Help Manual


Sigma Magic Help Version 15

Recursive Decision Tree


This analysis can be used to determine a decision tree based on recursive partitioning for classification and regression trees. This program builds classification or regression models of a very general structure using a two-stage procedure; the resulting models can be represented as binary trees. This model works well for variables where there is a definite ordering but the spacing between values is not necessarily equal. The tree is built by the following process: first, the single variable is found which best splits the data into two groups. The data is separated, and then this process is applied separately to each sub-group, and so on recursively until the subgroups either reach a minimum size or until no improvement can be made. Once the tree is developed, it can be used to make predictions.

This functionality is provided by the R software using the function rpart within the rpart package. Note that this functionality requires that R Script software be installed on your computer and linked to the Sigma Magic software within the options menu. Recursive Decision Tree worksheet can be added to your active workbook by clicking on Analytics and then selecting Decision Tree > Recursive.


Click on Analysis Setup to open the menu options for this tool. A sample screenshot of the menu is shown below.
menu 1
Data Type: Specify the type of output variable you are dealing with.
ContinuousContinuous data can take any value within a range.
CategoricalCategorical data only takes specific values
Input Type: Specify how input data is formatted. Currently, the only option for this analysis is Raw Data.
Training Set: Specify the data to be used for training the algorithms.
AutoRandom method for selection of the training data set is used./td>
RandomA random number algorithm is used to select the training set.
SequentialA sequential set of samples are picked. For example: 1st point, 3rd point, 5th point etc.
Training Size: Specify what % of the data points should be picked for the training set. These are used to build the model and the remaining points are used to test the model.
Min Split: Specify the minimum sum of weights in a node n order to be considered for splitting. If the sum of weights is below this value, the node is not split further.
Min Bucket: This is the minimum sum of weights in a terminal node. Typically, this is equal to min split divided by 3.
Complexity: The complexity parameter is used to determine the splits. Any split that does not decrease the overall lack of fit by a factor of cp is not attempted.
Cross Validation: Specify the number of cross-validations.
Max Depth: This is the maximum depth of the tree. The default value is 0, which means that there is no restriction applied on the tree size.
Use Surrogates: Specify how you want to use the surrogates in the splitting process. You could specify that any missing value for the primary split is not sent further down the tree, or you could use surrogates in order to split if there are missing values and finally if all surrogates are missing you could send the observation in the majority direction.
Max Surrogates: Specify the number of surrogate splits that should be retained in the output. If this is set to zero, then the compute time is reduced.
Surrogate Style: This controls the selection of a best surrogate. If set to the default value, the program uses the total number of correct classifications for a potential surrogate variable, or it uses the percent correct calculated over non-missing values of the surrogate.
Additional Options: This field is optional. You can specify any additional options for the R software program directly by typing it here.
Help Button: Click on the Help Button to view the help documentation for this tool.
Cancel Button: Click on the Cancel Button to discard your changes and exit this menu.
OK Button: Click on the OK Button to save your changes and try to execute the program. Note that you will need to specify the required data in order to complete the analysis and generate outputs. If there are any missing data, then the software will remind you to specify the data and click on Compute Outputs to generate analysis results.


