In causal mediation analysis, the definitions of the natural direct and indirect effects involve potential outcomes that can never be observed, so-called a priori counterfactuals. This conceptual challenge translates into issues in identification, which requires strong and often unverifiable assumptions, including sequential ignorability.…

In investigations of unusual testing behavior, a common question is whether a specific pattern of responses occurs unusually often within a group of examinees. In many current tests, modern communication techniques can permit quite large numbers of examinees to share keys, or common response patterns, to the entire test. To address this issue,…