Extended regression models

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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

Watch Extended regression models for panel data.

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:

Inferences

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

Extended Regression Models Reference Manual
Microeconometrics Using Stata, Second Edition, Volumes I and II by A. Colin Cameron and Pravin K. Trivedi
The Stata Blog: Ermistatas and Stata's new ERMs commands
Extended regression models (ERMs) flyer

See tests, predictions, and effects.

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

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