Random Forest Classification
Prepared by Dr Wayne Bovey
Objective
According to IBM, random forest is a commonly used machine learning algorithm that combines the output of multiple decision trees to reach a single result. Random forest handles both classification and regression problems. For classification tasks, the output of the random forest is the class selected by most trees. For regression tasks, the output of the random forest is the mean prediction of the individual trees.
This vignette demonstrates random forest classification with two objectives. First, develop a model identifying the most significant explanatory variables associated with the target variable, reaction to organisational change. Second, predict an individual’s reaction to change and evaluate the accuracy of these predictions.
The original dataset comprised 616 respondents from 10 public and private sector organisations experiencing organisational change. Respondents reported self-efficacy, irrational ideas, maladaptive defence mechanisms, emotion, behavioural intentions and reaction towards change in their organisation.
Workflow
The raw dataset was wrangled and tidied before processing. Conducted a brief exploratory analysis comprising a statistical summary, correlation, and comparative analysis to understand the variables.
The random forest classifier was developed and fitted on the training data using a workflow that considered resampling methods, feature engineering, model specifications and hyperparameter optimisation. Reviewed the results of the training model and identified important predictor variables associated with reaction to organisational change.
The trained model was then applied to the unseen test data to predict the target or outcome variable. Evaluated the model’s performance on the test data with classification metrics and visually with confusion matrix heatmap and ROC curve.
Results
1. Explore data
Commenced by reviewing the outcome variable for the random forest classifier (reaction). The existing seven-point Likert scale measuring reaction to organisational change was collapsed into a binary categorical variable. Because this classifier aims to predict either support or opposition to change, neutral responses on the Likert scale were dropped from the new binary factor. Tables 1 and 2 summarise the transformation of the outcome variable from an interval scale to a binary factor.
| Table 1 Original seven-point Likert scale | |
| Reaction to change | Freq |
|---|---|
| Totally Oppose | 73 |
| Oppose | 71 |
| Partially Oppose | 90 |
| Neutral | 124 |
| Partially Support | 189 |
| Support | 23 |
| Totally Support | 46 |
| Table 2 New binary scale for classification | |
| Reaction to change | Freq |
|---|---|
| oppose | 184 |
| support | 359 |
The dataset was filtered and reduced to analyse only those respondents who reported experiencing significant organisational change. Table 3 is a statistical summary for each of the proposed explanatory variables.
| Table 3 Statistical summary of explanatory variables | ||||||||||||
| variable | n | mean | sd | median | trimmed | mad | min | max | range | skew | kurtosis | se |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| self_efficacy | 208 | 5.55 | 0.81 | 5.65 | 5.63 | 0.78 | 1.71 | 6.94 | 5.24 | −1.19 | 2.71 | 0.06 |
| needs_approval | 208 | 4.19 | 1.40 | 4.00 | 4.22 | 1.48 | 1.00 | 7.00 | 6.00 | −0.14 | −0.73 | 0.10 |
| fears_failure | 208 | 4.06 | 1.51 | 4.00 | 4.07 | 1.48 | 1.00 | 7.00 | 6.00 | 0.00 | −0.83 | 0.10 |
| labelling_blame | 208 | 3.19 | 1.32 | 3.00 | 3.11 | 1.48 | 1.00 | 7.00 | 6.00 | 0.55 | −0.31 | 0.09 |
