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name: linear-and-formula-models description: "Use statsmodels linear, generalized linear, robust, mixed, GEE, GAM, and formula APIs for model fitting, prediction, summaries, missing data, robust covariance, and design-matrix troubleshooting." disable-model-invocation: true metadata: disco-role: operating license: BSD 3-Clause

Linear and formula models

Use this sub-skill for OLS/WLS/GLS/GLSAR, RollingOLS/RollingWLS, QuantReg, RLM, GLM, GEE, GAM, MixedLM, variance components, formula workflows, design matrices, missing-data handling, robust covariance, prediction, and summary interpretation.

Start here

1. Choose interface:
   • DataFrame plus formula: import statsmodels.formula.api as smf; call smf.ols(...), smf.glm(...), smf.mixedlm(...), or smf.gee(...).
   • Prepared arrays: import statsmodels.api as sm; add an intercept with sm.add_constant when required and call model classes such as sm.OLS(endog, exog) or sm.GLM(endog, exog, family=...).
2. Validate data before fitting: shape, missing values, categorical encoding, constant column, rank, and domain restrictions for the chosen family.
3. Fit once, inspect result attributes (params, bse, pvalues, conf_int(), summary()), and only then add robust covariance, predictions, or diagnostics.
4. For residual diagnostics, ANOVA/contrasts, or outlier influence details, cross-route to statistical-tests-and-diagnostics. For result export and plotting, cross-route to datasets-results-graphics.

Read or run

• Read references/api-reference.md for constructors, formula wrappers, families, covariance choices, and result methods.
• Read references/workflows.md for formula and matrix recipes, prediction, robust covariance, mixed models, and GLM/GEE patterns.
• Read references/troubleshooting.md for missing-data, rank, convergence, perfect fit, robust covariance, and formula errors.
• Run scripts/smoke_linear_models.py for a deterministic local OLS/GLM/robust-covariance smoke check.

Boundaries

• Route binary choice, multinomial choice, ordered models, count-model-specific marginal effects, zero-inflated, hurdle, and truncated count workflows to discrete-and-count-models.
• Route ARIMA/SARIMAX/VAR/forecasting and time-index problems to time-series-analysis.
• Route general hypothesis tests, influence/outlier procedures, and multiple testing to statistical-tests-and-diagnostics, but keep model-specific fit setup here.
• Do not recommend statsmodels.sandbox implementations for production linear modeling unless the user explicitly asks about sandbox code.

Quality checks before answering

• State whether the snippet uses formula or matrix API.
• Show how the intercept is handled.
• Mention missing-data policy when inputs may contain NaN.
• Keep new prediction data aligned with training columns and categorical levels.
• Explain convergence/rank warnings as statistical identification issues, not only software failures.