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Nonlinear Regression

Perform least-squares estimation to fit grouped or pooled data, compute confidence intervals, and plot fit quality statistics

Perform parameter estimation using local, global, or hybrid estimation methods. Fit each group in your data independently to obtain group-specific estimates or fit all groups simultaneously to get one set of parameter estimates. You can also compute confidence intervals for estimated parameters and predicted model responses. Use various plots to visualize and assess fit quality measures.


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)
sbiofitPerform nonlinear least-squares regression
sbionlinfitPerform nonlinear least-squares regression using SimBiology models (requires Statistics and Machine Learning Toolbox software)
createDosesCreate dose objects from groupedData object
createVariantsCreate variant objects from groupedData object (Since R2021b)
fitted(LeastSquaresResults,OptimResults,NLINResults)Return simulation results of SimBiology model fitted using least-squares regression
getdose (model)Return SimBiology dose object
predict(LeastSquaresResults,OptimResults,NLINResults)Simulate and evaluate fitted SimBiology model
random(LeastSquaresResults,OptimResults,NLINResults)Simulate SimBiology model, adding variations by sampling error model
resetoptionsReset optional SimBiology fit problem properties (Since R2021b)
boxplot(LeastSquaresResults,OptimResults,NLINResults)Create box plot showing the variation of estimated SimBiology model parameters
plot(LeastSquaresResults,OptimResults,NLINResults)Compare simulation results to the training data, creating a time-course subplot for each group
plotActualVersusPredicted(LeastSquaresResults,OptimResults,NLINResults)Compare predictions to actual data, creating a subplot for each response
plotResiduals(LeastSquaresResults,OptimResults,NLINResults)Plot residuals for each response, using time, group, or prediction as x-axis
plotResidualDistribution(LeastSquaresResults,OptimResults,NLINResults)Plot the distribution of the residuals
summary(LeastSquaresResults,OptimResults,NLINResults)Return structure array that contains estimated values and fit quality statistics
sbioparameterciCompute confidence intervals for estimated parameters (requires Statistics and Machine Learning Toolbox)
sbiopredictionciCompute confidence intervals for model predictions (requires Statistics and Machine Learning Toolbox)
ci2tableReturn summary table of confidence interval results
plotPlot parameter confidence interval results
plotPlot confidence interval results for model predictions


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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
LeastSquaresResults objectResults object containing estimation results from least-squares regression
OptimResults objectEstimation results object for any supported algorithm except nlinfit
NLINResults objectEstimation results object for nlinfit algorithm
ParameterConfidenceIntervalObject containing confidence interval results for estimated parameters
PredictionConfidenceIntervalObject containing confidence interval results for model predictions
ConfidenceIntervalObject containing confidence interval results


Nonlinear Regression Basics

  • Nonlinear Regression
    SimBiology® supports several fitting, parameter transformations, and estimation options for nonlinear regression.
  • Supported Methods for Parameter Estimation in SimBiology
    SimBiology supports a variety of optimization methods for least-squares and mixed-effects estimation problems.
  • Error Models
    SimBiology supports constant, proportional, combined, and exponential error models.
  • Progress Plot
    The progress plot provides the live feedback on the status of parameter estimation while using sbiofit, sbiofitmixed, or the Fit Data program in the SimBiology Model Analyzer app.

App Workflow

Programmatic Workflow