If you click on the Data button, you will see the following dialog box. Here you can specify the data required for this analysis. Data
Search Data: The available data displays all the columns of data that are available for analysis. You can use the search bar to filter this list and to speed up finding the right data to use for analysis. Enter a few characters in the search field and the software will filter and display the filtered data in the Available Data box.
Available Data: The available data box contains the list of data available for analysis. If your workbook does not have any data in tabular format, this box will display "No Data Found". The information displayed in this box includes the row number, whether the data is Numeric (N) or Text (T), and the name of the column variable. Note that the software displays data from all the tables in the current workbook. Even though data within the same table have unique column names, columns across different tables can have similar names. Hence, it is important that you not only specify the column name but also the table name.
Add or View Data: Click on this button either to add more data into your workbook for analysis or to view more details about the data listed in the available data box. When you click on this button, it opens up the Data Editor dialog box where you can import more data into your workbook, or you can switch from the list view to a table view to see the individual data values for each column.
Required Data: The code for the required data specifies what data can be specified for that box. An example code is N: 2-4. If the code starts with an N, then you will need to select only numeric columns. If the code starts with a T, then you can select both numeric and text columns. The numbers to the right of the colon specify the min-max values. For example, if the min-max values are 2-4, then you need to select a minimum of 2 columns of data and a maximum of 4 columns of data in this box. If the minimum value is 0, then no data is required to be specified for this box.
Select Button: Click on this button to select the data for analysis. Any data you select for the analysis is moved to the right. To select a column, click on the columns in the Available Databox to highlight them and then click on the Select Button. A second method to select the data is to double click on the columns in the list of Available Data. Finally, you can also drag and drop the columns you are interested in by holding down the select columns using your left mouse key and dragging and dropping them in one of the boxes on the right.
Selected Data: If the right amount of data columns has been specified, the list box header will be displayed in the black color. If sufficient data has not been specified, then the list box header will be displayed in the red color. Note that you can double-click on any of the columns in this box to remove them from the box.
View Selection: Click on this button to view the data you have specified for this analysis. The data can be viewed either in the tablular format or you can view a graphical summary of the data selected.


If you click on the Program button, the software will display the program code - an example screenshot is shown in the figure below. Pre-Process Inputs 3
R Program: You can view the R program that will be executed here. This program is usually automatically generated from the options you have specified in the setup earlier. This is the program that will be executed by the R program to generate analysis outputs. If you like, you can edit this program.
Auto Mode: If the radio button is selected as Auto, then the software will automatically update this code based on any changes you make in the input dialog box. We recommend that you use this option to generate the R program so that all your input settings are used to generate analysis results.
Manual Mode: If you use the Manual option, then you will be allowed to edit the R program before the program is executed. Make sure that you specify a syntactically correct program; otherwise, the R program may report errors.


If you click on the Verify button, the software will perform some checks on the data you have entered. A sample screenshot of the data is shown in this figure. Pre-Process Inputs 4
Verify Checks: The objective of this analysis as well as any checks that are performed are listed in this dialog box. For example, the software may check if you have correctly specified the input options and if you have specified the data correctly for analysis.
Check Status: The results of the analysis checks are listed here. If the checks are passed, then they are shown as a green-colored checkmark. If the verification checks fail, then they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange color exclamation mark and finally, any checks that are required to be performed by the user are shown as blue info icons.


Click on Compute Outputs to update the results on the worksheet. A sample screenshot of the worksheet is shown below.
Recursive Tree Example
Notes Section: The notes section provides a summary of the input data and the analysis results section shows the name of the response variable along with the names of the input variables. The final decision tree that was derived is shown in text format below. The output section contains the decision criteria, the number of data points in that segment, the error between the model and actual (deviance), and the predicted mpg for that segment.
Graph Section: The graph section shows the decision tree and the split criteria along with the number of data points in each node. For this analysis, the decision tree is based on 2 variables cyl (less than 5 and greater than or equal to 5) and hp (less than 192.5 and greater than or equal to 192.5). Based on this analysis, there are three terminal nodes. In the first terminal node, there are 7 cars with an average of 13.41 mpg. In the second terminal node, there are 14 cars with an average of 18.25 mpg. In the third terminal node, there are 11 cars with an average of 26.7 mpg.

Using this model, the predictions are shown in the prediction column. For example, for the first car, the actual mileage is 21 mpg while the prediction based on the decision tree is 18.26 mpg. If you have any data for which you need to make a prediction, you can specify those in the inputs section without specifying a response value. These rows of data will not be used to build your model, but they will be used to make the predictions.


Here are a few pointers regarding this analysis:
  • This analysis requires that the R software needs to be installed on your computer. Further, you will need to provide a link to the RScript executable file under Sigma Magic Options so that the software can use the R software to generate analysis results.


Following examples can be found in the Examples folder.
  • For the data given in the file, use the recursive decision tree to build a model between the output mpg and the other inputs. Use this model to make predictions for other cars. (Recursive Tree 1.xlsm)


For more information on this topic, please refer to the following articles. Do note that if any external links are mentioned below, they are for reference purposes only.