| catastrophising | 208 | 3.70 | 1.32 | 3.50 | 3.66 | 1.48 | 1.00 | 7.00 | 6.00 | 0.15 | −0.89 | 0.09 |
| managing_feelings | 208 | 3.88 | 1.31 | 4.00 | 3.88 | 1.48 | 1.00 | 6.50 | 5.50 | −0.05 | −0.72 | 0.09 |
| anxious_thoughts | 208 | 4.10 | 1.16 | 4.00 | 4.13 | 0.74 | 1.50 | 7.00 | 5.50 | −0.17 | −0.38 | 0.08 |
| avoidance | 208 | 2.25 | 0.99 | 2.00 | 2.14 | 0.74 | 1.00 | 5.50 | 4.50 | 1.05 | 0.90 | 0.07 |
| past_influences | 208 | 2.79 | 1.30 | 2.50 | 2.71 | 1.48 | 1.00 | 6.00 | 5.00 | 0.56 | −0.76 | 0.09 |
| facing_reality | 208 | 4.54 | 1.44 | 5.00 | 4.60 | 1.48 | 1.00 | 7.00 | 6.00 | −0.35 | −0.80 | 0.10 |
| passive_existence | 208 | 4.23 | 1.24 | 4.00 | 4.26 | 1.48 | 1.00 | 7.00 | 6.00 | −0.18 | −0.46 | 0.09 |
| dissociation | 208 | 2.74 | 1.21 | 2.50 | 2.61 | 0.74 | 1.00 | 6.50 | 5.50 | 0.90 | 0.24 | 0.08 |
| displacement | 208 | 3.04 | 1.28 | 3.00 | 2.99 | 1.48 | 1.00 | 7.00 | 6.00 | 0.34 | −0.50 | 0.09 |
| isolation_of_affect | 208 | 3.41 | 1.49 | 3.50 | 3.38 | 2.22 | 1.00 | 7.00 | 6.00 | 0.16 | −0.92 | 0.10 |
| reaction_formation | 208 | 4.17 | 1.25 | 4.00 | 4.17 | 1.48 | 1.50 | 7.00 | 5.50 | 0.07 | −0.65 | 0.09 |
| denial | 208 | 2.51 | 1.03 | 2.00 | 2.44 | 0.74 | 1.00 | 6.50 | 5.50 | 0.79 | 0.40 | 0.07 |
| projection | 208 | 2.49 | 1.11 | 2.00 | 2.39 | 0.74 | 1.00 | 6.00 | 5.00 | 0.88 | 0.09 | 0.08 |
| passive_aggression | 208 | 2.62 | 1.08 | 2.50 | 2.52 | 0.74 | 1.00 | 6.50 | 5.50 | 0.88 | 0.55 | 0.07 |
| acting_out | 208 | 3.55 | 1.34 | 3.50 | 3.54 | 1.48 | 1.00 | 6.50 | 5.50 | 0.04 | −0.88 | 0.09 |
| emotion | 208 | 3.80 | 1.15 | 3.80 | 3.79 | 1.19 | 1.00 | 6.90 | 5.90 | 0.09 | −0.32 | 0.08 |
| behavioural_intentions | 208 | 5.08 | 1.13 | 5.25 | 5.15 | 1.26 | 1.75 | 7.00 | 5.25 | −0.57 | −0.21 | 0.08 |
Chart 1 supports Table 3, showing correlations between the proposed explanatory variables.
Because of the number of explanatory variables under consideration, prepared a separate pairs plot for each latent variable. Chart 2 compares the relationship between irrational ideas and the outcome variable, reaction to organisational change. Chart 3 compares the relationship between maladaptive defence mechanisms and the outcome variable, reaction to organisational change.
2. Random forest classification
2.1 Train model
2.1.1 Build model
Commenced building the model by randomly splitting the data into a training and testing set at a 3:1 ratio using stratified sampling. Stratified sampling allocates approximately equal proportions of observations across the range of values for the outcome variable to balance the training and testing sets. Resampled data in the training set using five repeats of 10-fold cross-validation. The recipe for the random forest was a standard formula with no additional feature engineering. The model was specified, and a workflow created for implementation.
Because ideal parameters to tune and train the model are unknown, many models were tuned using different parameter values to assess model performance. This was implemented using parallel processing, as parameter tuning is computationally intensive. Chart 4 shows the results of the initial tuning. Various parameter values for min_n (minimum number of data points in a node required before splitting) and mtry (number of randomly sampled predictors) were assessed against the classification metric, area under the curve (auc).
Guided by initial tuning results in Chart 4, investigated a targeted short-list of parameter tuning combinations to extract the best parameter tuning combination. Chart 5 shows the result.
With parameter tuning complete, the workflow and model were finalised for fitting.
