Missing data and imputation

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Three mechanisms (assumptions) of data missing

Mechanisms (assumptions) of data missing

	Abbr.	Description	[Example] A cohort study in which participants self report their body weight every week via special app installed on their smartphones for 52 weeks in total
Missing not at random	MNAR	Missing depends on observed data	Some participants intentionally deny to report higher body weights they don't like and only report lower body weights they like Data of those participants are missed because of the values in the variable body weight themselves Researchers cannot explain/predict the missing mechanism by
Missing at randam	MAR	Missing does not depend on unobserved (missing) values themselves, but may depend on (other) observed values	15% of female participants denied to report their body weights after the agreement regardless of measured body weights, but only 1% of male denied to report: Unobserved (missing, unrepoted) values in the variable body weight themselves did not affect the missing, but another variable sex can explain the reason of missing Missing mechanism is at random, i.e., free from unobserved (missing) values only inside each participant Missing mechanism is NOT at random, i.e., NOT free from another variable sex; missing occurred depending on the values in the variable sex
Missing completely at random	MCAR	Missing does NOT depend on (other) observed values NOR on unobserved (missing) values themselves	A participant moved to outside cohort area because of family affair which has nothing to do with the study and is lost to follow up after the 10th week A participant fails to report body weights because of malfunction of the app between the 15th and 17th weeks The reasons (mechanisms) of missing have nothing to do with other observed (certainly reported) values, values in other variables, nor unobserved (missing) values themselves Missing mechanism is completely at random, i.e., completely free from either of observed values or unobserved (missing) values