StatsmodelsSAFE

Intelligent Skill routing and workflow orchestration for AI agents — +21.12 pp reward, −29.6% tokens on SkillsBench with DeepSeekV4Flash-VE.

The instruction file, verbatim from the audited commit — this is the text the model reads, and the surface the audit's instruction layer examines. Quoted here so you can judge it without cloning anything.

---
name: statsmodels
description: "Statistical modeling toolkit. OLS, GLM, logistic, ARIMA, time series, hypothesis tests, diagnostics, AIC/BIC, for rigorous statistical inference and econometric analysis."
---

# Statsmodels: Statistical Modeling and Econometrics

## Overview

Statsmodels is Python's premier library for statistical modeling, providing tools for estimation, inference, and diagnostics across a wide range of statistical methods. Apply this skill for rigorous statistical analysis, from simple linear regression to complex time series models and econometric analyses.

## When to Use This Skill

This skill should be used when:
- Fitting regression models (OLS, WLS, GLS, quantile regression)
- Performing generalized linear modeling (logistic, Poisson, Gamma, etc.)
- Analyzing discrete outcomes (binary, multinomial, count, ordinal)
- Conducting time series analysis (ARIMA, SARIMAX, VAR, forecasting)
- Running statistical tests and diagnostics
- Testing model assumptions (heteroskedasticity, autocorrelation, normality)
- Detecting outliers and influential observations
- Comparing models (AIC/BIC, likelihood ratio tests)
- Estimating causal effects
- Producing publication-ready statistical tables and inference

## Quick Start Guide

### Linear Regression (OLS)

```python
import statsmodels.api as sm
import numpy as np
import pandas as pd

# Prepare data - ALWAYS add constant for intercept
X = sm.add_constant(X_data)

# Fit OLS model
model = sm.OLS(y, X)
results = model.fit()

# View comprehensive results
print(results.summary())

# Key results
print(f"R-squared: {results.rsquared:.4f}")
print(f"Coefficients:\\n{results.params}")
print(f"P-values:\\n{results.pvalues}")

# Predictions with confidence intervals
predictions = results.get_prediction(X_new)
pred_summary = predictions.summary_frame()
print(pred_summary)  # includes mean, CI, prediction intervals

# Diagnostics
from statsmodels.stats.diagnostic import het_breuschpagan
bp_test = het_breuschpagan(results.resid, X)
print(f"Breusch-Pagan p-value: {bp_test[1]:.4f}")

# Visualize residuals
import matplotlib.pyplot as plt
plt.scatter(results.fittedvalues, results.resid)
plt.axhline(y=0, color='r', linestyle='--')
plt.xlabel('Fitted values')
plt.ylabel('Residuals')
plt.show()
```

### Logistic Regression (Binary Outcomes)

```python
from statsmodels.discrete.discrete_model import Logit

# Add constant
X = sm.add_constant(X_data)

# Fit logit model
model = Logit(y_binary, X)
results = model.fit()

print(results.summary())

# Odds ratios
odds_ratios = np.exp(results.params)
print("Odds ratios:\\n", odds_ratios)

# Predicted probabilities
probs = results.predict(X)

# Binary predictions (0.5 threshold)
predictions = (probs > 0.5).astype(int)

# Model evaluation
from sklearn.metrics import classification_report, roc_auc_score

print(classification_report(y_binary, predictions))
print(f"AUC: {roc_auc_score(y_binary, probs):.4f}")

# Marginal effects
marginal = results.get_margeff()
print(marginal.summary())
```

### Time Series (ARIMA)

```python
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf

# Check stationarity
from statsmodels.tsa.stattools import adfuller

adf_result = adfuller(y_series)
print(f"ADF p-value: {adf_result[1]:.4f}")

if adf_result[1] > 0.05:
    # Series is non-stationary, difference it
    y_diff = y_series.diff().dropna()

# Plot ACF/PACF to identify p, q
fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 8))
plot_acf(y_diff, lags=40, ax=ax1)
plot_pacf(y_diff, lags=40, ax=ax2)
plt.show()

# Fit ARIMA(p,d,q)
model = ARIMA(y_series, order=(1, 1, 1))
results = model.fit()

print(results.summary())

# Forecast
forecast = results.forecast(steps=10)
forecast_obj = results.get_forecast(steps=10)
forecast_df = forecast_obj.summary_frame()

print(forecast_df)  # includes mean and confidence intervals

# Residual diagnostics
results.plot_diagnostics(figsize=(12, 8))
plt.show()
```

### Generalized Linear Models (GLM)

```python
import statsmodels.api as sm

# Poisson regression for count data
X = sm.add_constant(X_data)
model = sm.GLM(y_counts, X, family=sm.families.Poisson())
results = model.fit()

print(results.summary())

# Rate ratios (for Poisson with log link)
rate_ratios = np.exp(results.params)
print("Rate ratios:\\n", rate_ratios)

# Check overdispersion
overdispersion = results.pearson_chi2 / results.df_resid
print(f"Overdispersion: {overdispersion:.2f}")

if overdispersion > 1.5:
    # Use Negative Binomial instead
    from statsmodels.discrete.count_model import NegativeBinomial
    nb_model = NegativeBinomial(y_counts, X)
    nb_results = nb_model.fit()
    print(nb_results.summary())
```

## Core Statistical Modeling Capabilities

### 1. Linear Regression Models

Comprehensive suite of linear models for continuous outcomes with various error structures.

**Available models:**
- **OLS**: Standard linear regression with i.i.d. errors
- **WLS**: Weighted least squares for heteroskedastic errors
- **GLS**: Generalized least squares for arbitrary covariance structure
- **GLSAR**: GLS with autoregressive errors for time series
- **Quantile Regression**: Conditional quantiles (robust to outliers)
- **Mixed Effects**: Hierarchical/multilevel models with random effects
- **Recursive/Rolling**: Time-varying parameter estimation

**Key features:**
- Comprehensive diagnostic tests
- Robust standard errors (HC, HAC, cluster-robust)
- Influence statistics (Cook's distance, leverage, DFFITS)
- Hypothesis testing (F-tests, Wald tests)
- Model comparison (AIC, BIC, likelihood ratio tests)
- Prediction with confidence and prediction intervals

**When to use:** Continuous outcome variable, want inference on coefficients, need diagnostics

**Reference:** See `references/linear_models.md` for detailed guidance on model selection, diagnostics, and best practices.

### 2. Generalized Linear Models (GLM)

Flexible framework extending linear models to non-normal distribution

SAFEgrade B · trust 89/100 Nothing in the source contradicts what it says it does. Grade A is reserved for packages that have also passed the behavioural sandbox.

What the source does

Filesystem

none-observed

Network

none-observed

Shell

none-observed

Dependencies

pinned

Secrets in source

none-found

Findings (0)

No findings outside the package's declared scope.

Gates applied: no_behavioural_pass.