plotResiduals

Load the fisheriris sample data set.

load fisheriris

The column vector species contains three iris flower species: setosa, versicolor, and virginica. The matrix meas contains four types of measurements for the flowers: the length and width of sepals and petals in centimeters.

Fit a multinomial regression model to predict the iris flower species using the measurements. Display the table of residuals for the fitted model.

mdl = fitmnr(meas,species);
mdl.Residuals

ans=150×3 table
        Raw          Pearson      Deviance
    ___________    ___________    ________

    0    0    0    0    0    0       0    
    0    0    0    0    0    0       0    
    0    0    0    0    0    0       0    
    0    0    0    0    0    0       0    
    0    0    0    0    0    0       0    
    0    0    0    0    0    0       0    
    0    0    0    0    0    0       0    
    0    0    0    0    0    0       0    
    0    0    0    0    0    0       0    
    0    0    0    0    0    0       0    
    0    0    0    0    0    0       0    
    0    0    0    0    0    0       0    
    0    0    0    0    0    0       0    
    0    0    0    0    0    0       0    
    0    0    0    0    0    0       0    
    0    0    0    0    0    0       0    
      ⋮

The output shows the raw, Pearson, and deviance residuals for the model.

Generate a probability density plot of the deviance residuals.

plotResiduals(mdl)

The histogram shows that most of the deviance residuals are small. However, several residuals are greater than one.

Inspect the observations with larger residuals. Sort the residuals from largest to smallest by using the sort function. Use the head function to display the four largest residuals and their corresponding indices.

[r, ind] = sort(mdl.Residuals.Deviance,"descend");
head(r,4)

    4.0443
    3.1707
    1.0378
    0.8035

head(ind,4)

    84
   134
    71
   139

The outputs show that observations corresponding to rows 84, 134, and 71 of meas and species have residuals larger than one. Given that most other residuals are close to zero, observations 84, 134, and 71 are most likely outliers.

Load the carbig sample data set.

load carbig

The vectors Displacement, Cylinders, and Model_Year contain data for car engine displacement, number of engine cylinders, and year the car was manufactured, respectively.

Fit a multinomial regression model using Displacement and Cylinders as predictors variables and Model_Year as the response.

mdl = fitmnr([Displacement Cylinders],Model_Year);

To determine whether the residuals are random, generate a lagged plot of the deviance residuals.

plotResiduals(mdl,"lagged")

The lagged plot of the deviance residuals shows a cluster of residuals trending toward the top right of the plot. The cluster indicates a mildly positive correlation between the residual for a data point and the residual for the previous data point, suggesting that the residuals might not be random.

Load the carbig sample data set.

load carbig

The vectors Displacement, Cylinders, and Model_Year contain of data for car engine displacement, number of engine cylinders, and year the car was manufactured, respectively.

Fit a nominal multinomial regression model using Displacement and Cylinders as predictors variables and Model_Year as the response.

mdl = fitmnr([Displacement Cylinders],Model_Year);

mdl is a multinomial regression model object that contains the results of fitting a nominal multinomial regression model to the data.

Display the name of the first response category.

mdl.ClassNames(1)

ans = 
70

The output shows that the first response category corresponds to cars manufactured in 1970.

To determine whether the raw residuals for cars manufactured in 1970 are randomly distributed, create a probability plot and return a graphics array of the plotted objects. By default, plotResiduals uses the raw residuals for the first response category to create the probability plot.

h = plotResiduals(mdl,"probability",ResidualType="raw")

h = 
  2×1 graphics array:

  Line            (main)
  FunctionLine

The output shows the data types for the elements in the graphics array h. The Line element corresponds to the raw residuals. The FunctionLine element corresponds to the line representing the theoretical normal distribution.

Specify the color red for the normal distribution line by modifying the Color property of the second element in h.

h(2).Color = "r"

h = 
  2×1 graphics array:

  Line            (main)
  FunctionLine

The plot shows that the residuals do not follow the red line, indicating that the raw residuals for cars manufactured in 1970 are not normally distributed.