What is 'categorical predictor' in decision tree for regression

Hi, I'd like to use Matlab's own example for the question. Please refer to https://uk.mathworks.com/help/stats/fitrtree.html for the original example.

>> load carsmall

>> whos
  Name                Size            Bytes  Class     Attributes

  Acceleration      100x1               800  double              
  Cylinders         100x1               800  double              
  Displacement      100x1               800  double              
  Horsepower        100x1               800  double              
  MPG               100x1               800  double              
  Mfg               100x13             2600  char                
  Model             100x33             6600  char                
  Model_Year        100x1               800  double              
  Origin            100x7              1400  char                
  Weight            100x1               800  double              

>> tree = fitrtree([Weight, Cylinders],MPG,...
                'categoricalpredictors',2,'MinParentSize',20,...
                'PredictorNames',{'W','C'})

tree = 

  RegressionTree
           PredictorNames: {'W'  'C'}
             ResponseName: 'Y'
    CategoricalPredictors: 2
        ResponseTransform: 'none'
          NumObservations: 94


  Properties, Methods

What exactly is the Categorical Predictors in this case and why it is 2?

Answer 1

[Adam Danz]

Matlab's fitrtree() function returns a regression tree object. Read more about this object and its properties here:

https://www.mathworks.com/help/stats/classreg.learning.partition.regressionpartitionedmodel-class.html

As you'll read in the link above, the "CategoricalPredictors" contains index values corresponding to the columns of the categorical predictor data (if none of the predictors are categorical, this will be empty []).

So, why is it CategoricalPredictors equal to 2?

Now read about the function you're using fitrtree()

https://www.mathworks.com/help/stats/fitrtree.html#bt6cr84-tree

One of the name-value pairs (<- link) is 'CategoricalPredictors' which, is specified in your call to fitrtree() as 2. That's because you have two predictors being treated as categorical variables, [Weight, Cylinders].

[Adam Danz]

This is also covered in the documentation I linked to. In general, it's a good idea to take a few minutes to read through the documentation when you're using a new function and the literature is generally short and terse.

Here's the section on 'PredictorNames' https://www.mathworks.com/help/stats/fitrtree.html#bt6cr84_sep_shared-PredictorNames

It's just a cell array of strings that name your predictors. If you add a 3rd predictor, you need to add a 3rd predictor name.

tree = fitrtree([Weight, Cylinders, Acceleration],MPG,...
                'categoricalpredictors',3,'MinParentSize',20,...
                'PredictorNames',{'W','C', 'A'})  % <- added 'A' for acceleration

[Salad Box]

Actually, as I read a few times, 'the "CategoricalPredictors" contains index values corresponding to the columns of the categorical predictor data', 'index value' (or the 'entry') means if index value is 1, that is the first column of the predictor data, in this case, it is 'Weight'; if 'index value' is 2, that is the second column of the predictor data, in this case, it is 'Cylinders'.

So

tree = fitrtree([Weight, Cylinders],MPG,...
                'categoricalpredictors',2,'MinParentSize',20,...
                'PredictorNames',{'W','C'})

indicates 'Cylinders' (the 2nd column in the predictor data) is a categorical predictor. In fact, there are only 4, 6, 8 cylinders, the number is not countinuous.

[Rui An]

how could i combine the tree with boxplot