Missing data and imputation

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Three mechanisms (assumptions) of data missing

Mechanisms (assumptions) of data missing

	Description	[*Example] A cohort study in which participants report their body weight every week to research center 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 data, but may depend on observed data The cause of missing can be explained by	15% of female participants deny to report their body weights after the agreement regardless of measured body weights, but only 1% of male deny to report: Data of female participants are more likely missed not because of data (body weights) themselves but because female are more likely reluctant to report their body weights In other words, values in the variable body weight themselves do not affect the missing but another variable sex affects the missing of values in the variable body weight
Missing completely at random MCAR	Missing does NOT depend on observed data NOR on unobserved data Missing occurs purely at random independely from any observed and unobserved data	A participant moves to outside cohort area because of family affair which has nothing to do with the study and is lost to follow up at the 10th week: Data after the move are missed not because of data (body weights) themselves, nor because of the participant's unobserved (unmeasured) characteristic related to the study