The representation of missing data mechanisms can be categorized into three standard types: Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR). MCAR indicates that the probability of missing values is independent of both the variable itself and other variables. MAR implies missing values depend on other observed variables. In contrast, MNAR relates to missingness that can depend on both observed values and the missing values themselves. Proper handling of MNAR data lacks a general method, complicating its analysis.
Missing completely at random (MCAR) occurs when the probability that a value is missing is independent of the variable itself and other variables. Its missingness probability depends neither on the missing variable nor on observed variables.
Missing at random (MAR) indicates that the missingness probability depends on other observed variables and is independent of the missing variables. The missing value can be predicted from the observed variables.
Missing not at random (MNAR) corresponds to cases where the missingness reasons can depend on both other variables and the missing value itself, making it unpredictable from observed data.
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