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Nonlinear Mixed-Effects Modeling

Perform maximum likelihood estimation of population parameters

A nonlinear mixed-effects (NLME) model is a statistical model that incorporates both fixed effects (population parameters) and random effects (individual variations). It recognizes correlations within sample subgroups and works with small sample sizes. You can estimate population parameters while considering individual variations using various mixed-effects methods, such as stochastic approximation of expectation-maximization (SAEM), first-order conditional estimate (FOCE), first-order estimate (FO), linear mixed-effects (LME), and restrict LME approximation. For details, see Nonlinear Mixed-Effects Modeling.


SimBiology Model BuilderBuild QSP, PK/PD, and mechanistic systems biology models interactively (Since R2020b)
SimBiology Model AnalyzerAnalyze QSP, PK/PD, and mechanistic systems biology models (Since R2019b)


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fitPerform parameter estimation using SimBiology problem object (Since R2021b)
sbiofitmixedFit nonlinear mixed-effects model (requires Statistics and Machine Learning Toolbox software)
predict(NLMEResults)Simulate and evaluate fitted SimBiology model
random(NLMEResults)Simulate a SimBiology model, adding variations by sampling the error model
sbiosampleparametersGenerate parameters by sampling covariate model (requires Statistics and Machine Learning Toolbox software)
sbiosampleerrorSample error based on error model and add noise to input data
covariateModel(NLMEResults)Return a copy of the covariate model that was used for the nonlinear mixed-effects estimation using sbiofitmixed
createDosesCreate dose objects from groupedData object
fitted(NLMEResults) Return the simulation results of a fitted nonlinear mixed-effects model
getCovariateData (pkdata)Create design matrix needed for fit
getdose (model)Return SimBiology dose object
constructDefaultFixedEffectValuesCreate structure containing initial estimates fixed effects needed for fit
verifyCheck covariate model for errors
sbiofitstatusplotPlot status of nonlinear mixed-effects estimation
boxplot(NLMEResults)Create box plot showing the variation of estimated SimBiology model parameters
plot(NLMEResults)Compare simulation results to the training data, creating a time-course subplot for each group
plotActualVersusPredicted(NLMEResults)Compare predictions to actual data, creating a subplot for each response
plotResiduals(NLMEResults)Plot the residuals for each response, using the time, group, or prediction as the x-axis
plotResidualDistribution(NLMEResults)Plot the distribution of the residuals


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fitproblemSimBiology problem object for parameter estimation (Since R2021b)
groupedData Table-like collection of data and metadata for fitting in SimBiology
EstimatedInfo objectObject containing information about estimated model quantities
NLMEResults objectResults object containing estimation results from nonlinear mixed-effects modeling
CovariateModelDefine relationship between parameters and covariates


NLME Basics

NLME Workflows