Logistic Regression

When to use this skill

Use for binary outcome prediction where interpretability matters as much as accuracy. Triggers:

• "Model churn / conversion / fraud / adoption"
• "Predict probability of X"
• "Build a propensity model"
• "What predicts <binary outcome>?"
• "Logistic regression for…"

For complex non-linear interactions, suggest a tree-based model after fitting logistic as the baseline. For continuous outcomes, use linear-regression. For time-to-event, use survival-analysis.

Required inputs

Workflow

1. Audit the data first (use data-quality-audit skill).

1. Check class balance.

   print(y.value_counts(normalize=True))

• Balanced (40-60%): standard logistic
• Mild imbalance (10-40%): use class_weight='balanced' and look at PR-AUC, not ROC-AUC alone
• Severe (< 5%): consider downsampling, but always evaluate calibration on the original distribution

1. Verify no leakage. The most common DS bug. Ask:

• Is any feature derived from data after the prediction time?
• Is the target ever used to build features?
• Are there features that are only defined for positives?

1. Split data temporally.

   train = df[df['as_of_date'] < cutoff]
   test  = df[df['as_of_date'] >= cutoff]

Random splits are only acceptable for exploratory analysis.

1. Fit baseline. Start with regularized logistic (LogisticRegression(C=1.0, penalty='l2') in sklearn).

1. Evaluate on holdout:

• AUC-ROC (ranking quality)
• AUC-PR (for imbalanced classes)
• Brier score (calibration)
• Calibration curve (visualize predicted vs observed probability)
• Confusion matrix at the operating threshold

1. Choose threshold based on business cost.

• If false negatives cost 10× false positives → lower threshold
• Plot precision-recall vs threshold to find the inflection
• Default to 0.5 only if cost is symmetric (rare in practice)

1. Interpret coefficients as odds ratios.

   odds_ratio = exp(beta)
   "A 1-unit increase in X multiplies the odds of Y by <odds_ratio>"

1. Write the readout with the structure below.

Output format

# Logistic Regression: <outcome>

## Setup
- **Outcome:** <binary_target> (positive class = <description>, base rate = <X%>)
- **Observation unit:** <user_id> as of <as_of_date>
- **Sample size:** <N_train> train, <N_test> test (temporal split at <date>)
- **Features:** <N> features (<categories>)

## Performance (test set)
| Metric | Value | Notes |
|---|---|---|
| AUC-ROC | 0.78 | Solid ranking |
| AUC-PR | 0.34 | Base rate 0.08 (random baseline = 0.08) |
| Brier score | 0.072 | |
| Calibration | well-calibrated below 0.4, slight underprediction above | see plot |
| Threshold @ 0.30 | precision 0.42, recall 0.61, F1 0.50 | chosen for business cost |

## Top coefficients (sorted by absolute effect)
| Feature | Coef (β) | Odds Ratio | Interpretation |
|---|---|---|---|
| days_since_last_login | +0.082 | 1.085 | +1 day → +8.5% odds of churn |
| support_tickets_30d | +0.610 | 1.840 | +1 ticket → +84% odds |
| has_active_subscription | -1.420 | 0.242 | active sub → -76% odds |
| ... | | | |

## Calibration check
<observed vs predicted probability table, by decile>

| Decile | Predicted | Observed | n |
|---|---|---|---|
| 1 (lowest) | 0.012 | 0.014 | 1,240 |
| 5 (middle) | 0.103 | 0.108 | 1,240 |
| 10 (highest) | 0.612 | 0.587 | 1,240 |

## Operational impact at chosen threshold
- Flag rate: <X%> of users
- Precision: <X%> (of flagged, correctly identified)
- Recall: <X%> (of true positives, caught)
- Estimated business impact: <e.g., "If we contact all 5,200 flagged users this month, we expect to retain 460 (lift over no-action: +180 retained)">

## Caveats
- <e.g., model trained on stable period; performance may degrade if user base shifts>
- <e.g., features 1-3 require real-time computation; ensure pipeline supports>
- Calibration may drift; re-evaluate quarterly.

## Next steps
- <e.g., A/B test intervention on flagged users>
- <e.g., monitor model performance over next 30 days>
- <e.g., consider tree-based model if interaction terms become important>

Validation checks

• [ ] No leakage: every feature is provably computed before the outcome window
• [ ] Temporal split used (or justified random split)
• [ ] Calibration checked, not just AUC
• [ ] Threshold chosen based on stated business cost
• [ ] Odds ratios reported (more interpretable than raw β)
• [ ] Operational impact estimated, not just statistical metrics

Edge cases & failure modes

• Perfect separation: one feature perfectly predicts outcome. Coefficient explodes. Usually a leakage bug.
• Multicollinearity: correlated features inflate individual coefficient variance. Use VIF check or regularization.
• Very rare class (< 1%): AUC-ROC is misleading. Use AUC-PR. Consider gradient boosting instead.
• Categorical with many levels: one-hot encoding explodes dimensions. Use target encoding or merge rare categories into "other."
• Calibration drift: model AUC stable but threshold-based decisions degrading. Re-calibrate with Platt scaling or isotonic regression every 3-6 months.

Scripts

• scripts/fit_logistic.py — End-to-end fit + evaluate + report from a CSV.

python scripts/fit_logistic.py \
    --input training_data.csv \
    --target churned \
    --features feature_list.txt \
    --split-by signup_date \
    --split-date 2026-03-01

Related skills

• data-quality-audit — always run on inputs first
• linear-regression — for continuous outcomes
• survival-analysis — when timing matters
• causal-inference — if you need to estimate intervention effect, not just predict
• stakeholder-readout — for packaging the model output