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| | !Missing at randam<br>MAR | | !Missing at randam<br>MAR |
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| − | *Missing does not depend on '''(other) unobserved data''', but may depend on '''observed data''' | + | *Missing does not depend on '''unobserved (missing) values''' themselves, but may depend on '''(other) observed values''' |
| − | *The cause of missing can be explained by
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| − | *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: | + | *15% of female participants denied to report their body weights after the agreement regardless of measured body weights, but only 1% of male denied 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 | + | **Unobserved (missing, unrepoted) values in the variable ''body weight'' themselves did not affect the missing, but another variable ''sex'' can explain the reason of missing |
| − | **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 mechanism is at random, i.e., free from unobserved (missing) values only inside each participant |
| | + | **Missing mechanism is NOT at random, i.e., NOT free from another variable ''sex''; missing occurred depending on the values in the variable ''sex'' |
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| | !Missing completely at random<br>MCAR | | !Missing completely at random<br>MCAR |
2023年12月10日 (日) 15:37時点における版
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Three mechanisms (assumptions) of data missing
Mechanisms (assumptions) of data missing
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Description
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[Example]
A cohort study in which participants self report their body weight every week via special app installed on their smartphones for 52 weeks in total
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Missing not at random
MNAR
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- Missing depends on observed data
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- 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
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Missing at randam
MAR
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- Missing does not depend on unobserved (missing) values themselves, but may depend on (other) observed values
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- 15% of female participants denied to report their body weights after the agreement regardless of measured body weights, but only 1% of male denied to report:
- Unobserved (missing, unrepoted) values in the variable body weight themselves did not affect the missing, but another variable sex can explain the reason of missing
- Missing mechanism is at random, i.e., free from unobserved (missing) values only inside each participant
- Missing mechanism is NOT at random, i.e., NOT free from another variable sex; missing occurred depending on the values in the variable sex
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Missing completely at random
MCAR
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- Missing does NOT depend on (other) observed values NOR on unobserved (missing) values themselves
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- A participant moved to outside cohort area because of family affair which has nothing to do with the study and is lost to follow up after the 10th week
- A participant fails to report body weights because of malfunction of the app between the 15th and 17th weeks
- The reasons (mechanisms) of missing have nothing to do with other observed (certainly reported) values, values in other variables, nor unobserved (missing) values themselves
- Missing mechanism is completely at random, i.e., completely free from either of observed values or unobserved (missing) values
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