Missing data and imputation

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Three mechanisms (assumptions) of data missing

Mechanisms (assumptions) of data missing

	Abbr.	Missing depends on/ Missing occurs because of		[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. Demographic variables are also collected.
		missing value itself	other observed variable(s)
Missing not at random	MNAR	YES	—	Some participants intentionally denied to report higher body weights they didn't like and only reported lower body weights they accepted Researchers have no information why they denied to report body weights in several weeks Missing occurred because of the values themselves Researchers cannot explain/predict the missing mechanism from other observed (reported) body weights or other variables
Missing at randam	MAR	NO	YES	15% of female participants denied to report their body weights after participation regardless of measured body weights, but only 1% of male denied to report Researchers can identify that female participants more likely denied to report body weights than male Missing occurred not because of body weights themselves but because of another variable sex Missing mechanism is at random, i.e., free from missing values, but it's applicable only inside each participant Missing mechanism is NOT at random, i.e., NOT free from variable sex; missing occurred depending on the values in the variable sex
Missing completely at random	MCAR	NO	NO	A participant moved to outside cohort area because of family affair and was lost to follow up after the 10th week A participant failed to report body weights because of malfunction of the app between the 15th and 17th weeks Missing occurred not because of body weights themselves nor other variables Missing mechanism is completely at random, i.e., completely free from both of missing (unobserved) values and observed values in body weight or in other variables