「Missing data and imputation」の版間の差分

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|+Mechanisms (assumptions) of data missing
 
|+Mechanisms (assumptions) of data missing
 
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|-
!
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!style="width:7em" rowspan="2"|
!Description
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!style="witdh:4em" rowspan="2"|Abbr.
![*Example]<br>A cohort study in which participants report their body weight every week to research center for 52 weeks in total
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!colspan="2"|Missing depends on/<br>Missing occurs because of
 +
!rowspan="2"|[Example]<br>A cohort study in which participants self report their body weight every week via special app installed on their smartphones. Demographic variables are also collected.
 
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!Missing not at random<br>MNAR
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!style="width:7em"|missing (unobserved) value itself
|Missing depends on observed data
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!style="width:7em"|other observed variable(s)
|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
 
 
|-
 
|-
!Missing at randam<br>MAR
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!Missing not at random
 +
!MNAR
 +
|style="text-align:center"|<big>YES</big>
 +
|style="text-align:center"|&mdash;
 
|
 
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*Missing may depend on '''observed data''' but does not depend on ''unobserved data''
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*Some participants '''intentionally denied to report higher body weights they didn't like''' and only reported lower body weights they accepted
*Missing can be explained
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*Researchers have no information why they denied to report body weights in several weeks
|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:
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**Missing occurred '''because of the missing values themselves'''
*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
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**Researchers cannot explain/predict the missing mechanism from other observed (reported) body weights or other variables
*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 completely at random<br>MCAR
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!Missing at randam
 +
!MAR
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|style="text-align:center"|<big>NO</big>
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|style="text-align:center"|<big>YES</big>
 
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*Missing does NOT depend on '''observed data''' NOR on ''unobserved data''
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*'''15% of female participants denied to report''' their body weights after participation '''regardless of measured body weights''', but only 1% of male denied to report
*Missing occurs purely at random independely from any observed and unobserved data
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*Researchers can identify that female participants more likely denied to report body weights than male
|A participant moves to outside cohort area because of family affair which has nothing to do with the study and is lost to follow up at the 10th week:
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**Missing occurred NOT because of body weights themselves but '''because of another variable ''sex'''''
*Data after the move are missed not because of data (body weights) themselves, nor because of the participant's unobserved (unmeasured) characteristic related to the study
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**Missing mechanism is at random, i.e., free from missing values only inside each participant, but NOT at random, i.e., NOT free from variable ''sex''
 +
|-
 +
!Missing completely at random
 +
!MCAR
 +
|style="text-align:center"|<big>NO</big>
 +
|style="text-align:center"|<big>NO</big>
 +
|
 +
*A participant '''moved to outside cohort area''' because of family affair and was lost to follow up
 +
*A participant '''failed to report body weights because of malfunction of the app'''
 +
**Missing occurred NOT because of body weights themselves NOR other variables
 +
**Missing mechanism is completely at random, i.e., completely free from both of missing (unobserved) values and observed values in body weight or in other variables
 
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2023年12月10日 (日) 17:18時点における最新版

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Three mechanisms (assumptions) of data missing

Mechanisms (assumptions) of data missing
Abbr. Missing depends on/
Missing occurs because of
[Example]
A cohort study in which participants self report their body weight every week via special app installed on their smartphones. Demographic variables are also collected.
missing (unobserved) value itself other observed variable(s)
Missing not at random MNAR YES
  • Some participants intentionally denied to report higher body weights they didn't like and only reported lower body weights they accepted
  • Researchers have no information why they denied to report body weights in several weeks
    • Missing occurred because of the missing values themselves
    • Researchers cannot explain/predict the missing mechanism from other observed (reported) body weights or other variables
Missing at randam MAR NO YES
  • 15% of female participants denied to report their body weights after participation regardless of measured body weights, but only 1% of male denied to report
  • Researchers can identify that female participants more likely denied to report body weights than male
    • Missing occurred NOT because of body weights themselves but because of another variable sex
    • Missing mechanism is at random, i.e., free from missing values only inside each participant, but NOT at random, i.e., NOT free from variable sex
Missing completely at random MCAR NO NO
  • A participant moved to outside cohort area because of family affair and was lost to follow up
  • A participant failed to report body weights because of malfunction of the app
    • Missing occurred NOT because of body weights themselves NOR other variables
    • Missing mechanism is completely at random, i.e., completely free from both of missing (unobserved) values and observed values in body weight or in other variables