Female Representation in Management of Australian Organisations

Research Question

Data Description – Overview

Source: Workplace Gender Equality Agency (WGEA) Public Dataset 2024

• Legally mandated survey responses from 7,415 Australian employers (≥100 staff)
• 7 linked datasets covering workforce composition and organisational policies

Data Description – Target Variable

Female representation in management (as a percentage of total managers):

• Represented by five equally sized ordinal classes (quintiles)

🟥 Very Low  🟨 Low  🟩 Moderate   🟦High  🟪 Very High

Constructed using data from Workforce Management Statistics:

% female managers = Number of Female Managers / Total Managers

Data Description – Challenges

Integration: Datasets in long format, linked by employer_abn.

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 p o s i t i o n : N A A 1 A D U A M g A = 
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 s u f f i x : :31b8e172-b470-440e-83d8-e6b185028602

</tr>

→ Each employer appears multiple times across occupations and policies, including multi-choice questions.

Data Description – Challenges (cont.)

Data Cleaning and Preparation

The WGEA data was consolidated into a single employer-level dataset for classification.

Data Integration

• Merged seven raw datasets using employer_abn as key.
• Combined workforce statistics and policy indicators into one wide table.
  
  

Feature Engineering

• Workforce Composition Features: % employee count in each subcategory.

• Organisational Policy Features: Binary policy presence flags.

• Workforce Movement Features: Gender-specific promotion and resignation rates.

Data Cleaning and Preparation (cont.)

Target Variable Creation

• Transformed management_female_percent into 5 categorical quantiles, each with ~20% of organisations.
  

Handling Missing Values

• Dropped records without a valid employer_abn.
• “numeric and binary NAs” -> 0 (absence = attribute not present).
• “categorical NAs” -> “None Reported” (preserve informative missingness).
  
  

Result

Final dataset: 6673 employer-level records & 32 features fit for identifying patterns of gender representation in management.

EDA – Target Variable Distribution

• Underlying distribution of female management share is right-skewed.
• Most organisations have < 40% female representation in management.
• Only a minority of firms reach or exceed gender parity.
• Overall under representation of women in management roles.

EDA – PCA

• PCA: parametric, global, linear view.
• PC1 = 35.3%, PC2 = 18.4% together explain about 53.7% of total variance
• PCA scatterplot: overlap between classes but a slight separation trend along PC1.
• Scree plot: variance sharply declines after the first 3 components.

EDA – tSNE

• t-SNE: non-parametric, local, non-linear view.
• Organisations grouped by similar female management levels.
• Very Low (red) and Very High (purple) categories form partial clusters.
• Middle groups overlap, suggesting gradual structural transitions.
• Non-linear models (eg. XGBoost, Decision Tree) better suited to capture complex patterns.

Modelling Plan

Trained Models

• Multinomial Logistic Regression:
  • Interpretable linear baseline for multi-class data.
    
  • Ridge and Lasso regression were also test but were excluded due to performance.
• Decision Tree:
  • Interpretable model using hierarchical feature splits.
  • Simple non-linear model trained with rpart, tuning cp between 0.001 and 0.05.
• k-Nearest Neighbours:
  • Non-parametric model capturing non-linear boundaries.
  • Tuned neighbour count (k = 1–20) with feature standardisation (center, scale).
• Support Vector Machine (RBF Kernel):
  • Kernel method effective for non-linear, high-dimensional data.
    
  • Tuned cost (C) and kernel width (sigma) via grid search (tuneLength = 15).
• XGBoost:
  • Ensemble learner handling complex patterns with regularisation.
  • Gradient boosting model tuned via random search (tuneLength = 40)

Modelling Plan (cont.)

Model Training Pipeline

• All models used same 5-fold stratified cross-validation with an 80/20 train-test split to ensure fair comparison.
• Implemented with the caret package for consistent preprocessing, tuning, and evaluation.
  
• Shared trainControl parameters across all models:
  • method = “cv”, number = 5
    
  • classProbs = TRUE for probability outputs
    
  • preProcess = c(“zv”, “center”, “scale”)
    
  • summaryFunction = multiClassSummary for macro metrics
    
  • savePredictions = “final” to retain fold-level predictions
    

Evaluation

• Primary Metric: Macro F1-Score (equal weight to all five classes).
  
• Secondary Metrics: Precision, Recall, AUC, and Ordinal Mean Absolute Error (MAE) for interpretability.
  

Model Results – Summary

Model Results – Confusion Matrix

Top Features – Logistic Regression

Note: The V.Low category is omitted as it serves as the base (reference) class in the multinomial logistic regression. All reported coefficients are expressed relative to this baseline.

Top Policy Features – Logistic Regression

Note: The V.Low category is omitted as it serves as the base (reference) class in the multinomial logistic regression. All reported coefficients are expressed relative to this baseline.

Conclusion

Summary

• Moderate predictive accuracy (AUC ≈ 0.9, MAE ≈ 0.4)
  
• Full-time female share = dominant driver
  
• Policies add incremental but smaller signal
  
  

Limitations

• Cross-sectional → no causality
  
• Self-reported data may inflate policy adoption
  
• Sparse binary vars, 5-class bucketing hides nuance
  
  

Future Work

• Analyse drivers of full-time female employment
  
• Use ordinal-aware or hierarchical models
  
• Add temporal data to assess causal impact