plotResiduals

Plot residuals of linear mixed-effects model

Syntax

``plotResiduals(lme,plottype)``
``plotResiduals(lme,plottype,Name,Value)``
``plotResiduals(ax,___)``
``h = plotResiduals(___)``

Description

example

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

example

````plotResiduals(lme,plottype,Name,Value)` specifies additional options using one or more name-value arguments. For example, you can specify the residual type and the graphical properties of residual data points.`plotResiduals` also accepts some name-value arguments that specify the properties of the primary line in the plot. For those name-value arguments, see `plot`. ```
````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.```

Examples

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Load the sample data.

`load('weight.mat')`

`weight` contains data from a longitudinal study, where 20 subjects are randomly assigned to 4 exercise programs, and their weight loss is recorded over six 2-week time periods. This is simulated data.

Store the data in a table. Define `Subject` and `Program` as categorical variables.

```tbl = table(InitialWeight,Program,Subject,Week,y); tbl.Subject = categorical(tbl.Subject); tbl.Program = categorical(tbl.Program);```

Fit a linear mixed-effects model where the initial weight, type of program, week, and the interaction between the week and type of program are the fixed effects. The intercept and week vary by subject.

`lme = fitlme(tbl,'y ~ InitialWeight + Program*Week + (Week|Subject)');`

Plot the histogram of the raw residuals.

`plotResiduals(lme)`

Plot the residuals versus the fitted values.

`plotResiduals(lme,'fitted')`

There is no obvious pattern, so there are no immediate signs of heteroscedasticity.

Create the normal probability plot of residuals.

`plotResiduals(lme,'probability')`

Data appears to be normal.

Find the observation number for the data that appears to be an outlier to the right of the plot.

`find(residuals(lme)>0.25)`
```ans = 101 ```

Create a box plot of the raw, Pearson, and standardized residuals.

```r = residuals(lme); pr = residuals(lme,'ResidualType','Pearson'); st = residuals(lme,'ResidualType','Standardized'); X = [r pr st]; boxplot(X,'labels',{'Raw','Pearson','Standardized'})```

All three box plots point out the outlier on the right tail of the distribution. The box plots of raw and Pearson residuals also point out a second possible outlier on the left tail. Find the corresponding observation number.

`find(pr<-2)`
```ans = 10 ```

Plot the raw residuals versus lagged residuals.

`plotResiduals(lme,'lagged')`

There is no obvious pattern in the graph. The residuals do not appear to be correlated.

Input Arguments

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Linear mixed-effects model, specified as a `LinearMixedModel` object constructed using `fitlme` or `fitlmematrix`.

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

 `'histogram'` Default. Histogram of residuals `'caseorder'` Residuals versus case (row) order `'fitted'` Residuals versus fitted values `'lagged'` Residuals versus lagged residual (r(t) versus r(t – 1)) `'probability'` Normal probability plot `'symmetry'` Symmetry plot

Example: `plotResiduals(lme,'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.

Example: `plotResiduals(lme,plottype,'ResidualType','Standardized')`

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

Residual TypeConditionalMarginal
`'Raw'`

`${r}_{i}^{C}={\left[y-X\stackrel{^}{\beta }-Z\stackrel{^}{b}\right]}_{i}$`

`${r}_{i}^{M}={\left[y-X\stackrel{^}{\beta }\right]}_{i}$`

`'Pearson'`

`$p{r}_{i}^{C}=\frac{{r}_{i}^{C}}{{\sqrt{\left[{\stackrel{^}{Var}}_{y,b}\left(y-X\beta -Zb\right)\right]}}_{ii}}$`

`$p{r}_{i}^{M}=\frac{{r}_{i}^{M}}{\sqrt{{\left[{\stackrel{^}{Var}}_{y}\left(y-X\beta \right)\right]}_{ii}}}$`

`'Standardized'`

`$s{t}_{i}^{C}=\frac{{r}_{i}^{C}}{\sqrt{{\left[{\stackrel{^}{Var}}_{y}\left({r}^{C}\right)\right]}_{ii}}}$`

`$s{t}_{i}^{M}=\frac{{r}_{i}^{M}}{\sqrt{{\left[{\stackrel{^}{Var}}_{y}\left({r}^{M}\right)\right]}_{ii}}}$`

For more information on the conditional and marginal residuals and residual variances, see `Definitions` at the end of this page.

Example: `'ResidualType','Standardized'`

Output Arguments

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Handle to the residual plot, returned as a handle.

Version History

Introduced in R2013b

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