MNAR stands for “Missing Not at Random,” which is another type of missing data mechanism in which the missingness of data is related to the missing values themselves, and not just to other variables in the dataset. In other words, the probability of missing data depends on the value of the missing data points themselves.
For example, suppose we have a dataset that includes information about income and health status. Suppose that people with higher income levels are more likely to not report their health problems, while people with lower income levels are more likely to report their health problems accurately. In this scenario, the missingness of the health data would be considered MNAR because it is related to the income level of the respondent and their actual health status.
When data are MNAR, missing data can lead to biased estimates if not handled properly. The missing data is not random, so statistical analyses that ignore the missing data or assume MCAR or MAR may be biased.
Several methods have been developed to handle MNAR data, including selection models, pattern mixture models, and joint models. These methods aim to model the missingness mechanism explicitly and account for it in the analysis, thereby minimizing bias in the estimates.
It is worth noting that MNAR is the most difficult type of missingness to handle and often requires strong assumptions about the missingness mechanism to be made. In practice, it is challenging to know whether data are MNAR or MAR, and careful consideration is required when handling missing data in statistical analyses.