「Missing data and imputation」の版間の差分

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10行目: 10行目:
 
!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.
 
!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.
 
|-
 
|-
!style="width:7em"|missing value itself
+
!style="width:7em"|missing (unobserved) value itself
 
!style="width:7em"|other observed variable(s)
 
!style="width:7em"|other observed variable(s)
 
|-
 
|-
 
!Missing not at random
 
!Missing not at random
 
!MNAR
 
!MNAR
|style="text-align:center"|YES
+
|style="text-align:center"|<big>YES</big>
 
|style="text-align:center"|&mdash;
 
|style="text-align:center"|&mdash;
 
|
 
|
25行目: 25行目:
 
!Missing at randam
 
!Missing at randam
 
!MAR
 
!MAR
|style="text-align:center"|NO
+
|style="text-align:center"|<big>NO</big>
|style="text-align:center"|YES
+
|style="text-align:center"|<big>YES</big>
 
|
 
|
 
*'''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
 
*'''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
 
*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 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 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
 
!Missing completely at random
 
!MCAR
 
!MCAR
|style="text-align:center"|NO
+
|style="text-align:center"|<big>NO</big>
|style="text-align:center"|NO
+
|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 '''moved to outside cohort area''' because of family affair and was lost to follow up

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