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This skill covers the full educational data mining (EDM) pipeline: ingesting LMS event
logs, modelling student knowledge with Bayesian Knowledge Tracing, predicting dropout
with survival analysis, mining activity sequences, and running Item Response Theory
assessments.
Installation
pip install numpy pandas scipy scikit-learn lifelines matplotlib
# Optional: pyBKT for a production-grade BKT implementation
pip install pyBKT
1. Loading and Preparing LMS Logs
Moodle exports a CSV with columns such as Time, User full name, Event name,
Component. Canvas exports a similar structure.
Example A — Predict At-Risk Students from Early LMS Engagement
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import StratifiedKFold
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import roc_auc_score
from sklearn.preprocessing import StandardScaler
# Suppose we have a Moodle log exported as CSV# df_logs = load_lms_logs("/data/moodle_course_2024.csv")# Simulate a feature table (replace with real feature engineering from LMS logs)
np.random.seed(42)
n = 400
df_students = pd.DataFrame({
"user_id": range(n),
"week1_logins": np.random.poisson(5, n),
"week1_forum_posts": np.random.poisson(1.5, n),
"week1_quiz_score": np.random.beta(3, 2, n) * 100,
"week1_video_minutes": np.random.exponential(30, n),
"dropout_week": np.random.randint(2, 16, n),
"dropped_out": np.random.binomial(1, 0.25, n),
})
covariates = ["week1_logins", "week1_forum_posts", "week1_quiz_score", "week1_video_minutes"]
# Cox PH model
cox_result = predict_dropout_cox(
df_students,
time_col="dropout_week",
event_col="dropped_out",
covariates=covariates,
)
print(f"Cox C-index: {cox_result['concordance_index']:.3f}")
print(cox_result["summary"][["coef", "exp(coef)", "p"]].to_string())
# Logistic regression (early binary warning)
X = df_students[covariates].fillna(0).values
y = df_students["dropped_out"].values
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
cv = StratifiedKFold(n_splits=5, shuffle=True, random_state=42)
aucs = []
for train_idx, val_idx in cv.split(X_scaled, y):
clf = LogisticRegression(max_iter=500)
clf.fit(X_scaled[train_idx], y[train_idx])
proba = clf.predict_proba(X_scaled[val_idx])[:, 1]
aucs.append(roc_auc_score(y[val_idx], proba))
print(f"\nLogistic Regression 5-fold AUC: {np.mean(aucs):.3f} ± {np.std(aucs):.3f}")
# Survival plot for top-risk vs low-risk students
model = cox_result["model"]
df_test = df_students.head(20).copy()
df_test[covariates] = StandardScaler().fit_transform(df_test[covariates])
sf = model.predict_survival_function(df_test[covariates])
fig, ax = plt.subplots(figsize=(8, 5))
for col in sf.columns[:5]:
sf[col].plot(ax=ax, alpha=0.6)
ax.set_title("Predicted Survival Functions (first 5 students)")
ax.set_xlabel("Week")
ax.set_ylabel("P(still enrolled)")
plt.tight_layout()
plt.savefig("/tmp/dropout_survival.png", dpi=150)
plt.show()
Example B — Knowledge Tracing for a Mathematics Curriculum
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
# Simulate a mathematics quiz log
np.random.seed(0)
skills = ["addition", "subtraction", "multiplication", "division", "fractions"]
n_students = 50
records = []
for student inrange(n_students):
for skill in skills:
p_know = 0.1for attempt inrange(1, 11):
correct = int(np.random.rand() < (p_know * 0.9 + (1 - p_know) * 0.2))
records.append({
"user_id": f"s{student:03d}",
"skill": skill,
"attempt": attempt,
"correct": correct,
})
# Simulate learning
p_know = p_know + (1 - p_know) * 0.15
df_quiz = pd.DataFrame(records)
# Run BKT with default parameters
bkt_results = run_bkt(df_quiz, skill_col="skill")
print(bkt_results.head(20).to_string(index=False))
# Plot knowledge state for one student and one skill
fig, axes = plt.subplots(1, len(skills), figsize=(18, 4), sharey=True)
for ax, skill inzip(axes, skills):
plot_knowledge_state(bkt_results, user_id="s000", skill=skill, ax=ax)
plt.suptitle("BKT Knowledge State — Student s000", fontsize=13)
plt.tight_layout()
plt.savefig("/tmp/bkt_knowledge_state.png", dpi=150)
plt.show()
# Learning curve analysis for 'fractions'
lc = compute_learning_curves(df_quiz, skill="fractions")
print(f"\nFractions learning curve — R²: {lc['r2']:.3f}")
print(f"Parameters: {lc['params']}")
# IRT analysis
response_matrix = (
df_quiz[df_quiz["skill"] == "fractions"]
.pivot_table(index="user_id", columns="attempt", values="correct")
.values.astype(float)
)
irt = fit_irt_1pl(response_matrix)
print(f"\nIRT item difficulties: {np.round(irt['difficulty'], 3)}")
print(f"IRT ability range: [{irt['ability'].min():.2f}, {irt['ability'].max():.2f}]")
# Sequence mining — find common patterns in activity sequences
activity_seqs = []
for sid, grp in df_quiz.groupby("user_id"):
seq = grp.sort_values(["skill", "attempt"])["skill"].tolist()
activity_seqs.append(seq)
patterns = mine_activity_sequences(activity_seqs, min_support=0.8, max_pattern_len=3)
print("\nFrequent learning sequences (support >= 80%):")
for pattern, count in patterns[:10]:
print(f" {' → '.join(pattern)}: {count} students")
8. Tips and Gotchas
BKT identifiability: The four BKT parameters are not jointly identifiable from
response data alone. Fix p_slip and p_guess from domain knowledge or use EM
fitting with pyBKT for proper parameter estimation.
IRT convergence: The 1PL MLE can diverge for students who answer everything
correctly or incorrectly. Add a small regularisation penalty or use Bayesian priors.
Cox PH assumptions: Test the proportional hazards assumption with
lifelines.statistics.proportional_hazard_test before interpreting coefficients.
Sequence mining scalability: The pure-Python PrefixSpan above is fine for
hundreds of students but slow for tens of thousands. Use the prefixspan PyPI
package for production.
Class imbalance in dropout: Typical dropout rates are 10-30%. Use
class_weight='balanced' in scikit-learn and report AUC-ROC, not accuracy.
9. References
Corbett & Anderson (1994). Knowledge tracing. User Modeling and User-Adapted Interaction, 4.
Baker & Yacef (2009). The State of EDM. JEDM, 1(1).
Pei, J. et al. (2004). Mining Sequential Patterns by Pattern-Growth. IEEE TKDE.
Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests.
