Partial Identifiability in Discrete Data With Measurement Error

Understand

When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest.

• These assumptions should be justifiable on substantive grounds, but are often motivated by mathematical convenience, for the sake of exactly identifying the target of inference.
• We adopt the view that it is preferable to present bounds under justifiable assumptions than to pursue exact identification under dubious ones.
• To that end, we demonstrate how a broad class of modeling assumptions involving discrete variables, including common measurement error and conditional independence assumptions, can be expressed as linear constraints on the parameters of the model.