predict

Load the fisheriris sample data set.

load fisheriris

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

Divide the species and measurement data into training and test data by using the cvpartition function. Get the indices of the training data rows by using the training function.

n = length(species);
partition = cvpartition(n,'Holdout',0.05);
idx_train = training(partition);

Create training data by using the indices of the training data rows to create a matrix of measurements and a vector of species labels.

meastrain = meas(idx_train,:);
speciestrain = species(idx_train,:);

Fit a multinomial regression model using the training data.

mdl = fitmnr(meastrain,speciestrain)

mdl = 
Multinomial regression with nominal responses

                               Value       SE       tStat        pValue  
                              _______    ______    ________    __________

    (Intercept_setosa)         86.305    12.541      6.8817    5.9158e-12
    x1_setosa                 -1.0728    3.5795    -0.29971        0.7644
    x2_setosa                  23.846    3.1238      7.6336    2.2835e-14
    x3_setosa                 -27.289    3.5009      -7.795    6.4409e-15
    x4_setosa                  -59.58    7.0214     -8.4855    2.1472e-17
    (Intercept_versicolor)     42.637    5.2214      8.1659    3.1906e-16
    x1_versicolor              2.4652    1.1263      2.1887      0.028619
    x2_versicolor              6.6808     1.474      4.5325     5.829e-06
    x3_versicolor             -9.4292    1.2946     -7.2837     3.248e-13
    x4_versicolor             -18.286    2.0833     -8.7775     1.671e-18


143 observations, 276 error degrees of freedom
Dispersion: 1
Chi^2-statistic vs. constant model: 302.0378, p-value = 1.5168e-60

mdl is a multinomial regression model object that contains the results of fitting a nominal multinomial regression model to the data. The table output shows coefficient statistics for each predictor in meas. By default, fitmnr uses virginica as the reference category.

Get the indices of the test data rows by using the test function. Create test data by using the indices of the test data rows to create a matrix of measurements and a vector of species labels.

idx_test = test(partition);
meastest = meas(idx_test,:);
speciestest = species(idx_test,:);

Predict the iris species for the measurements in meastest.

speciespredict = predict(mdl,meastest)

speciespredict = 7×1 cell
    {'setosa'    }
    {'setosa'    }
    {'setosa'    }
    {'setosa'    }
    {'setosa'    }
    {'versicolor'}
    {'versicolor'}

Compare the predictions in speciespredict with the category names in speciestest.

speciestest

speciestest = 7×1 cell
    {'setosa'    }
    {'setosa'    }
    {'setosa'    }
    {'setosa'    }
    {'setosa'    }
    {'versicolor'}
    {'versicolor'}

The output shows that the model accurately predicts the iris species for the measurements in meastest.

Load the carbig sample data set.

load carbig

The variables Acceleration and Displacement contain data for car acceleration and displacement, respectively. The variable Cylinders contains data for the number of cylinders in each car engine.

Create a table from the car data variables using the table function.

tbl = table(Acceleration,Displacement,Cylinders,VariableNames=["Acceleration","Displacement","Cylinders"])

tbl=406×3 table
    Acceleration    Displacement    Cylinders
    ____________    ____________    _________

          12            307             8    
        11.5            350             8    
          11            318             8    
          12            304             8    
        10.5            302             8    
          10            429             8    
           9            454             8    
         8.5            440             8    
          10            455             8    
         8.5            390             8    
        17.5            133             4    
        11.5            350             8    
          11            351             8    
        10.5            383             8    
          11            360             8    
          10            383             8    
      ⋮

The Cylinders data has an inherent ordering. Fit an ordinal multinomial regression model using Acceleration and Displacement as predictor variables and Cylinders as the response.

mdl = fitmnr(tbl,"Cylinders",ModelType="ordinal");

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

Predict the response category, cumulative category probabilities, and 99% confidence interval bounds for a car with an acceleration of 16 and an engine displacement of 80.

[cylinderspredict,cumprobs,lower,upper] = predict(mdl,[16 80],Alpha=0.01,ProbabilityType="cumulative")

cylinderspredict = 
4

cumprobs = 1×4

    0.0792    1.0000    1.0000    1.0000

lower = 1×4

    0.0787    1.0000    1.0000    1.0000

upper = 1×4

    0.0798    1.0000    1.0000    1.0000

The output shows that the predicted response category is 4. The vector cumprobs shows the cumulative probabilities for each category in Cylinders. To view the category probabilities on which the prediction is based, calculate the category probabilities.

[~,catprobs] = predict(mdl,[16 80])

catprobs = 1×5

    0.0792    0.9208    0.0000    0.0000    0.0000

The second value in the vector catprobs has the highest probability. Display an ordered list of the categories in Cylinders.

mdl.ClassNames

ans = 5×1

     3
     4
     5
     6
     8

The output shows that the second category corresponds to cars with four cylinders. Therefore, the category with the highest category probability is 4.