Abstract
Researchers who generate data often optimize efficiency and robustness by choosing stratified over simple random sampling designs. Yet, all theories of inference proposed to justify matching methods are based on simple random sampling. This is all the more troubling because, although these theories require exact matching, most matching applications resort to some form of ex post stratification (on a propensity score, distance metric, or the covariates) to find approximate matches, thus nullifying the statistical properties these theories are designed to ensure. Fortunately, the type of sampling used in a theory of inference is an axiom, rather than an assumption vulnerable to being proven wrong, and so we can replace simple with stratified sampling, so long as we can show, as we do here, that the implications of the theory are coherent and remain true. Properties of estimators based on this theory are much easier to understand and can be satisfied without the unattractive properties of existing theories, such as assumptions hidden in data analyses rather than stated up front, asymptotics, unfamiliar estimators, and complex variance calculations. Our theory of inference makes it possible for researchers to treat matching as a simple form of preprocessing to reduce model dependence, after which all the familiar inferential techniques and uncertainty calculations can be applied. This theory also allows binary, multicategory, and continuous treatment variables from the outset and straightforward extensions for imperfect treatment assignment and different versions of treatments.
Highlights
Edited by Jeff GillPolitical science has increasingly embraced the experimental method to establish causal relationships suggested by theories and observational studies—from experiments’ traditional subdisciplinary home, political psychology, to international relations
Eye-tracking allowed the authors to validate the interpretation of average marginal component effects (AMCEs) as the relative importance of components in the decision
They measured the change in information processing that occurs as conjoint tables become increasingly complex, showing that while the AMCEs remained consistent, respondents transitioned from one processing strategy to another in a manner that is consistent with bounded rationality
Summary
Political science has increasingly embraced the experimental method to establish causal relationships suggested by theories and observational studies—from experiments’ traditional subdisciplinary home, political psychology, to international relations. Eye-tracking allows for the measurement of information accrual and processing, which gives insight into the cognitive models employed behind a choice Another weakness in testing causal mechanisms is that average causal mediation effects rely on strong assumptions that are often known to be false. Conjoint analysis permits the identification of component-specific effects while allowing scholars to test causal hypotheses about multidimensional preferences efficiently, in a single experiment. Eye-tracking allowed the authors to validate the interpretation of AMCEs as the relative importance of components in the decision They measured the change in information processing that occurs as conjoint tables become increasingly complex, showing that while the AMCEs remained consistent, respondents transitioned from one processing strategy to another in a manner that is consistent with bounded rationality. CCM estimands should be used whenever designs feature multiple treatments
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