2.1.2 Fit and review model
The tuned model was fitted on the training set. Chart 6 illustrates the importance of explanatory variables on the target variable, reaction to organisational change. The most important variables were behavioural intentions and emotion.
2.2 Test model
2.2.1 Predict on test data
The model fitted on the training data was then applied to the unseen testing data to predict the outcome variable. Table 4 compares actual reaction and predicted reaction (.pred_class) in a small sample of observations extracted from the testing data.
| Table 4 Sample of outcome variable predictions in test data | ||||||||||||||||||||||
| reaction | .pred_class | self_efficacy | needs_approval | fears_failure | labelling_blame | catastrophising | managing_feelings | anxious_thoughts | avoidance | past_influences | facing_reality | passive_existence | dissociation | displacement | isolation_of_affect | reaction_formation | denial | projection | passive_aggression | acting_out | emotion | behavioural_intentions |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| oppose | oppose | 5.71 | 3.00 | 3.00 | 2.00 | 3.00 | 3.00 | 4.00 | 2.00 | 2.00 | 3.00 | 2.00 | 2.00 | 3.00 | 4.00 | 5.00 | 2.00 | 2.00 | 2.00 | 3.00 | 3.75 | 3.40 |
| support | support | 5.29 | 4.50 | 5.00 | 3.00 | 3.50 | 3.50 | 4.00 | 2.00 | 2.50 | 5.00 | 2.00 | 6.00 | 1.00 | 4.50 | 3.50 | 4.50 | 2.00 | 2.00 | 4.50 | 6.00 | 5.60 |
| oppose | oppose | 4.94 | 4.50 | 4.00 | 5.00 | 5.00 | 4.00 | 4.50 | 3.00 | 5.00 | 5.50 | 5.50 | 2.50 | 4.50 | 4.50 | 3.50 | 3.50 | 4.00 | 4.00 | 5.50 | 2.40 | 4.00 |
| oppose | oppose | 6.12 | 2.00 | 4.50 | 2.50 | 2.00 | 2.00 | 1.50 | 2.50 | 1.00 | 3.00 | 4.50 | 1.50 | 2.00 | 1.50 | 3.50 | 1.50 | 2.00 | 1.50 | 1.00 | 3.75 | 4.30 |
| support | oppose | 4.82 | 3.00 | 4.50 | 6.00 | 3.50 | 6.50 | 4.50 | 4.00 | 3.50 | 5.50 | 6.50 | 4.50 | 6.00 | 4.50 | 3.00 | 3.50 | 6.00 | 6.50 | 4.00 | 3.65 | 3.89 |
| oppose | oppose | 5.59 | 4.00 | 2.50 | 3.50 | 2.50 | 3.50 | 3.50 | 2.00 | 5.00 | 5.00 | 4.00 | 2.00 | 3.50 | 2.00 | 3.00 | 3.50 | 2.50 | 3.50 | 3.50 | 3.00 | 3.90 |
| support | support | 5.29 | 3.50 | 3.00 | 4.00 | 4.50 | 4.50 | 4.00 | 3.50 | 1.50 | 6.00 | 5.00 | 5.00 | 4.00 | 3.00 | 3.50 | 4.00 | 4.50 | 2.00 | 6.00 | 4.70 | 4.80 |
| oppose | oppose | 3.41 | 6.50 | 2.50 | 5.00 | 4.00 | 6.00 | 5.50 | 3.50 | 5.50 | 6.00 | 5.50 | 1.00 | 4.00 | 4.00 | 3.50 | 2.00 | 4.00 | 3.00 | 5.00 | 1.55 | 3.90 |
| support | support | 5.82 | 3.50 | 5.00 | 4.00 | 3.50 | 3.00 | 4.50 | 2.50 | 2.50 | 4.50 | 4.50 | 2.50 | 3.50 | 3.50 | 5.50 | 3.50 | 3.50 | 3.50 | 4.50 | 4.30 | 5.40 |
| oppose | oppose | 6.24 | 5.00 | 3.50 | 1.50 | 3.50 | 5.00 | 3.50 | 1.50 | 1.50 | 3.00 | 4.00 | 5.50 | 1.50 | 1.50 | 4.00 | 3.00 | 2.00 | 1.50 | 6.00 | 3.45 | 4.90 |
| support | oppose | 5.25 | 5.50 | 6.00 | 4.50 | 4.50 | 6.50 | 5.00 | 5.00 | 5.00 | 6.50 | 4.00 | 1.50 | 3.50 | 4.00 | 4.50 | 2.00 | 3.50 | 4.00 | 3.00 | 3.05 | 6.00 |
