Estimate the predictor importance for all predictor variables in the data.

Load the carsmall data set.

load carsmall

Grow a regression tree for MPG using Acceleration, Cylinders, Displacement, Horsepower, Model_Year, and Weight as predictors.

X = [Acceleration Cylinders Displacement Horsepower Model_Year Weight];
tree = fitrtree(X,MPG);

Estimate the predictor importance for all predictor variables.

imp = predictorImportance(tree)

imp = 1×6

    0.0647    0.1068    0.1155    0.1411    0.3348    2.6565

Weight, the last predictor, has the most impact on mileage. The predictor with the minimal impact on making predictions is the first variable, which is Acceleration.

Estimate the predictor importance for all variables in the data and where the regression tree contains surrogate splits.

Load the carsmall data set.

load carsmall

Grow a regression tree for MPG using Acceleration, Cylinders, Displacement, Horsepower, Model_Year, and Weight as predictors. Specify to identify surrogate splits.

X = [Acceleration Cylinders Displacement Horsepower Model_Year Weight];
tree = fitrtree(X,MPG,'Surrogate','on');

Estimate the predictor importance for all predictor variables.

imp = predictorImportance(tree)

imp = 1×6

    1.0449    2.4560    2.5570    2.5788    2.0832    2.8938

Comparing imp to the results in Estimate Predictor Importance, Weight still has the most impact on mileage, but Cylinders is the fourth most important predictor.

Load the carsmall data set. Consider a model that predicts the mean fuel economy of a car given its acceleration, number of cylinders, engine displacement, horsepower, manufacturer, model year, and weight. Consider Cylinders, Mfg, and Model_Year as categorical variables.

load carsmall
Cylinders = categorical(Cylinders);
Mfg = categorical(cellstr(Mfg));
Model_Year = categorical(Model_Year);
X = table(Acceleration,Cylinders,Displacement,Horsepower,Mfg,...
    Model_Year,Weight,MPG);

Display the number of categories represented in the categorical variables.

numCylinders = numel(categories(Cylinders))

numCylinders = 3

numMfg = numel(categories(Mfg))

numMfg = 28

numModelYear = numel(categories(Model_Year))

numModelYear = 3

Because there are 3 categories only in Cylinders and Model_Year, the standard CART, predictor-splitting algorithm prefers splitting a continuous predictor over these two variables.

Train a regression tree using the entire data set. To grow unbiased trees, specify usage of the curvature test for splitting predictors. Because there are missing values in the data, specify usage of surrogate splits.

Mdl = fitrtree(X,'MPG','PredictorSelection','curvature','Surrogate','on');

Estimate predictor importance values by summing changes in the risk due to splits on every predictor and dividing the sum by the number of branch nodes. Compare the estimates using a bar graph.

imp = predictorImportance(Mdl);

figure;
bar(imp);
title('Predictor Importance Estimates');
ylabel('Estimates');
xlabel('Predictors');
h = gca;
h.XTickLabel = Mdl.PredictorNames;
h.XTickLabelRotation = 45;
h.TickLabelInterpreter = 'none';

In this case, Displacement is the most important predictor, followed by Horsepower.