Which mechanism describes missing not at random, where missingness relates to unobserved data?

• A. MAR: missing at random
• B. MNAR: missing not at random
• C. MCAR: missing completely at random
• D. All of the above

Answer: (C)

Missing not at random means the chance that a value is missing depends on the unobserved values themselves (or on unobserved information). In other words, the missingness is linked to data we don’t have, so simply using observed data to explain missingness isn’t enough. This is different from missing completely at random, where missingness is unrelated to any data, and from missing at random, where missingness can be related to observed data but not to the unseen values once you account for what you have observed. An example is survey income data where individuals with very high incomes are less likely to report their income; the reason for the missingness is tied to the income value that is not observed. Because the missingness depends on unobserved information, standard methods that assume MAR or MCAR can be biased, and addressing MNAR typically requires modeling the missing data mechanism or performing sensitivity analyses across plausible MNAR scenarios. So the mechanism described is MNAR.