  The causal structure for measurement bias (MB) remains controversial. Aided
by the Directed Acyclic Graph (DAG), this paper proposes a new structure for
measuring one singleton variable whose MB arises in the selection of an
imperfect I/O device-like measurement system. For effect estimation, however,
an extra source of MB arises from any redundant association between a measured
exposure and a measured outcome. The misclassification will be bidirectionally
differential for a common outcome, unidirectionally differential for a causal
relation, and non-differential for a common cause between the measured exposure
and the measured outcome or a null effect. The measured exposure can actually
affect the measured outcome, or vice versa. Reverse causality is a concept
defined at the level of measurement. Our new DAGs have clarified the structures
and mechanisms of MB.
