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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 6 axes objects. Axes object 1 is empty. Axes object 2 with title 3 contains 4 objects of type line. One or more of the lines displays its values using only markers Axes object 3 with title 2 contains 4 objects of type line. One or more of the lines displays its values using only markers Axes object 4 with title 1 contains 4 objects of type line. One or more of the lines displays its values using only markers 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.Central.Drug_Central), Observed (Observed.CentralConc). Hidden axes object 6 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 ylabel PeripheralConc contains 6 objects of type line. One or more of the lines displays its values using only markers Axes object 2 with ylabel 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 ylabel PeripheralConc contains 6 objects of type line. One or more of the lines displays its values using only markers Axes object 2 with ylabel 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 xlabel Peripheral.Drug_Peripheral (milligram/liter), ylabel PeripheralConc (milligram/liter) contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 2 with xlabel Central.Drug_Central (milligram/liter), ylabel CentralConc (milligram/liter) 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.

boxplot(fitResults)

Figure contains an axes object. The axes object contains 28 objects of type line. One or more of the lines displays its values using only markers

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 ylabel 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 Individual Residuals, ylabel 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 ylabel PeripheralConc contains 2 objects of type line. One or more of the lines displays its values using only markers Axes object 2 with ylabel 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.

stats = summary(fitResults);
stats.Name
ans = 
'Unpooled Parameter Estimates'

ans = 
'Statistics'

ans = 
'Unpooled Beta'

ans = 
'Residuals'

ans = 
'Covariance Matrix'

ans = 
'Error Model'

stats.Table
ans=3×9 table
    Group    Central Estimate    Central StandardError    Peripheral Estimate    Peripheral StandardError    Q12 Estimate    Q12 StandardError    Cl_Central Estimate    Cl_Central StandardError
    _____    ________________    _____________________    ___________________    ________________________    ____________    _________________    ___________________    ________________________

    {'1'}          1.422                0.12334                 1.5619                   0.36355               0.47163            0.15196                0.5291                  0.036978        
    {'2'}         1.8322               0.019672                 5.3364                   0.65327                0.2764           0.030799               0.86035                  0.026257        
    {'3'}         1.6657               0.038529                 5.5632                   0.37063               0.78361           0.058657                1.0233                  0.027311        


ans=3×7 table
    Group      AIC        BIC      LogLikelihood    DFE      MSE         SSE  
    _____    _______    _______    _____________    ___    ________    _______

    {'1'}     60.961     64.051       -26.48        12        2.138     25.656
    {'2'}    -7.8379    -4.7475       7.9189        12     0.029012    0.34814
    {'3'}    -1.4336     1.6567       4.7168        12     0.043292     0.5195


ans=3×9 table
    Group    Central Estimate    Central StandardError    Peripheral Estimate    Peripheral StandardError    Q12 Estimate    Q12 StandardError    Cl_Central Estimate    Cl_Central StandardError
    _____    ________________    _____________________    ___________________    ________________________    ____________    _________________    ___________________    ________________________

    {'1'}        0.35208               0.086736                 0.44589                   0.23277              0.47163            0.15196                0.5291                  0.036978        
    {'2'}        0.60551               0.010737                  1.6746                   0.12242               0.2764           0.030799               0.86035                  0.026257        
    {'3'}        0.51027                0.02313                  1.7162                  0.066621              0.78361           0.058657                1.0233                  0.027311        


ans=24×4 table
    ID    Time    CentralConc    PeripheralConc
    __    ____    ___________    ______________

    1       0              0               0   
    1       1        0.10646        -0.74394   
    1       4         1.3745          1.2726   
    1       8       -0.68825         -4.2435   
    1      12        0.67383         0.21806   
    1      18        0.88823          1.0269   
    1      24        0.48941         0.66755   
    1      36        0.13632         0.22948   
    2       0              0               0   
    2       1      -0.026731       -0.058311   
    2       4      -0.033299        -0.20544   
    2       8       -0.20466         0.20696   
    2      12       -0.12223        0.045409   
    2      18       0.041224         0.33883   
    2      24      -0.059498       0.0036257   
    2      36      -0.051645         0.27616   
      ⋮


ans=12×6 table
    Group      Parameters        Central      Peripheral        Q12        Cl_Central 
    _____    ______________    ___________    __________    ___________    ___________

    {'1'}    {'Central'   }       0.015213     -0.022539     -0.0086672       0.001159
    {'1'}    {'Peripheral'}      -0.022539       0.13217       0.045746     -0.0073135
    {'1'}    {'Q12'       }     -0.0086672      0.045746       0.023092     -0.0021484
    {'1'}    {'Cl_Central'}       0.001159    -0.0073135     -0.0021484      0.0013674
    {'2'}    {'Central'   }     0.00038701     -0.002161    -0.00010177     9.7448e-05
    {'2'}    {'Peripheral'}      -0.002161       0.42676       0.019101      -0.015755
    {'2'}    {'Q12'       }    -0.00010177      0.019101     0.00094857    -0.00073328
    {'2'}    {'Cl_Central'}     9.7448e-05     -0.015755    -0.00073328     0.00068942
    {'3'}    {'Central'   }      0.0014845    -0.0054648     -0.0013216     0.00016639
    {'3'}    {'Peripheral'}     -0.0054648       0.13737       0.016903     -0.0072722
    {'3'}    {'Q12'       }     -0.0013216      0.016903      0.0034406    -0.00082538
    {'3'}    {'Cl_Central'}     0.00016639    -0.0072722    -0.00082538     0.00074587


ans=3×5 table
    Group     Response      ErrorModel        a        b 
    _____    __________    ____________    _______    ___

    {'1'}    {0x0 char}    {'constant'}     1.2663    NaN
    {'2'}    {0x0 char}    {'constant'}    0.14751    NaN
    {'3'}    {0x0 char}    {'constant'}    0.18019    NaN

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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