Random Forest

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 random forest to model data. Afterwards, the model can be used to make predictions for other datasets.

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

Fit Random Forest to Data

To use a random forest model in ‘Cornerstone’ open a dataset, e.g. ‘irisdata’ and choose menu ‘Analysis’ -> ‘CornerstoneR’ -> ‘Random Forest’ as shown in the following screenshot.

Random Forest: Menu

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 random forest models at once.

Random Forest: Variable Selection

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

Random Forest: R Script

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.

Random Forest: Result Menu

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.

Random Forest: Statistics Dataset

For instance, the ‘Type’ shows whether the random forest used a classification or regression model. The ‘Sample Size’ let 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. Via ‘Graphs’ -> ‘Variable Importance’ these values can be plotted as bar graph. You can clearly see that ‘petal_length’ and ‘petal_width’ have a higher influence on the response variable then the other two predictors.

Random Forest: Variable Importance

Predictions

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

Random Forest: Predictions

The first column ‘Used.iris_type’ indicates whether this observation was used (1) or not (0) to fit the random forest 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 I manually deleted the second observation. The result is shown in the following screenshot.

Random Forest: Missing Response Observation

Now this row isn’t 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 an additional menu we add an additional menu for each classification.

Random Forest: Confusion Table

The table shows for each level the number of corresponding predictions. For the ‘irisdata’ dataset all predictions match to their observations. For example, no ‘setosa’ was predicted as ‘versicolor’ which is listed in line 6.

Random Forest Models

All models in the ‘Cornerstone’ object ‘randomForest’ can be exported to the workmap via ‘Summaries’ -> ‘Random Forest Models’.

Random Forest: RF Models

We need this export to use existing random forest models in additional datasets for predictions.

Use Fitted Random Forest 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 form this dataset we want to predict the original response ‘iris_type’. Via menu ‘Analyses’ -> ‘CornerstoneR’ -> ‘Model Prediction’ as shown in the following screenshot.

Model Prediction: Menu

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

Model Prediction: Variable Selection

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

Model Prediction: R Script

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

Model Prediction: Input R Objects

We choose ‘Random Forest Models’ as selected ‘R’ objects and click ‘OK’.

Model Prediction: Result Menu

This menu opens a dataset ‘Predictions’ with the input dataset and 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.

Random Forest: Final Workmap

Options in the Script Variables Dialog

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

Random Forest: Script Variables

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 random forest fitting as an additional dichotomous prediction variable. After brushing observations in a graph or dataset execute the random forest ‘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 random forest 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 random forest 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 Random Forest Options

Setting ‘Number of Trees’ to a different value changes the number of trees used to fit the random forest model.

The option ‘Variable Importance Mode’ can be changed between ‘permutation’, ‘impurity’, and ‘impurity_corrected’. The measure is the Gini index for classification and the variance of the response for regression.

Handling of unordered predictors with the option to choose between ‘ignore’, ‘order’, and ‘partition’. For ‘ignore’ all factors are regarded ordered, for ‘partition’ all possible 2-partitions are considered for splitting. For ‘order’ and 2-class classification the predictor levels are ordered by their proportion falling in the second class, for regression by their mean response. For multi-class classification the predictor levels are ordered by the first principal component of the weighted covariance matrix of the contingency table. For details take a look into the documentation of ranger::ranger().

Dirk Surmann, Alessandra Corvonato

2022-04-28