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.


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

 

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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