Identifying Groups of listed companies by profitability and liquidity through Gaussian Mixture Model

Project info

• Field of studyAccounting and Auditing
• LevelDoctoral dissertation (S3)
• Method typeClustering
• Estimated build time± 7 working days
• Toolsscikit-learn GaussianMixture, bic, predict_proba
• PriceUS$31 - US$194

Research goal

Apply Gaussian Mixture Model to synthetic data to cluster listed companies by profitability and liquidity and interpret each group's characteristics.

Variables

Example result

• 1Components
• 2917.404BIC
• -8.455Avg log-likelihood
• 0Silhouette
• 1Mean confidence
• 0ARI vs. true groups

The Gaussian mixture selects 1 components by BIC (2917.4) for Company and Return on assets; mean assignment confidence is 1.000.

Computed from illustrative synthetic data, not from a real study.

About Gaussian Mixture Model

A Gaussian Mixture Model represents data as a mixture of several normal distributions and gives cluster membership probabilities. It suits overlapping, elliptical clusters where soft assignment is needed.

Steps

1. 1Standardise numeric features
2. 2Fit a GMM for several numbers of components
3. 3Choose the number of components by BIC or AIC
4. 4Fit the final model and obtain membership probabilities
5. 5Inspect component means, covariances, and weights
6. 6Plot clusters and the BIC curve

Assumptions to check

• Data in each cluster are close to normal
• The number of components is selected by an information criterion
• EM results depend on initialisation, so several restarts are needed

Reading and reporting the results

Report the number of components chosen via BIC, the weights, and a profile of each component. Show membership probabilities for ambiguous points where relevant.

Example Python code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

import numpy as np
import matplotlib.pyplot as plt
from sklearn.mixture import GaussianMixture
from sklearn.datasets import make_blobs
from sklearn.preprocessing import StandardScaler

X, _ = make_blobs(n_samples=500, centers=3, cluster_std=[1.0, 1.5, 0.8], random_state=18)
X = StandardScaler().fit_transform(X)
return_on_assets = X[:, 0]
current_ratio = X[:, 1]

ks = range(1, 8)
bic = []
for k in ks:
    g = GaussianMixture(n_components=k, covariance_type="full", n_init=5, random_state=18).fit(X)
    bic.append(g.bic(X))
    print("k =", k, "BIC =", round(bic[-1], 1))

best_k = list(ks)[int(np.argmin(bic))]
gmm = GaussianMixture(n_components=best_k, covariance_type="full", n_init=5, random_state=18).fit(X)
company = gmm.predict(X)
prob = gmm.predict_proba(X)
print("Chosen k:", best_k, "weights:", gmm.weights_.round(3))
print("Ambiguous points (max prob < 0.8):", int((prob.max(axis=1) < 0.8).sum()))

fig, ax = plt.subplots(1, 2, figsize=(10, 4))
ax[0].plot(list(ks), bic, marker="o"); ax[0].set_xlabel("Components"); ax[0].set_ylabel("BIC")
ax[1].scatter(return_on_assets, current_ratio, c=company, s=15)
plt.tight_layout()
plt.show()

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions