「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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!style="width:7em" rowspan="2"|
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!style="witdh:4em"|Abbr.
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!style="witdh:4em" rowspan="2"|Abbr.
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!style="width:15em"|Description
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!colspan="2"|Missing depends on/<br>Missing occurs because of
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![Example]<br>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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!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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!style="width:7em"|missing (unobserved) value itself
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!style="width:7em"|other observed variable(s)
 
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!Missing not at random
 
!Missing not at random
 
!MNAR
 
!MNAR
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|style="text-align:center"|<big>YES</big>
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|style="text-align:center"|&mdash;
 
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*Missing depends on observed 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
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*Researchers have no information why they denied to report body weights in several weeks
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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
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**Missing occurred '''because of the missing values themselves'''
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**Data of those participants are missed '''because of the values in the variable ''body weight'' themselves'''
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**Researchers cannot explain/predict the missing mechanism from other observed (reported) body weights or other variables
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**Researchers cannot explain/predict the missing mechanism by
 
 
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!Missing at randam
 
!Missing at randam
 
!MAR
 
!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 '''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 participation '''regardless of measured body weights''', but only 1% of male denied to report
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*Researchers can identify that female participants more likely denied to report body weights than male
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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:
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**Missing occurred NOT because of body weights themselves but '''because of another variable ''sex'''''
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**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
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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''
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**Missing mechanism is at random, i.e., free from unobserved (missing) values only inside each participant
 
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**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
 
!Missing completely at random
 
!MCAR
 
!MCAR
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|style="text-align:center"|<big>NO</big>
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|style="text-align:center"|<big>NO</big>
 
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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 and was lost to follow up
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*A participant '''failed to report body weights because of malfunction of the app'''
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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
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**Missing occurred NOT because of body weights themselves NOR other variables
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*A participant fails to report body weights because of malfunction of the app between the 15th and 17th weeks
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**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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**The reasons (mechanisms) of missing have nothing to do with other observed (certainly reported) values, values in other variables, nor unobserved (missing) values themselves
 
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**Missing mechanism is completely at random, i.e., completely free from either of observed values or unobserved (missing) values
 
 
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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
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