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Also known as: Missing At Random
Missing at random: missingness depends only on observed data, not on the missing values themselves.
DESCRIPTION
MAR defines a mechanism where the probability of missingness can be explained by observed variables but not by the unobserved missing values. It enables valid inference using model-based or multiple imputation when models include predictors of missingness. MAR is common in practice and weaker than MCAR. Misclassification of mechanisms can bias results, so diagnostics and sensitivity analyses are important.
ALTERNATIVE DEFINITIONS
Wikipedia
Data are missing at random (MAR) if the probability of missingness is related to observed data but not to the missing data itself.
Highlights dependence on observed variables only.
UCLA Statistical Consulting
MAR means that the probability of missingness is related to the observed data but not the missing values themselves.
Clarifies mechanism in practical terms for applied analysts.
Penn State Eberly College of Science
Missing at random (MAR) means the missingness depends only on measured variables included in the dataset.
Emphasizes dependence on observed/measured variables.
RELATED TERMS
Missing Data Multiple Imputation Rubin’s Rules
COMPETING TERMS
KNOWLEDGE AREAS
Data Science AI Data Quality Mathematics
TARGET AUDIENCE
Data Scientist AI Engineer Data Steward Analytics Engineer
EXTERNAL SOURCES
- Wikipedia - Missing data
- UCLA Statistical Consulting - Guide to missing data mechanisms
- Penn State Eberly College of Science - Lesson covering MAR and other mechanisms
- Wikipedia - Overview of missing data mechanisms
TOP QUESTIONS
Why is MAR important in modeling missing data?
Under MAR, multiple imputation and model-based methods produce valid inference when predictors of missingness are included.
Category: Relevancy
What is a common misunderstanding about MAR?
Confusing MAR with MCAR; MAR allows dependence on observed variables, while MCAR forbids any dependence.
Category: Misunderstanding
How do you assess plausibility of MAR?
Use diagnostics correlating missingness with observed covariates and consult domain knowledge, then perform sensitivity analyses.
Category: Validation
What risks arise when MAR is misclassified?
If missingness is actually MNAR, imputation under MAR can bias estimates and standard errors.
Category: Risks
What methods work well under MAR?
Multiple imputation, EM algorithms, and full-information maximum likelihood can yield valid inference.
Category: HowTo
How does MAR compare with MNAR?
MNAR depends on unobserved values; MAR does not. MNAR requires modeling the missingness mechanism or sensitivity analyses.
Category: Alternatives
Is MAR common in real data?
More common than MCAR; many processes link missingness to observed variables like time, demographics, or prior behavior.
Category: Opinion
How should models incorporate MAR?
Include covariates predictive of missingness in imputation and analysis models to satisfy MAR assumptions.
Category: Management
What hot topic affects MAR handling?
Bayesian and generative models offer flexible imputation that better captures complex MAR relationships.
Category: Topic