# Help Manual

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Sigma Magic Help Version 15

# Conditional Decision Tree

## Overview

This analysis can be used to determine a decision tree based on a conditional inference framework. The tree split is determined by the P-values (the split is implemented if the P-value is less than alpha, typically 0.05). This statistical approach ensures that the right-sized tree is grown without requiring additional pruning or cross-validation. Once the tree is developed, it can be used to make predictions.

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

## Inputs

Click on Analysis Setup to open the menu options for this tool. A sample screenshot of the menu is shown below.
1
Data Type: Specify the type of output variable you are dealing with.
OptionDescription
ContinuousContinuous data can take any value within a range.
CategoricalCategorical data only take specific values.
2
Input Type: You can specify the type of input data. Currently, the only option that can be specified is Raw Data.
3
Training Set: Specify the data to be used for training the algorithms.
OptionDescription
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.
4
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.
5
Test Stat: To convert the observed multivariate test statistic into a real number for analysis, we can either use the quadratic form or the maximum value.
OptionDescription
AutoThe default is to use the quadratic method./td>
MaxUse the maximum value as the test statistic.
QuadThe quadratic form is computationally more expensive compared to max values.
6
Test Type: Specify how to compute the distribution of the test statistic. Available methods are:
OptionDescription
AutoUses the Bonferroni method as the default.
BonferroniUses this correction for multiple comparisons.
MonteCarloUses the test statistic rather than comparing the P values.
UnivariateDoes not use any correction for multiple comparisons.
7
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.
8
Min Bucket: This is the minimum sum of weights in a terminal node. Typically this is equal to min split divided by 3.
9
Max Depth: This is the maximum depth of the tree. The default value is 0, which means that there is no restriction applied to the tree size.
10
Confidence Level: The confidence level for this analysis. If the P-value should be less than (1 - Confidence Level) in order for a node to be split further.
11
Help Button: Click on the Help Button to view the help documentation for this tool.
12
Cancel Button: Click on the Cancel Button to discard your changes and exit this menu.
13
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.

### Data

If you click on the Data button, you will see the following dialog box. Here you can specify the data required for this analysis.
 1 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. 2 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. 3 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. 4 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. 5 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. 6 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. 7 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.

### Program

If you click on the Program button, the software will display the program code - an example screenshot is shown in the figure below.
 1 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. 2 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. 3 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.

### Verify

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.
 1 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. 2 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.

## Outputs

Click on Compute Outputs to update the results on the worksheet. A sample screenshot of the worksheet is shown below.
 1 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 names of the input variables. The final decision tree that was derived is shown in text format below. 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. For this example, for the first car, the actual mpg is 21, and the predicted mpg is 20.75. The difference between these two values is the model error. 2 Graph Section: The graph section shows the decision tree and the split criteria, along with the number of data points in each node. The prediction of the response variable using this decision tree is also shown in the outputs section. For this example shown, two variables were used to build a decision tree model. The first is weight, and the second is displacement. If the weight is less than 2.32, it belongs to one category, and if the weight is greater than 2.32, it belongs to another category. For a weight greater than 2.32, the displacement greater than 258 is in one category, and displacement less than 258 is in another category. This decision tree has 3 terminal nodes. The first node has 7 cars, the second node has 11 cars, and the third node has 14 cars. The box plot within each node shows the variation in the mpg. For this analysis, only 2 variables (weight and disp) are sufficient to make reasonably good predictions of the car mpg values.

## Notes

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.

## Examples

Following examples can be found in the Examples folder.
• For the data given in the file, determine the conditional decision tree. (Conditional Tree 1.xlsm)

## References

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.