Home  /  Products  /  Features  /  Linear models

Linear models

Linear regression

Watch Fitting and interpreting regression models tutorials

Censored outcomes

  • Interval censored (such as income reported in ranges)
  • Tobit model
  • Correlated data corrections to standard errors
  • Heteroskedastic consistent standard errors
  • Model heteroskedasticity
  • Predictions
    • Outcome in the absence of censoring
    • Outcome conditional on being in the censoring interval
    • Outcome with censoring imposed
    • Probability of censoring
  • Finite mixture models
  • Bayesian estimation
  • Interval regression with endogenous regressors, treatment effects, and sample selection

Sample-selection linear models

  • Maximum likelihood and Heckman's two-step estimation
  • Robust, cluster–robust, bootstrap, and jackknife standard errors
  • Linear constraints
  • Combine with endogenous regressors and treatment effects

Hurdle models

  • Linear and exponential
  • Lower or upper boundary values
  • Robust, cluster—robust, bootstrap, and jackknife standard errors

Stochastic frontier models

  • Production and cost frontiers
  • Half-normal, exponential, and truncated-normal distributions
  • Modeling of conditional heteroskedasticity

Quantile regression

  • Median regression
  • Least absolute deviations (LAD)
  • Regression of any quantile
  • Interquantile range regression
  • Standard errors
    • Koenker and Bassett
    • Robust — choose bandwidth and kernel
    • Bootstrap
  • Multiple imputation
  • Bayesian estimation StataNow

Fractional polynomial regression

  • Support for a wide variety of models
  • Component-plus-residual plots
  • Support for zero-inflated regressors

Extended regression models

  • Combine endogeneity, Heckman-style selection, and treatment effects
  • Linear regression
  • Random effects in one or all equations
  • Exogenous or endogenous regressors
  • Exogenous or endogenous treatment assignment
    • Binary treatment–untreated/treated
    • Ordinal treatment levels–0 doses, 1 dose, 2 doses, etc.
  • Endogenous selection using probit or tobit
  • All standard postestimation command available, including predict and margins

Linear mixed models

Endogeneity and simultaneous systems

  • Two-stage least-squares regression
  • LIML estimation
  • GMM estimation
  • Instrumental variables
  • Tests of instrumental relevance
  • Tests of overidentifying restrictions
  • Tests and confidence intervals robust to weak instruments StataNow
  • Three-stage least-squares regression
  • Linear constraints within and across equations
  • Finite mixture models
  • Linear regression with endogenous regressors, treatment effects, and sample selection
  • Robust (Huber/White/sandwich) and cluster–robust standard errors
  • Finite mixture models

Instrumental-variables quantile regression New

  • Inverse quantile regression estimator
  • Smoothed estimating equations estimator
  • Simultaneously estimate at different quantiles
  • Hypothesis testing of endogenous effects
  • Confidence intervals robust to weak instruments

Seemingly unrelated regressions

  • Robust (Huber/White/sandwich) and cluster–robust standard errors New
  • Linear constraints within and across equations

Postestimation Selector

  • View and run all postestimation features for your command
  • Automatically updated as estimation commands are run

Factor variables

  • Automatically create indicators based on categorical variables
  • Form interactions among discrete and continuous variables
  • Include polynomial terms
  • Perform contrasts of categories/levels
Watch Introduction to factor variables in Stata tutorials

Marginal analysis

  • Estimated marginal means
  • Marginal and partial effects
  • Average marginal and partial effects
  • Least-squares means
  • Predictive margins
  • Adjusted predictions, means, and effects
  • Works with multiple outcomes simultaneously
  • Contrasts of margins
  • Pairwise comparisons of margins
  • Profile plots
  • Interaction plots
  • Graphs of margins and marginal effects
Watch Introduction to margins in Stata tutorials
Watch Profile plots and interaction plots in Stata tutorials


  • Analysis of main effects, simple effects, interaction effects, partial
  • interaction effects, and nested effects
  • Comparisons against reference groups, of adjacent levels, or against
  • the grand mean
  • Orthogonal polynomials
  • Helmert contrasts
  • Custom contrasts
  • ANOVA-style tests
  • Contrasts of nonlinear responses
  • Multiple-comparison adjustments
  • Balanced and unbalanced data
  • Contrasts in odds-ratio metric
  • Contrasts of means, intercepts, and slopes
  • Graphs of contrasts

Pairwise comparisons

  • Compare estimated means, intercepts, and slopes
  • Compare marginal means, intercepts, and slopes
  • Balanced and unbalanced data
  • Nonlinear responses
  • Multiple-comparison adjustments: Bonferroni, Šidák, Scheffé, Tukey HSD, Duncan, and Student–Newman–Keuls adjustments
  • Group comparisons that are significant
  • Graphs of pairwise comparisons

Additional resources

See tests, predictions, and effects.

See New in Stata 18 to learn about what was added in Stata 18.