| oppose | oppose | 6.94 | 5.00 | 3.00 | 5.00 | 5.00 | 5.00 | 6.00 | 1.50 | 3.00 | 3.00 | 5.00 | 1.50 | 4.00 | 2.00 | 6.00 | 1.00 | 2.00 | 2.00 | 1.00 | 2.60 | 4.35 |
| oppose | oppose | 3.94 | 5.00 | 4.00 | 5.50 | 5.00 | 6.00 | 4.00 | 2.00 | 2.00 | 5.00 | 5.00 | 3.50 | 5.50 | 2.00 | 3.50 | 2.00 | 2.50 | 1.50 | 5.50 | 2.30 | 4.10 |
| oppose | oppose | 4.76 | 3.50 | 4.00 | 4.00 | 5.50 | 4.00 | 4.00 | 2.00 | 2.00 | 6.50 | 4.50 | 1.00 | 4.50 | 3.00 | 3.00 | 1.00 | 3.00 | 1.50 | 1.00 | 1.75 | 3.95 |
| support | support | 6.65 | 2.00 | 1.50 | 1.00 | 1.50 | 1.50 | 3.50 | 1.00 | 1.50 | 1.50 | 2.00 | 3.50 | 2.00 | 2.00 | 4.00 | 1.50 | 1.00 | 2.00 | 3.50 | 4.80 | 6.30 |
2.2.2 Evaluate model on test data
Table 5 summarises key classification metrics for test set predictions.
| Table 5 Key classification metrics for the test set | |||
| .metric | .estimator | .estimate | .config |
|---|---|---|---|
| accuracy | binary | 0.8868 | Preprocessor1_Model1 |
| roc_auc | binary | 0.9551 | Preprocessor1_Model1 |
Chart 7 confusion matrix heatmap summarises predictions by categorising and comparing predicted against the actual response for the binary outcome variable. The confusion matrix calculates model accuracy at 88.68 per cent (true positive and true negative).
The ROC curve (receiver operating characteristic curve) plots the true positive rate (sensitivity) against the false positive rate (specificity) at all classification thresholds. AUC (area under the curve) measures the entire two-dimensional area underneath the ROC curve. Chart 8 illustrates the random forest classifier’s ROC curve with a favourable AUC result that is greater than 0.90.
References:
Self-efficacy was measured using the ‘Self-efficacy scale:
Construction and validation’ by Sherer, Maddux, Mercandante,
Prentice-Dunn and Rogers, published in Psychological
Reports.
Irrational ideas were measured using the ‘Irrational belief scale’
developed by Malouff and Schutte, published in the Sourcebook of
Adult Assessment Strategies, based on Ellis and Harper’s work,
published in A New Guide to Rational Living.
Maladaptive defence mechanisms were measured using selected items from
‘The Defense Style Questionnaire’ by Andrews, Singh and Bond, published
in The Journal of Nervous and Mental Disease.
Emotion was measured using ‘A semantic differential mood scale’ by Lorr
and Wunderlich, published in the Journal of Clinical
Psychology.
Session information and package update
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## xtable 1.8-4 2019-04-21 [1] CRAN (R 4.4.0)
## yaml 2.3.9 2024-07-05 [1] CRAN (R 4.4.1)
## yardstick * 1.3.1 2024-03-21 [1] CRAN (R 4.4.0)
##
## [1] C:/Users/wayne/AppData/Local/R/win-library/4.4
## [2] C:/Program Files/R/R-4.4.0/library
##
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