## Initial Situation and Goal

In addition to the ‘Cornerstone’ core methods of fitting data by a linear regression or perform a MANOVA it is possible to use a decision tree to model data.

How do we use the method ‘Decision Tree’ in ‘Cornerstone’ from ‘CornerstoneR’?

## Fit a Decision Tree to Data

To use a decision tree model in ‘Cornerstone’ open a dataset, e.g. ‘irisdata’ and choose menu ‘Analyses’ -> ‘CornerstoneR’ -> ‘Decision Tree’ as shown in the following screenshot.

In the appearing dialog select all ‘sepal_*’ and ‘petal_*’ variables to predictors. ‘iris_type’ is the response variable. It is also possible to select multiple responses to fit multiple decision tree models at once.

‘OK’ confirms your selection and the following window appears.

Now, click the execute button (green arrow) or choose the menu ‘R Script’ -> ‘Execute’ and all calculations are done via ‘R’. Calculations are done if the text at the lower left status bar contains ‘Last execute error state: OK’. Our result is available via the ‘Summaries’ menu as shown in the following screenshot.

### Statistics

Via ‘Summaries’ -> ‘Statistics’ the following dataset with some essential statistics is shown. When you selected multiple response variables these statistics are shown row-wise for each variable.

For instance, the ‘Type’ shows whether the tree used a classification or regression model. The ‘Sample Size’ lets you check on how many observations the model learns. To estimate the calculation time for bigger data ‘Runtime R Script [s]’ shows the corresponding time ‘R’ needed.

### Variable Importance

Via ‘Summaries’ -> ‘Variable Importance’ the following dataset is shown. For multiple responses the variable importance is shown row-wise for each variable. The values are scaled between 0 and 100.

The related variable importance barplot can be found in ‘Graphs’ -> ‘Variable Importance’.

### Predictions

Via ‘Summaries’ -> ‘Predictions’ the following dataset is shown. Each additional response variable gets four additional columns with its corresponding data.

The first column ‘Used.iris_type’ indicates whether this observation was used (1) or not (0) to fit the decision tree model. You find the original data in column ‘iris_type’. The corresponding prediction by the model is shown in column ‘Pred.iris_type’. ‘Resid.iris_type’, as the fourth column, shows the calculated residuum. For classification models it is 0 (matching prediction) or 1 (not matching prediction). In case of regression models we calculate the difference between observation and prediction.

If a response is not observed the model predicts automatically its value. To demonstrate this case, we manually deleted the second observation. The result is shown in the following screenshot.

Now this row is not used to fit the model (‘Used.iris_type’ = 0), its observation is missing as expected, the observation is predicted as ‘setosa’ in column ‘Pred.iris_type’, and it is not possible to calculate a residuum.

### Confusion Table

Confusion tables are only calculated for classification models and available via ‘Summaries’ -> ‘Confusion Table’. For multiple response variables, we add an additional menu for each classification.

The table shows for each level the number of corresponding predictions. For the ‘irisdata’ dataset most predictions match to their observations.

### Tree Plot

By selecting ‘Graphs’ -> ‘Tree Plot’, the tree plot for each response variable shows up. This plot gives a concrete insight into the decision tree model.

### Decision Tree Models

All models in the ‘Cornerstone’ object ‘decisionTree’ can be exported to the workmap via ‘Summaries’ -> ‘Decision Tree Models’.

We need this export to use existing Decision Tree models in additional datasets for predictions.

## Use Fitted Decision Tree for Predictions

In this section we discuss prediction of a response in a new dataset with the existing model from above. Therefore, we open the dataset ‘irisdata’ in ‘Cornerstone’ again and delete the column ‘iris_type’. Starting from this dataset, we want to predict the original response ‘iris_type’. Via menu ‘Analyses’ -> ‘CornerstoneR’ -> ‘Model Prediction’ as shown in the following screenshot.

In the appearing dialog select all ‘sepal_*’ and ‘petal_*’ variables to predictors. We have no response variable.

‘OK’ confirms your selection and the following window appears.

At this point we add the existing Decision Tree model to the prediction dialog at hand. It is possible via menu ‘R Script’ -> ‘Input R Objects’ which brings up the following dialog.

We choose ‘Decision Tree Models’ as selected ‘R’ objects and click ‘OK’.

Now, click the execute button (green arrow) or choose the menu ‘R Script’ -> ‘Execute’ and all calculations are done via ‘R’. Calculations are done if the text at the lower left status bar contains ‘Last execute error state: OK’. Our result is available via the ‘Summaries’ menu as shown in the following screenshot.

This menu opens a dataset with all response columns that are predictable from the chosen random forest models.

Finally, the ‘Cornerstone’ workmap with all generated objects looks like the following screenshot.

## Options in the Script Variables Dialog

Some options are exported from the used ‘R’ method to ‘Cornerstone’. Starting from the ‘R’ analysis object for the Decision Tree, you find the ‘Script Variables’ dialog via the menu ‘R Script’ -> ‘Script Variables’. The following dialog appears.

### Use Brush as Additional Predictor

During the data exploration phase you probably realize a pattern and want to check its impact on your responses. By checking ‘Use Brush State as Additional Predictor’ the current brush selection is used in the decision tree fitting as an additional dichotomous prediction variable. After brushing observations in a graph or dataset execute the decision tree ‘R’ script and the model is updated using the brush as predictor variable.

### Only Use Brushed / Non-brushed Rows for Fitting

As an alternative you can use only brushed or non-brushed observations to fit the decision tree model. Hence, after brushing a number of observations it is not necessary to create a ‘Cornerstone’ subset to exclude or include specific rows, you can just use this option to fit the decision tree model on the brushed or non-brushed set of rows.

If you use the option above, this selection is automatically overwritten by the setting ‘all’ rows.

### Miscellaneous Decision Tree Options

The option ‘Splitting Criterion (for Classification)’ can be changed between ‘Gini’ and ‘Information’ (also called Entropy). The measure for regression is always the Sum of Square Error.

Setting ‘Minimal Node Size’ to a different value changes the minimal node size used to fit the decision tree model. The flag ‘Prune Tree’ can be checked if automatic pruning is required. Both are used for regularization of the model, i.e. to prevent overfitting.

For details, take a look into the documentation of rpart::rpart() and rpart.plot::rpart.plot().

The options ‘Graphic Size: Width’ and ‘Graphic Size: Height’ control the size of the outputted tree plot. Default size is 700x700, which corresponds to a quadratic graphic. For big trees with a lot of nods, it might be helpful to increase the Width of the graphic (e.g. 1300x700) to better distinguish the nods and read the texts in the graphic.