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) Logistic Regression (Binary Outcomes) Time Series (ARIMA) Generalized Linear Models (GLM) 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 distributions. Distribution families: Binomial : Binary outcomes or proportions (logistic regression) Poisson : Count data Negative Binomial : Overdispersed counts Gamma : Positive continuous, right skewed data Inverse Gaussian : Positive continuous with specific variance structure Gaussian : Equivalent to OLS Tweedie : Flexible family for semi continuous data Link functions: Logit, Probit, Log, Identity, Inverse, Sqrt, CLogLog, Power Choose based on interpretation needs and model fit Key features: Maximum likelihood estimation via IRLS Deviance and Pearson residuals Goodness of fit statistics Pseudo R squared measures Robust standard errors When to use: Non normal outcomes, need flexible variance and link specifications Reference: See references/glm.md for family selection, link functions, interpretation, and diagnostics. 3. Discrete Choice Models Models for categorical and count outcomes. Binary models: Logit : Logistic regression (odds ratios) Probit : Probit regression (normal distribution) Multinomial models: MNLogit : Unordered categories (3+ levels) Conditional Logit : Choice models with alternative specific variables Ordered Model : Ordinal outcomes (ordered categories) Count models: Poisson : Standard count model Negative Binomial : Overdispersed counts Zero Inflated : Excess zeros (ZIP, ZINB) Hurdle Models : Two stage models for zero heavy data Key features: Maximum likelihood estimation Marginal effects at means or average marginal effects Model comparison via AIC/BIC Predicted probabilities and classification Goodness of fit tests When to use: Binary, categorical, or count outcomes Reference: See references/discrete choice.md for model selection, interpretation, and evaluation. 4. Time Series Analysis Comprehensive time series modeling and forecasting capabilities. Univariate models: AutoReg (AR) : Autoregressive models ARIMA : Autoregressive integrated moving average SARIMAX : Seasonal ARIMA with exogenous variables Exponential Smoothing : Simple, Holt, Holt Winters ETS : Innovations state space models Multivariate models: VAR : Vector autoregression VARMAX : VAR with MA and exogenous variables Dynamic Factor Models : Extract common factors VECM : Vector error correction models (cointegration) Advanced models: State Space : Kalman filtering, custom specifications Regime Switching : Markov switching models ARDL : Autoregressive distributed lag Key features: ACF/PACF analysis for model identification Stationarity tests (ADF, KPSS) Forecasting with prediction intervals Residual diagnostics (Ljung Box, heteroskedasticity) Granger causality testing Impulse response functions (IRF) Forecast error variance decomposition (FEVD) When to use: Time ordered data, forecasting, understanding temporal dynamics Reference: See references/time series.md for model selection, diagnostics, and forecasting methods. 5. Statistical Tests and Diagnostics Extensive testing and diagnostic capabilities for model validation. Residual diagnostics: Autocorrelation tests (Ljung Box, Durbin Watson, Breusch Godfrey) Heteroskedasticity tests (Breusch Pagan, White, ARCH) Normality tests (Jarque Bera, Omnibus, Anderson Darling, Lilliefors) Specification tests (RESET, Harvey Collier) Influence and outliers: Leverage (hat values) Cook's distance DFFITS and DFBETAs Studentized residuals Influence plots Hypothesis testing: t tests (one sample, two sample, paired) Proportion tests Chi square tests Non parametric tests (Mann Whitney, Wilcoxon, Kruskal Wallis) ANOVA (one way, two way, repeated measures) Multiple comparisons: Tukey's HSD Bonferroni correction False Discovery Rate (FDR) Effect sizes and power: Cohen's d, eta squared Power analysis for t tests, proportions Sample size calculations Robust inference: Heteroskedasticity consistent SEs (HC0 HC3) HAC standard errors (Newey West) Cluster robust standard errors When to use: Validating assumptions, detecting problems, ensuring robust inference Reference: See references/stats diagnostics.md for comprehensive testing and diagnostic procedures. Formula API (R style) Statsmodels supports R style formulas for intuitive model specification: Model Selection and Comparison Information Criteria Likelihood Ratio Test (Nested Models) Cross Validation 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: Common Pitfalls to Avoid 1. Forgetting constant term : Always us

statsmodels