plotResiduals
Class: GeneralizedLinearMixedModel
Plot residuals of generalized linear mixed-effects model
Syntax
Description
plotResiduals(
plots the conditional residuals of glme
,plottype
,Name,Value
)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.
returns
a handle, h
= plotResiduals(___)h
, to the lines or patches in the plot
of residuals.
Input Arguments
glme
— Generalized linear mixed-effects model
GeneralizedLinearMixedModel
object
Generalized linear mixed-effects model, specified as a GeneralizedLinearMixedModel
object.
For properties and methods of this object, see GeneralizedLinearMixedModel
.
plottype
— Type of residual plot
"histogram"
(default) | "caseorder"
| "fitted"
| "lagged"
| "probability"
| "observed"
| "symmetry"
Type of residual plot, specified as one of the following.
Value | Description |
---|---|
"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")
ax
— Target axes
Axes
object
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.
ResidualType
— Residual type
'raw'
(default) | 'Pearson'
Residual type, specified by the comma-separated pair consisting
of ResidualType
and one of the following.
Residual Type | Formula |
---|---|
'raw' |
|
'Pearson' |
|
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.
and 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
h
— Handle to residual plot
graphics object
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
Create Plots of Residuals
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
, orC
) 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:
This corresponds to the generalized linear mixed-effects model
where
is the number of defects observed in the batch produced by factory during batch .
is the mean number of defects corresponding to factory (where ) during batch (where ).
, , and are the measurements for each variable that correspond to factory during batch . For example, indicates whether the batch produced by factory during batch used the new process.
and are dummy variables that use effects (sum-to-zero) coding to indicate whether company
C
orB
, respectively, supplied the process chemicals for the batch produced by factory during batch .is a random-effects intercept for each factory 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')
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')
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')
There is no pattern to the plot, so there are no signs of correlation among the residuals.
Version History
R2024b: Plot observed versus fitted values
You can now plot observed versus fitted values by specifying the
plottype
input argument as
"observed"
.
R2024a: Specify target axes
Specify the target axes for the plot by using the ax
input
argument.
See Also
GeneralizedLinearMixedModel
| fitglme
| fitted
| plot
| residuals
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