for which a range of different software solutions are available. The statistical properties of nonlinear mixed-effects models make direct estimation by a BLUE estimator impossible.

Key takeaways

Non-linear mixed-effects modeling software belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Non-linear mixed-effects modeling software to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Non-linear mixed-effects modeling software from memory before moving on to harder problems.

Reference excerpt

Nonlinear mixed-effects models are a special case of regression analysis for which a range of different software 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 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 frameworks is performed using the Metropolis-Hastings or the NUTS 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 provides multiple estimation methods in their nlmefit system. SPSS at the moment does not support non-linear mixed effects methods.

Software dedicated to a single estimation method WinBUGS 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 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 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 based methods, various stiff solvers and switching solvers such as LSODA of the LAPACK suite. A specialized form of pharmacokinetics modeling, physiology-based pharmacokinetic (PBPK) modeling can in some cases also be seen as a nonlinear mixed-effects implementation, see also the software section of that lemma. Optimal design software such as PopED can be used in conjunction with estimation.

References

Worked examples

Example 1 — a first encounter with Non-linear mixed-effects modeling software

Start with the simplest possible case. Write down what Non-linear mixed-effects modeling software claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Non-linear mixed-effects modeling software before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Non-linear mixed-effects modeling software ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Non-linear mixed-effects modeling software

In research: Non-linear mixed-effects modeling software appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Non-linear mixed-effects modeling software in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Non-linear mixed-effects modeling software is common in secondary-school and first-year university syllabi. It links to neighbouring topics Numerical software, Regression analysis, so understanding it makes those chapters shorter.
In everyday life: Look for Non-linear mixed-effects modeling software outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Non-linear mixed-effects modeling software in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Non-linear mixed-effects modeling software means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Non-linear mixed-effects modeling software out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Non-linear mixed-effects modeling software in simple terms?

Why does Non-linear mixed-effects modeling software matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Non-linear mixed-effects modeling software?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Non-linear mixed-effects modeling software.