Main Content

plotResiduals

Class: GeneralizedLinearMixedModel

Plot residuals of generalized linear mixed-effects model

expand all in page

Syntax

plotResiduals(glme,plottype)
plotResiduals(glme,plottype,Name,Value)
plotResiduals(ax,___)
h = plotResiduals(___)

Description

plotResiduals(glme,plottype) plots the raw conditional residuals of the generalized linear mixed-effects model glme in a plot of the type specified by plottype.

plotResiduals(glme,plottype,Name,Value) plots the conditional residuals of glme using additional options specified by one or more Name,Value pair arguments. For example, you can specify the residual type and the graphical properties of residual data points.

example

plotResiduals(ax,___) plots into the axes specified by ax instead of the current axes (gca) using any of the input argument combinations in the previous syntaxes. (since R2024a)

h = plotResiduals(___) returns a handle, h, to the lines or patches in the plot of residuals.

Input Arguments

expand all

Generalized linear mixed-effects model, specified as a GeneralizedLinearMixedModel object. For properties and methods of this object, see GeneralizedLinearMixedModel.

Type of residual plot, specified as one of the following.

ValueDescription
"histogram"Histogram of residuals
"caseorder"Residuals versus case order. Case order is the same as the row order used in the input data tbl when fitting the model using fitglme.
"fitted"Residuals versus fitted values
"lagged"Residuals versus lagged residual (r(t) versus r(t – 1))
"probability"Normal probability plot
"observed"Observed vs. fitted values. This plot includes a dotted reference line of y = x. Each residual is represented by the vertical distance from the corresponding observed value to the reference line.
"symmetry" Symmetry plot

Example: plotResiduals(glme,"lagged")

Since R2024a

Target axes, specified as an Axes object. If you do not specify the axes, then plotResiduals uses the current axes (gca).

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Residual type, specified by the comma-separated pair consisting of ResidualType and one of the following.

Residual TypeFormula
'raw'

rci=yi−g−1(xiTβ^+ziTb^+δi)

'Pearson'

rcipearson=rciσ2^wivi(μi(β^,b^))

In each of these equations:

  • yi is the ith element of the n-by-1 response vector, y, where i = 1, ..., n.

  • g-1 is the inverse link function for the model.

  • xiT is the ith row of the fixed-effects design matrix X.

  • ziT is the ith row of the random-effects design matrix Z.

  • δi is the ith offset value.

  • σ2 is the dispersion parameter.

  • wi is the ith observation weight.

  • vi is the variance term for the ith observation.

  • μi is the mean of the response for the ith observation.

  • β^ and b^ are estimated values of β and b.

Raw residuals from a generalized linear mixed-effects model have nonconstant variance. Pearson residuals are expected to have an approximately constant variance, and are generally used for analysis.

Example: 'ResidualType','Pearson'

Output Arguments

expand all

Handle to the residual plot, returned as a graphics object. You can use dot notation to change certain property values of the object, including face color for a histogram, and marker style and color for a scatterplot. For more information, see Access Property Values.

Examples

expand all

Open Live Script

Load the sample data.

load mfr

This simulated data is from a manufacturing company that operates 50 factories across the world, with each factory running a batch process to create a finished product. The company wants to decrease the number of defects in each batch, so it developed a new manufacturing process. To test the effectiveness of the new process, the company selected 20 of its factories at random to participate in an experiment: Ten factories implemented the new process, while the other ten continued to run the old process. In each of the 20 factories, the company ran five batches (for a total of 100 batches) and recorded the following data:

  • Flag to indicate whether the batch used the new process (newprocess)

  • Processing time for each batch, in hours (time)

  • Temperature of the batch, in degrees Celsius (temp)

  • Categorical variable indicating the supplier (A, B, or C) of the chemical used in the batch (supplier)

  • Number of defects in the batch (defects)

The data also includes time_dev and temp_dev, which represent the absolute deviation of time and temperature, respectively, from the process standard of 3 hours at 20 degrees Celsius.

Fit a generalized linear mixed-effects model using newprocess, time_dev, temp_dev, and supplier as fixed-effects predictors. Include a random-effects term for intercept grouped by factory, to account for quality differences that might exist due to factory-specific variations. The response variable defects has a Poisson distribution, and the appropriate link function for this model is log. Use the Laplace fit method to estimate the coefficients. Specify the dummy variable encoding as 'effects', so the dummy variable coefficients sum to 0.

The number of defects can be modeled using a Poisson distribution:

defectsij∼Poisson(μij)

This corresponds to the generalized linear mixed-effects model

log(μij)=β0+β1newprocessij+β2time_devij+β3temp_devij+β4supplier_Cij+β5supplier_Bij+bi,

where

  • defectsij is the number of defects observed in the batch produced by factory i during batch j.

  • μij is the mean number of defects corresponding to factory i (where i=1,2,...,20) during batch j (where j=1,2,...,5).

  • newprocessij, time_devij, and temp_devij are the measurements for each variable that correspond to factory i during batch j. For example, newprocessij indicates whether the batch produced by factory i during batch j used the new process.

  • supplier_Cij and supplier_Bij are dummy variables that use effects (sum-to-zero) coding to indicate whether company C or B, respectively, supplied the process chemicals for the batch produced by factory i during batch j.

  • bi∼N(0,σb2) is a random-effects intercept for each factory i that accounts for factory-specific variation in quality.

glme = fitglme(mfr,'defects ~ 1 + newprocess + time_dev + temp_dev + supplier + (1|factory)','Distribution','Poisson','Link','log','FitMethod','Laplace','DummyVarCoding','effects');

Create diagnostic plots using Pearson residuals to test the model assumptions.

Plot a histogram to visually confirm that the mean of the Pearson residuals is equal to 0. If the model is correct, we expect the Pearson residuals to be centered at 0. 

plotResiduals(glme,'histogram','ResidualType','Pearson')

Figure contains an axes object. The axes object with title Histogram of residuals, xlabel Residuals, ylabel Probability density contains an object of type patch.

The histogram shows that the Pearson residuals are centered at 0.

Plot the Pearson residuals versus the fitted values, to check for signs of nonconstant variance among the residuals (heteroscedasticity). We expect the conditional Pearson residuals to have a constant variance. Therefore, a plot of conditional Pearson residuals versus conditional fitted values should not reveal any systematic dependence on the conditional fitted values. 

plotResiduals(glme,'fitted','ResidualType','Pearson')

Figure contains an axes object. The axes object with title Plot of residuals vs. fitted values, xlabel Fitted values, ylabel Residuals contains 2 objects of type line. One or more of the lines displays its values using only markers

The plot does not show a systematic dependence on the fitted values, so there are no signs of nonconstant variance among the residuals.

Plot the Pearson residuals versus lagged residuals, to check for correlation among the residuals. The conditional independence assumption in GLME implies that the conditional Pearson residuals are approximately uncorrelated. 

plotResiduals(glme,'lagged','ResidualType','Pearson')

Figure contains an axes object. The axes object with title Plot of residuals vs. lagged residuals, xlabel Residual(t-1), ylabel Residual(t) contains 3 objects of type line. One or more of the lines displays its values using only markers

There is no pattern to the plot, so there are no signs of correlation among the residuals.

Version History

expand all

See Also

| | | |