predict

Predict responses of multinomial regression model

Since R2023a

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    Syntax

    Ypred = predict(mdl,XNew)
    [Ypred,probs] = predict(mdl,XNew)
    [Ypred,probs,lower,upper] = predict(mdl,XNew)
    [___] = predict(___,Name=Value)

    Description

    Ypred = predict(mdl,XNew) returns predicted class labels for the predictor data XNew and MultinomialRegression model object mdl.

    example

    [Ypred,probs] = predict(mdl,XNew) also returns probability estimates for the response categories.

    [Ypred,probs,lower,upper] = predict(mdl,XNew) also returns lower and upper confidence interval bounds for the responses Ypred.

    [___] = predict(___,Name=Value) specifies options using one or more name-value arguments in addition to any of the input argument combinations in previous syntaxes. For example, you can specify the type of probability for the probability estimates returned in probs.

    Examples

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    Open Live Script

    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)         86.297    12.541       6.881    5.9436e-12
    x1_setosa                 -1.0653    3.5795    -0.29761         0.766
    x2_setosa                  23.849    3.1238      7.6347    2.2637e-14
    x3_setosa                 -27.273    3.5009     -7.7903    6.6846e-15
    x4_setosa                 -59.644    7.0214     -8.4947    1.9852e-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.

    Open Live Script

    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.

    Input Arguments

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    Multinomial regression model object, specified as a MultinomialRegression model object created with the fitmnr function.

    New predictor input values, specified as a table or an n-by-p matrix, where n is the number of observations to predict, and p is the number of predictor variables used to fit mdl.

    • If XNew is a table, it must contain all the names of the predictors used to fit mdl. You can find the predictor names in the mdl.PredictorNames property.

    • If XNew is a matrix, it must have the same number of columns as the number of estimated coefficients. You can find the number of estimated coefficients in the mdl.NumPredictors property. You can specify XNew as a matrix only when all names in mdl.PredictorNames refer to numeric predictors.

    Example: predict(mdl,[6.2 3.4; 5.9 3.0]) evaluates the two-predictor model mdl at the points p1 = [6.2 3.4] and p2 = [5.9 3.0].

    Data Types: single | double | table

    Name-Value Arguments

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    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.

    Example: [Ypred,probs,lower,upper] = predict(model,X,Alpha=0.01,ProbabilityType="cumulative") specifies a 99% confidence level for the probability estimates and their type as cumulative.

    Significance level for the probability estimates, specified as a scalar value in the range (0,1). The confidence level of the confidence intervals is 100(1 − α)%. The default value for Alpha is 0.05, which returns 95% confidence intervals for the estimates.

    Example: Alpha=0.01

    Data Types: single | double

    Type of probability estimates to return in probs, specified as one of the following options.

    OptionDescription
    "category" (default)Calculate a distinct probability for each response category.
    "cumulative"Calculate a cumulative probability for each response category.
    "conditional"Calculate a conditional probability for each response category.

    Example: ProbabilityType="conditional"

    Data Types: char | string

    Output Arguments

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    Predicted response categories, returned as a categorical or character array, logical or numeric vector, or cell array of character vectors. Ypred has the same data type as mdl.ClassNames.

    Probability estimates for the response categories, returned as a numeric matrix. Each column of probs corresponds to the entry at the same index in mdl.ClassNames.

    Upper confidence interval bound for the probability estimates in probs, returned as a numeric matrix.

    Lower confidence interval bound for the probability estimates in probs, returned as a numeric matrix.

    Alternative Functionality

    • feval returns the same predictions as predict. The feval function can take multiple input arguments, with one input for each predictor variable. Note that the feval function does not give confidence intervals on predictions.

    • random returns predictions with added noise.

    Version History

    Introduced in R2023a

    See Also

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