Statsmodels

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.

Current Compatibility

Examples target statsmodels 0.14.6, released Dec 5, 2025. For reproducible environments, pin the primary package:

uv pip install statsmodels==0.14.6

Use statsmodels.api and statsmodels.formula.api for stable high-level imports, and direct module imports when examples require newer or specialized classes such as HurdleCountModel.

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, Capabilities, and Model Selection

• references/quick_start_guide.md: minimal worked examples for OLS, logistic regression, ARIMA, and GLM, and how to read the summary.
• references/modeling_capabilities.md: linear models, GLMs, discrete choice, time series, and the statistical tests and diagnostics.
• references/model_selection.md: the R-style formula API and model comparison.
• Per-topic detail: references/linear_models.md, references/glm.md, references/discrete_choice.md, references/time_series.md, and references/stats_diagnostics.md.

statsmodels is for inference — standard errors, confidence intervals, and hypothesis tests. Reach for scikit-learn when prediction is the goal and the coefficients do not need interpreting.

Best Practices

Data Preparation

1. Always add constant: Use sm.add_constant() unless excluding intercept
2. Check for missing values: Handle or impute before fitting
3. Scale if needed: Improves convergence, interpretation (but not required for tree models)
4. Encode categoricals: Use formula API or manual dummy coding

Model Building

1. Start simple: Begin with basic model, add complexity as needed
2. Check assumptions: Test residuals, heteroskedasticity, autocorrelation
3. Use appropriate model: Match model to outcome type (binary→Logit, count→Poisson)
4. Consider alternatives: If assumptions violated, use robust methods or different model

Inference

1. Report effect sizes: Not just p-values
2. Use robust SEs: When heteroskedasticity or clustering present
3. Multiple comparisons: Correct when testing many hypotheses
4. Confidence intervals: Always report alongside point estimates

Model Evaluation

1. Check residuals: Plot residuals vs fitted, Q-Q plot
2. Influence diagnostics: Identify and investigate influential observations
3. Out-of-sample validation: Test on holdout set or cross-validate
4. Compare models: Use AIC/BIC for non-nested, LR test for nested

Reporting

1. Comprehensive summary: Use .summary() for detailed output
2. Document decisions: Note transformations, excluded observations
3. Interpret carefully: Account for link functions (e.g., exp(β) for log link)
4. Visualize: Plot predictions, confidence intervals, diagnostics

Common Workflows

Workflow 1: Linear Regression Analysis

1. Explore data (plots, descriptives)
2. Fit initial OLS model
3. Check residual diagnostics
4. Test for heteroskedasticity, autocorrelation
5. Check for multicollinearity (VIF)
6. Identify influential observations
7. Refit with robust SEs if needed
8. Interpret coefficients and inference
9. Validate on holdout or via CV

Workflow 2: Binary Classification

1. Fit logistic regression (Logit)
2. Check for convergence issues
3. Interpret odds ratios
4. Calculate marginal effects
5. Evaluate classification performance (AUC, confusion matrix)
6. Check for influential observations
7. Compare with alternative models (Probit)
8. Validate predictions on test set

Workflow 3: Count Data Analysis

1. Fit Poisson regression
2. Check for overdispersion
3. If overdispersed, fit Negative Binomial
4. Check for excess zeros (consider ZIP/ZINB)
5. Interpret rate ratios
6. Assess goodness of fit
7. Compare models via AIC
8. Validate predictions

Workflow 4: Time Series Forecasting

1. Plot series, check for trend/seasonality
2. Test for stationarity (ADF, KPSS)
3. Difference if non-stationary
4. Identify p, q from ACF/PACF
5. Fit ARIMA or SARIMAX
6. Check residual diagnostics (Ljung-Box)
7. Generate forecasts with confidence intervals
8. Evaluate forecast accuracy on test set

Reference Documentation

This skill includes comprehensive reference files for detailed guidance:

references/linear_models.md

Detailed coverage of linear regression models including:

• OLS, WLS, GLS, GLSAR, Quantile Regression
• Mixed effects models
• Recursive and rolling regression
• Comprehensive diagnostics (heteroskedasticity, autocorrelation, multicollinearity)
• Influence statistics and outlier detection
• Robust standard errors (HC, HAC, cluster)
• Hypothesis testing and model comparison

references/glm.md

Complete guide to generalized linear models:

• All distribution families (Binomial, Poisson, Gamma, etc.)
• Link functions and when to use each
• Model fitting and interpretation
• Pseudo R-squared and goodness of fit
• Diagnostics and residual analysis
• Applications (logistic, Poisson, Gamma regression)

references/discrete_choice.md

Comprehensive guide to discrete outcome models:

• Binary models (Logit, Probit)
• Multinomial models (MNLogit, Conditional Logit)
• Count models (Poisson, Negative Binomial, Zero-Inflated, Hurdle)
• Ordinal models
• Marginal effects and interpretation
• Model diagnostics and comparison

references/time_series.md

In-depth time series analysis guidance:

• Univariate models (AR, ARIMA, SARIMAX, Exponential Smoothing)
• Multivariate models (VAR, VARMAX, Dynamic Factor)
• State space models
• Stationarity testing and diagnostics
• Forecasting methods and evaluation
• Granger causality, IRF, FEVD

references/stats_diagnostics.md

Comprehensive statistical testing and diagnostics:

• Residual diagnostics (autocorrelation, heteroskedasticity, normality)
• Influence and outlier detection
• Hypothesis tests (parametric and non-parametric)
• ANOVA and post-hoc tests
• Multiple comparisons correction
• Robust covariance matrices
• Power analysis and effect sizes

When to reference:

• Need detailed parameter explanations
• Choosing between similar models
• Troubleshooting convergence or diagnostic issues
• Understanding specific test statistics
• Looking for code examples for advanced features

Search patterns:

# Find information about specific models
rg "Quantile Regression" references/

# Find diagnostic tests
rg "Breusch-Pagan" references/stats_diagnostics.md

# Find time series guidance
rg "SARIMAX" references/time_series.md

Common Pitfalls to Avoid

1. Forgetting constant term: Always use sm.add_constant() unless no intercept desired
2. Ignoring assumptions: Check residuals, heteroskedasticity, autocorrelation
3. Wrong model for outcome type: Binary→Logit/Probit, Count→Poisson/NB, not OLS
4. Not checking convergence: Look for optimization warnings
5. Misinterpreting coefficients: Remember link functions (log, logit, etc.)
6. Using Poisson with overdispersion: Check dispersion, use Negative Binomial if needed
7. Not using robust SEs: When heteroskedasticity or clustering present
8. Overfitting: Too many parameters relative to sample size
9. Data leakage: Fitting on test data or using future information
10. Not validating predictions: Always check out-of-sample performance
11. Comparing non-nested models: Use AIC/BIC, not LR test
12. Ignoring influential observations: Check Cook's distance and leverage
13. Multiple testing: Correct p-values when testing many hypotheses
14. Not differencing time series: Fit ARIMA on non-stationary data
15. Confusing prediction vs confidence intervals: Prediction intervals are wider

Getting Help

For detailed documentation and examples:

• Official docs: https://www.statsmodels.org/stable/
• User guide: https://www.statsmodels.org/stable/user-guide.html
• Examples: https://www.statsmodels.org/stable/examples/index.html
• API reference: https://www.statsmodels.org/stable/api.html