「Missing data and imputation」の版間の差分

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.
	Abbr.	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

@@ 5行目: / 5行目: @@
 |+Mechanisms (assumptions) of data missing
 |-
-!
+!style="width:7em" rowspan="2"|
-!Description
+!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
+!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.
 |-
-!Missing not at random<br>MNAR
+!style="width:7em"|missing (unobserved) value itself
-|
+!style="width:7em"|other observed variable(s)
-*Missing depends on observed data
+|-
+!Missing not at random
+!MNAR
+|style="text-align:center"|<big>YES</big>
+|style="text-align:center"|&mdash;
 |
-*Some participants '''intentionally deny to report higher body weights they don't like''' and only report lower body weights they like
+*Some participants '''intentionally denied to report higher body weights they didn't like''' and only reported lower body weights they accepted
-**Data of those participants are missed '''because of the values in the variable ''body weight'' themselves'''
+*Researchers have no information why they denied to report body weights in several weeks
-**Researchers cannot explain/predict the missing mechanism by
+**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<br>MAR
+!Missing at randam
-|
+!MAR
-*Missing does not depend on '''unobserved data''', but may depend on '''observed data'''
+|style="text-align:center"|<big>NO</big>
-*The cause of missing can be explained by
+|style="text-align:center"|<big>YES</big>
 |
-*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 participation '''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
+*Researchers can identify that female participants more likely denied to report body weights than male
-**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 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<br>MCAR
+!Missing completely at random
-|
+!MCAR
-*Missing does NOT depend on '''observed data''' NOR on '''unobserved data'''
+|style="text-align:center"|<big>NO</big>
-*Missing occurs purely at random independely from any observed and unobserved data
+|style="text-align:center"|<big>NO</big>
 |
-*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:
+*A participant '''moved to outside cohort area''' because of family affair and was lost to follow up
-**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
+*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
 |}

「Missing data and imputation」の版間の差分

2023年12月10日 (日) 17:18時点における最新版

Three mechanisms (assumptions) of data missing

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