Detecting Latent Heterogeneity

We ask whether it is possible to determine, from statistical averages alone, whether a population under study consists of several subpopulations, unknown to the investigator, each responding differently to a given treatment? We show that such determination is feasible in three cases: (1) randomized trials with binary treatments, (2) models where treatment effects can be identified by adjustment for covariates, and (3) models in which treatment effects can be identified by mediating instruments. In each of these cases we provide an explicit condition which, if observed empirically, proves that treatment-effect is not uniform, but varies across individuals.

[1]  E. H. Simpson,et al.  The Interpretation of Interaction in Contingency Tables , 1951 .

[2]  H. Simon,et al.  Cause and Counterfactual , 1966 .

[3]  C. Blyth.  On Simpson's Paradox and the Sure-Thing Principle , 1972 .

[4]  D. Rubin,et al.  The central role of the propensity score in observational studies for causal effects , 1983 .

[5]  James J. Heckman,et al.  Alternative methods for evaluating the impact of interventions: An overview , 1985 .

[6]  J. Heckman,et al.  Longitudinal Analysis of Labor Market Data: Alternative methods for evaluating the impact of interventions , 1985 .

[7]  James J. Heckman,et al.  Longitudinal Analysis of Labor Market Data , 1985 .

[8]  James J. Heckman,et al.  Alternative methods for solving the problem of selection bias in evaluating the impact of treatments , 1986 .

[9]  Sander Greenland,et al.  On the Logical Justification of Conditional Tests for Two-By-Two Contingency Tables , 1991 .

[10]  James J. Heckman,et al.  Randomization and Social Policy Evaluation , 1991 .

[11]  Joshua D. Angrist,et al.  Identification of Causal Effects Using Instrumental Variables , 1993 .

[12]  J. Pearl.  [Bayesian Analysis in Expert Systems]: Comment: Graphical Models, Causality and Intervention , 1993 .

[13]  Judea Pearl,et al.  Counterfactual Probabilities: Computational Methods, Bounds and Applications , 1994, UAI.

[14]  Judea Pearl,et al.  Probabilistic Evaluation of Counterfactual Queries , 1994, AAAI.

[15]  J. Pearl.  Causal diagrams for empirical research , 1995 .

[16]  James J. Heckman,et al.  Identification of Causal Effects Using Instrumental Variables: Comment , 1996 .

[17]  Joseph Y. Halpern.  Axiomatizing Causal Reasoning , 1998, UAI.

[18]  J. Pearl,et al.  An Axiomatic Characterization of Causal Counterfactuals , 1998 .

[19]  Joshua D. Angrist,et al.  Estimating the Labor Market Impact of Voluntary Military Service Using Social Security Data on Military Applicants , 1998 .

[20]  Francine D. Blau,et al.  Handbook of Labor Economics , 1999 .

[21]  Christopher Winship,et al.  THE ESTIMATION OF CAUSAL EFFECTS FROM OBSERVATIONAL DATA , 1999 .

[22]  S Greenland,et al.  Relation of probability of causation to relative risk and doubling dose: a methodologic error that has become a social problem. , 1999, American journal of public health.

[23]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[24]  J. Brand,et al.  Regression and matching estimates of the effects of elite college attendance on educational and career achievement , 2006 .

[25]  Judea Pearl,et al.  Identification of Conditional Interventional Distributions , 2006, UAI.

[26]  James J Heckman,et al.  Understanding Instrumental Variables in Models with Essential Heterogeneity , 2006, The Review of Economics and Statistics.

[27]  J. Robins,et al.  Four Types of Effect Modification: A Classification Based on Directed Acyclic Graphs , 2007, Epidemiology.

[28]  H. White,et al.  An Extended Class of Instrumental Variables for the Estimation of Causal Effects , 2011 .

[29]  Christopher Winship,et al.  Counterfactuals and Causal Inference: Methods and Principles for Social Research , 2007 .

[30]  Stephen L. Morgan,et al.  6. A Diagnostic Routine for the Detection of Consequential Heterogeneity of Causal Effects , 2008 .

[31]  J. Pearl,et al.  Effects of Treatment on the Treated: Identification and Generalization , 2009, UAI.

[32]  Sander Greenland,et al.  Adjustments and their Consequences—Collapsibility Analysis using Graphical Models , 2010 .

[33]  Joshua D. Angrist,et al.  The Credibility Revolution in Empirical Economics: How Better Research Design is Taking the Con Out of Econometrics , 2010, SSRN Electronic Journal.

[34]  R. Dechter,et al.  Effect Heterogeneity and Bias in Main-Effects-Only Regression Models , 2010 .

[35]  Judea Pearl,et al.  The Curse of Free-Will and the Paradox of Inevitable Regret , 2010 .

[36]  R. Dechter,et al.  Heuristics, Probability and Causality. A Tribute to Judea Pearl , 2010 .

[37]  J. Pearl.  The Causal Mediation Formula—A Guide to the Assessment of Pathways and Mechanisms , 2012, Prevention Science.

[38]  Yu Xie,et al.  Estimating Heterogeneous Treatment Effects with Observational Data , 2012, Sociological methodology.

[39]  S. Morgan.  Handbook of Causal Analysis for Social Research , 2013 .

[40]  J. Pearl.  Understanding Simpson's Paradox , 2013 .

[41]  J. Brand,et al.  California Center for Population Research On-line Working Paper Series Causal Effect Heterogeneity Causal Effect Heterogeneity Author Biography Page Causal Effect Heterogeneity , 2022 .

[42]  J. Pearl.  TRYGVE HAAVELMO AND THE EMERGENCE OF CAUSAL CALCULUS , 2013, Econometric Theory.

[43]  P. Ding.  A paradox from randomization-based causal inference , 2014, 1402.0142.

[44]  J. Pearl.  Comment: Understanding Simpson’s Paradox , 2013, Probabilistic and Causal Inference.

[45]  Jin Tian,et al.  On the Identification of Causal Effects , 2015 .

[46]  Elias Bareinboim,et al.  External Validity: From Do-Calculus to Transportability Across Populations , 2014, Probabilistic and Causal Inference.

[47]  Yu Xie,et al.  Estimating Heterogeneous Treatment Effects with Observational Data , 2022 .