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Results object containing estimation results from nonlinear mixed-effects modeling


The NLMEResults object contains estimation results from fitting a nonlinear mixed-effects model using sbiofitmixed.


Use the sbiofitmixed function to create an NLMEResults object.


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Table of the estimated fixed effects and their standard errors, specified as a table.

Table of the estimated random effects for each group, specified as a table.

Table of estimated parameter values, including fixed and random effects, specified as a table.

Table of estimated parameter values, including only fixed effects, specified as a table.

Table of the covariance matrix of the random effects, specified as a table.

Statistics returned by the nlmefit (Statistics and Machine Learning Toolbox) and nlmefitsa (Statistics and Machine Learning Toolbox) algorithm, specified as a structure array.

Covariate names, specified as a cell array of character vectors.

Data used for fitting, specified as a groupedData object.

This Data property contains a copy of groupedData specified as the input data in the sbiofitmixed call or the Data property of a fitproblem object.

Estimated parameter names, specified as a cell array of character vectors.

Table describing the error models and estimated error model parameters, specified as a table.

The table has one row with three variables: ErrorModel, a, and b. The ErrorModel variable is categorical. The variables a and b can be NaN when they do not apply to a particular error model.

There are four built-in error models. Each model defines the error using a standard mean-zero and unit-variance (Gaussian) variable e, the function value f, and one or two parameters a and b. In SimBiology®, the function f represents simulation results from a SimBiology model.

  • 'constant': y=f+ae

  • 'proportional': y=f+b|f|e

  • 'combined': y=f+(a+b|f|)e

  • 'exponential': y=fexp(ae)

Name of the estimation function, specified as 'nlmefit' or 'nlmefitsa'.

Maximized loglikelihood for the fitted model, specified as a scalar.

Akaike Information Criterion (AIC), specified as a scalar. The AIC is calculated as AIC = 2*(-LogLikelihood + P), where P is the number of parameters. For details, see nlmefit (Statistics and Machine Learning Toolbox).

Bayes Information Criterion (BIC), specified as a scalar. The BIC is calculated as BIC = -2*LogLikelihood + P*log(N), where N is the number of observations or groups, and P is the number of parameters. For details, see nlmefit (Statistics and Machine Learning Toolbox).

Degrees of freedom for error (DFE), specified as a scalar. The DFE is calculated as DFE = N-P, where N is the number of observations and P is the number of parameters.


If you are using the nlmefitsa method, Loglikelihood, AIC, and BIC properties are empty by default. To calculate these values, specify the 'LogLikMethod' option of nlmefitsa (Statistics and Machine Learning Toolbox) when you run sbiofitmixed as follows.

opt.LogLikMethod = 'is';
fitResults = sbiofitmixed(...,'nlmefitsa',opt);

Object Functions

boxplotCreate box plot showing the variation of estimated SimBiology model parameters
covariateModelReturn a copy of the covariate model that was used for the nonlinear mixed-effects estimation using sbiofitmixed
fitted Return the simulation results of a fitted nonlinear mixed-effects model
plotCompare simulation results to the training data, creating a time-course subplot for each group
plotActualVersusPredictedCompare predictions to actual data, creating a subplot for each response
plotResidualDistributionPlot the distribution of the residuals
plotResidualsPlot the residuals for each response, using the time, group, or prediction as the x-axis
predictSimulate and evaluate fitted SimBiology model
randomSimulate a SimBiology model, adding variations by sampling the error model


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This example uses data collected on 59 preterm infants given phenobarbital during the first 16 days after birth [1]. Each infant received an initial dose followed by one or more sustaining doses by intravenous bolus administration. A total of between 1 and 6 concentration measurements were obtained from each infant at times other than dose times, for a total of 155 measurements. Infant weights and APGAR scores (a measure of newborn health) were also recorded.

Load the data.

load pheno.mat ds

Convert the dataset to a groupedData object, a container for holding tabular data that is divided into groups. It can automatically identify commonly used variable names as the grouping variable or independent (time) variable. Display the properties of the data and confirm that GroupVariableName and IndependentVariableName are correctly identified as 'ID' and 'TIME', respectively.

data = groupedData(ds);
ans = struct with fields:
                Description: ''
                   UserData: []
             DimensionNames: {'Observations'  'Variables'}
              VariableNames: {'ID'  'TIME'  'DOSE'  'WEIGHT'  'APGAR'  'CONC'}
       VariableDescriptions: {}
              VariableUnits: {}
         VariableContinuity: []
                   RowNames: {}
           CustomProperties: [1×1 matlab.tabular.CustomProperties]
          GroupVariableName: 'ID'
    IndependentVariableName: 'TIME'

Create a simple one-compartment PK model with bolus dosing and linear clearance to fit such data. Use the PKModelDesign object to construct the model. Each compartment is defined by a name, dosing type, a clearance type, and whether or not the dosing requires a lag parameter. After constructing the model, you can also get a PKModelMap object map that lists the names of species and parameters in the model that are most relevant for fitting.

pkmd = PKModelDesign;
[onecomp, map] = pkmd.construct;

Describe the experimentally measured response by mapping the appropriate model component to the response variable. In other words, indicate which species in the model corresponds to which response variable in the data. The PKModelMap property Observed indicates that the relevant species in the model is Drug_Central, which represents the drug concentration in the system. The relevant data variable is CONC, which you visualized previously.

ans = 1×1 cell array

Map the Drug_Central species to the CONC variable.

responseMap = 'Drug_Central = CONC';

The parameters to estimate in this model are the volume of the central compartment Central and the clearance rate Cl_Central. The PKModelMap property Estimated lists these relevant parameters. The underlying algorithm of sbiofit assumes parameters are normally distributed, but this assumption may not be true for biological parameters that are constrained to be positive, such as volume and clearance. Specify a log transform for the estimated parameters so that the transformed parameters follow a normal distribution. Use an estimatedInfo object to define such transforms and initial values (optional).

ans = 2×1 cell
    {'Central'   }

Define such estimated parameters, appropriate transformations, and initial values.

estimatedParams = estimatedInfo({'log(Central)','log(Cl_Central)'},'InitialValue',[1 1]);

Each infant received a different schedule of dosing. The amount of drug is listed in the data variable DOSE. To specify these dosing during fitting, create dose objects from the data. These objects use the property TargetName to specify which species in the model receives the dose. In this example, the target species is Drug_Central, as listed by the PKModelMap property Dosed.

ans = 1×1 cell array

Create a sample dose with this target name and then use the createDoses method of groupedData object data to generate doses for each infant based on the dosing data DOSE.

sampleDose = sbiodose('sample','TargetName','Drug_Central');
doses = createDoses(data,'DOSE','',sampleDose);

Fit the model.

[nlmeResults,simI,simP] = sbiofitmixed(onecomp,data,responseMap,estimatedParams,doses,'nlmefit');

Visualize the fitted results using individual-specific parameter estimates.


Visualize the fitted results using population parameter estimates.


Display the variation of estimated parameters using boxplot.


Compare the model predictions to the actual data.


Plot the distribution of residuals.


Plot residuals for each response using the model predictions on x-axis.


Version History

Introduced in R2014a

See Also

| | (Statistics and Machine Learning Toolbox) | (Statistics and Machine Learning Toolbox)