Outcome types


Interval-measured (interval-censored)




Complications addressed

Endogenous covariates

Sample selection

Nonrandom treatment assignment

Exogenous, based on observed variables

Endogenous, based partially on unobservables


Endogenous covariate types




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


Expected values for specific covariate values

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

Watch Extended regression models (ERMs).


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


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


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 resource

Extended Regression Models Reference Manual