Missing Data Mechanisms

Three types of missingness (Rubin, 1976):

MCAR: Missing Completely at Random

Definition: Probability of missingness is the same for all observations.

Mathematically: \(P(R | Y_{obs}, Y_{mis}) = P(R)\)

Example: Data lost due to random computer error.

For MICE: Complete case analysis is unbiased under MCAR, but MICE improves efficiency.

Definition: Probability of missingness depends on observed data but not on the missing values themselves.

Mathematically: \(P(R | Y_{obs}, Y_{mis}) = P(R | Y_{obs})\)

Example: Younger people less likely to report income (age observed, income missing).

For MICE: This is the key assumption. MICE produces valid results under MAR.

Definition: Probability of missingness depends on the unobserved (missing) values.

Example: People with higher incomes less likely to report income.

For MICE: MICE may produce biased results under MNAR. Consider sensitivity analyses.

Making MAR plausible: Include variables that:

See Understanding Missing Data for practical guidance.