plotResidualDistribution

Plot the distribution of the residuals

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Syntax

plotResidualDistribution(resultsObj)

Description

plotResidualDistribution(resultsObj) shows the normal probability plot and the corresponding histogram of the residuals. Use the plot to check if the distribution of the residuals deviates from the normality.

example

Examples

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Open Live Script

Load the sample data set. 

load data10_32R.mat
gData = groupedData(data);
gData.Properties.VariableUnits = ["","hour","milligram/liter","milligram/liter"];

Create a two-compartment PK model.

pkmd                 = PKModelDesign;
pkc1                 = addCompartment(pkmd,"Central");
pkc1.DosingType      = "Infusion";
pkc1.EliminationType = "linear-clearance";
pkc1.HasResponseVariable = true;
pkc2                 = addCompartment(pkmd,"Peripheral");
model                = construct(pkmd);
configset            = getconfigset(model);
configset.CompileOptions.UnitConversion = true;
responseMap = ["Drug_Central = CentralConc","Drug_Peripheral = PeripheralConc"];

Provide model parameters to estimate.

paramsToEstimate   = ["log(Central)","log(Peripheral)","Q12","Cl_Central"];
estimatedParam     = estimatedInfo(paramsToEstimate,'InitialValue',[1 1 1 1]);

Assume every individual receives an infusion dose at time = 0, with a total infusion amount of 100 mg at a rate of 50 mg/hour.

dose             = sbiodose("dose","TargetName","Drug_Central");
dose.StartTime   = 0;
dose.Amount      = 100;
dose.Rate        = 50;
dose.AmountUnits = "milligram";
dose.TimeUnits   = "hour";
dose.RateUnits   = "milligram/hour";

Estimate model parameters. By default, the function estimates a set of parameter for each individual (unpooled fit).

fitResults =  sbiofit(model,gData,responseMap,estimatedParam,dose);

Plot the results.

plot(fitResults);

Figure contains 5 axes objects. Axes object 1 with title 3 contains 4 objects of type line. One or more of the lines displays its values using only markers Axes object 2 with title 2 contains 4 objects of type line. One or more of the lines displays its values using only markers Axes object 3 with title 1 contains 4 objects of type line. One or more of the lines displays its values using only markers Hidden axes object 4 contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Predicted (Predicted.Central.Drug_Central), Observed (Observed.CentralConc). Hidden axes object 5 contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Predicted (Predicted.Peripheral.Drug_Peripheral), Observed (Observed.PeripheralConc).

Plot all groups in one plot.

plot(fitResults,"PlotStyle","one axes");

Figure contains 5 axes objects. Axes object 1 with title PeripheralConc contains 6 objects of type line. One or more of the lines displays its values using only markers Axes object 2 with title CentralConc contains 6 objects of type line. One or more of the lines displays its values using only markers Hidden axes object 3 contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Predicted (Predicted.Central.Drug_Central), Observed (Observed.CentralConc). Hidden axes object 4 contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Predicted (Predicted.Peripheral.Drug_Peripheral), Observed (Observed.PeripheralConc). Hidden axes object 5 contains 3 objects of type line. These objects represent 3, 2, 1.

Change some axes properties.

s = struct;
s.Properties.XGrid = "on";
s.Properties.YGrid = "on";
plot(fitResults,"PlotStyle","one axes","AxesStyle",s);

Figure contains 5 axes objects. Axes object 1 with title PeripheralConc contains 6 objects of type line. One or more of the lines displays its values using only markers Axes object 2 with title CentralConc contains 6 objects of type line. One or more of the lines displays its values using only markers Hidden axes object 3 contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Predicted (Predicted.Central.Drug_Central), Observed (Observed.CentralConc). Hidden axes object 4 contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Predicted (Predicted.Peripheral.Drug_Peripheral), Observed (Observed.PeripheralConc). Hidden axes object 5 contains 3 objects of type line. These objects represent 3, 2, 1.

Compare the model predictions to the actual data.

plotActualVersusPredicted(fitResults);

Figure contains 2 axes objects. Axes object 1 with title PeripheralConc contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 2 with title CentralConc contains 2 objects of type line. One or more of the lines displays its values using only markers

Use boxplot to show the variation of estimated model parameters.

plotParameterStats(fitResults,"box");

Figure contains an axes object. The axes object contains an object of type boxchart.

Plot the distribution of residuals. This normal probability plot shows the deviation from normality and the skewness on the right tail of the distribution of residuals. The default (constant) error model might not be the correct assumption for the data being fitted.

plotResidualDistribution(fitResults);

Figure contains 4 axes objects. Axes object 1 contains 2 objects of type bar, line. Axes object 2 with title PeripheralConc contains 3 objects of type line. One or more of the lines displays its values using only markers Axes object 3 contains 2 objects of type bar, line. Axes object 4 with title CentralConc contains 3 objects of type line. One or more of the lines displays its values using only markers

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

plotResiduals(fitResults,"Predictions");

Figure contains 2 axes objects. Axes object 1 with title PeripheralConc contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 2 with title CentralConc contains 2 objects of type line. One or more of the lines displays its values using only markers

Get the summary of the fit results. stats.Name contains the name for each table from stats.Table, which contains a list of tables with estimated parameter values and fit quality statistics.

fitMetrics = summary(fitResults);

Display the table that contains parameter estimates summary statistics. 

tableToShow = "Parameter Estimates Summary Statistics";
tableNames = {fitMetrics.Name};
tfShowTable = matches(tableNames,tableToShow);
disp(fitMetrics(tfShowTable).Table);
          Statistic           Central    Peripheral     Q12      Cl_Central
    ______________________    _______    __________    ______    __________

    {'Minimum'           }     1.422       0.5291      1.5619      0.2764  
    {'Lower Quartile'    }     1.483      0.61191      2.5055     0.32521  
    {'Median'            }    1.6657      0.86035      5.3364     0.47163  
    {'Upper Quartile'    }    1.7906      0.98252      5.5065     0.70562  
    {'Maximum'           }    1.8322       1.0233      5.5632     0.78361  
    {'Mean'              }      1.64      0.80423      4.1539     0.51055  
    {'Standard Deviation'}    0.2063      0.25181      2.2476     0.25583

Input Arguments

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Estimation results, specified as an OptimResults object or NLINResults object, or vector of results objects which contains estimation results from running sbiofit.

Version History

Introduced in R2014a

See Also

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