Linear models, generalized linear models, discrete choice models, time series analysis, and statistical tests and diagnostics — what statsmodels offers in each area and which class to use.
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.
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.
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.
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.
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.