Which situation best satisfies the Missing at Random assumption and therefore allows standard multiple-imputation methods that rely on MAR to yield unbiased estimates?
At a diabetes clinic, laboratory staff sometimes leave the blood-glucose field blank when the measured value exceeds 400 mg/dL and triggers an outlier warning.
A wearable fitness tracker's heart-rate sensor occasionally loses connection because of random Bluetooth interference, producing gaps unrelated to any user characteristics or physiology.
Fasting triglyceride measurements are missing more often for study participants who are under 18 years old, and every participant's age is fully recorded in the dataset.
In an anonymous salary survey, respondents earning very low or very high incomes are less likely to disclose their pay, and no other collected variable predicts this behavior.
Under MAR, the probability a value is missing can be fully explained by other observed variables-but not by the (unobserved) value itself. The triglyceride study in which younger participants (an observed variable: age) drive the pattern of missingness meets this criterion. Once age is included in the imputation model, the missingness mechanism no longer depends on the unobserved triglyceride values themselves.
The sensor dropout caused by random Bluetooth interference is independent of both observed and unobserved data, so it is Missing Completely at Random (MCAR). The suppressed glucose outliers are Missing Not at Random (MNAR) because the probability of being missing increases with the (unseen) glucose value. Similarly, skipped salary responses that depend on the unknown salary amount constitute MNAR. Only the second scenario aligns with MAR.
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What is the key difference between MAR, MCAR, and MNAR missing data classifications?
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Why is the triglyceride study considered MAR but not MCAR or MNAR?
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How does knowing the missingness mechanism impact data imputation methods?