Home  /  Products  /  Features  /  ERMs

Extended regression models (ERMs)

Extended regression models (ERMs) is our name for a specific class of models that address several complications that arise frequently in data: 1) endogenous covariates, 2) sample selection, 3) nonrandom treatment assignment, and 4) within-panel correlation. These complications can occur alone or in any combination. ERMs allow you to make valid inferences as if these complications did not occur in your data.

Learn about Extended regression models.

Outcome types

  • Continuous
  • Interval-measured (interval-censored)
  • Binary
  • Ordinal

Complications addressed

  • Endogenous covariates
  • Unobserved confounding
  • Sample selection
  • Outcomes missing not at random
  • Trials with informative dropout
  • Nonrandom treatment assignment
    • Exogenous, based on observed variables
    • Endogenous, based partially on unobservables
  • Within-panel correlation
  • Within-group correlation

Endogenous covariate types

  • Continuous
  • Binary
  • Ordinal
  • Interactions with exogenous covariates
  • Interactions with endogenous covariates
  • Quadratic and other polynomial forms

Treatment effects/Causal analysis

  • Binary or ordinal treatments
  • Average treatment effects (ATEs)
  • ATEs on the treated (ATETs)
  • ATEs on the untreated (ATEUs)
  • Potential-outcome means (POMs)
  • ATEs, ATETs, ATEUs, and POMs for
    • Full population
    • Subpopulations
    • Expected values for specific covariate values

“Treatment effects” are sometimes called “Causal effects”.

Panel or otherwise grouped data

  • Random effects in one or all equations
  • Two-level models

Watch Extended regression models:


  • Inference statistics
    • Expected means
    • Expected probabilities
    • Contrasts (differences) of expected means and probabilities (also called effects)
    • Marginal effects
    • Partial effects
    • Average structural function (ASF) means and effects
    • Average structural probability (ASP) means and effects
  • Estimates of statistics are available for:
    • Full population
    • Subpopulations
    • Expected values for specific covariate values
    • Censored and uncensored outcomes
  • Conditional analysis—specify values of all covariates
  • Population-averaged analysis—specify values of some covariates, or no covariates, and average (margin) over the rest
  • Inferences types
    • Tests against zero or any other value
    • Tests of equality
    • Contrasts
    • Pairwise comparisons
    • Confidence intervals for every statistic

Most inferences are performed via a tight integration with Stata's marginal analysis facilities

Profile plots

  • Any inference statistic
  • Any statistic over subpopulations or subgroups (e.g, age groups or treatment levels)
  • Any statistic at multiple fixed levels of one or more covariates
  • Confidence intervals

Additional resourcess

See tests, predictions, and effects.

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