M Éc E n
I NTERLUDE
D ONNÉES MANQUANTES
Julie Scholler - Bureau B246
I. Introduction
“The best thing to do with missing value is not to have any.”
Gertrude Mary Cox
Que faire quand il y en a ?
• supprimer les individus ayant des données manquantes
• faire avec en utilisant des méthodes adapter à la présence de données manquantes
• imputer des valeurs là où elles sont manquantes
Mais toujours commencer par regarder et visualiser les données.
I. Introduction
Différents types de données manquantes
• Données manquantes de façon complètement aléatoire : MCAR (Missing Completely At Random)
La probabilité qu’une donnée soit manquante ne dépend pas des données observées et non observée(s) de l’individu.
• Données manquantes de façon aléatoire : MAR (Missing At Random)
La probabilité qu’une donnée soit manquante ne dépend pas des données non observées de l’individu.
• Données manquantes de façon non aléatoire : MNAR (Missing Not At Random)
La probabilité qu’une donnée soit manquante dépend des données non observées de l’individu.
II. Visualisation
Données sur le ronflement
age (3%) w eight (9%) siz e (5%)
alcohol (5%) se x (3%)
snore (6%) tobacco (7%)
0
25
50
75
100
Obser v ations
Missing (5.4%)
Present
(94.6%)
7
6
5 5
4
3
2 2
1
0 2 4 6 8
Intersection Siz e
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weight_NA tobacco_NA
snore_NA alcohol_NA
size_NA sex_NA age_NA
0.0 2.5 5.0 7.5
Set Size
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N Y NA
0 2 4 6 0 2 4 6 0 2 4 6
age sex alcohol size tobacco weight
# Missing
V ar iab les
snore
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M W NA
0 2 4 6 8 0 2 4 6 8 0 2 4 6 8
age alcohol size snore tobacco weight
# Missing
V ar iab les
sex
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N Y NA
0 2 4 6 0 2 4 6 0 2 4 6
age sex alcohol size snore weight
# Missing
V ar iab les
tobacco
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weight
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size
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alcohol
w eight
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alcohol
III. Imputation
Imputation de données manquantes
Imputation par la valeur moyenne
R : le package e1071 et la fonction impute
-2 -1 0 1 2
-2 -1 0 1 2
x
y
-2 -1 0 1 2
-2 -1 0 1 2
x
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alcohol
III. Imputation
Imputation de données manquantes
Utilisation de l’information apportée par les données des variables renseignées
Différentes méthodes
1. Prédiction : construire un modèle de régression à partir des individus complètement renseignés et l’utiliser pour prédire les données correspondant aux données manquantes.
R
• à la main
• package VIM et fonction regressionImp
• package mice et une des fonctions mice.impute.norm...
III. Imputation
Imputation par régression
-2 -1 0 1 2
-2 -1 0 1 2
x
y
III. Imputation
Imputation par régression bruitée
-2 -1 0 1 2
-2 -1 0 1 2
x
y
III. Imputation
Méthodes non supervisées
1. Imputation par la moyenne (ou mode) au sein de sous-groupes homogènes
Nécessite de définir/découvrir des sous-groupes homogènes Classification non supervisée
2. Utilisation des méthodes d’analyse factorielle
R : package missMDA et les fonctions imputePCA et
imputeMCA
III. Imputation
Illustration
x y
-2.00 -2.01 -1.50 -1.48 0.00 -0.01
1.50 NA
2.0 1.98 +
+
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III. Imputation
Illustration
x y
-2.00 -2.01 -1.50 -1.48 0.00 -0.01 1.50 1.46
2.0 1.98 +
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alcohol
III. Imputation
Imputation simple
Ne reflète pas l’incertitude dans l’imputation Imputation multiple
Génération de plusieurs imputations
●
−0.5 0.5 1.0 1.5
−3 −2 −1 0 1 2 3
Multiple imputation using Procrustes
Dim 1 (42.51%)
Dim 2 (35.14%)
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41 42
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51 52
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64 65 66 67 68
69 70 71
72 73
74 75 76
77 78
79 80
81 82 84 83 85
86 87
88
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90 91
92 93
94 95 96
97
98 99 100
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−1.0 0.0 0.5 1.0
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Projection of the Principal Components
Dim 1 (42.51%)
Dim 2 (35.14%)
●
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Supplementary projection individuals
Dim 1 (42.51%)
Dim 2 (35.14%)
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X1 X2
X3 X4 X5
X6 X7
X8 X9 X10 X11 X12 X13 X14
X15 X16
X17 X18
X19 X20 X21
X22
X23 X24 X25 X26
X27 X28
X29 X30
X31 X32 X33
X34 X35 X36
X37 X38 X39 X40
X41 X42
X43 X44
X45 X46
X47 X48
X49 X50
X51 X52
X53 X54
X55 X56
X57 X58
X59 X60
X61 X62 X63
X64 X65 X66 X67 X68
X69 X70 X71 X72 X73 X74
X75 X76
X77 X78
X79 X80
X81 X82 X83
X84 X85 X86
X87
X88
X89
X90 X91
X92 X93
X94 X95 X96
X97
X98 X99 X100
Dim 1 (42.51%)
Dim 2 (35.14%)
●
−1.0 0.0 1.0
−2 0 2 4
Supplementary projection categories
Dim 1 (42.51%)
Dim 2 (35.14%)
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M
W
snore_N snore_Y
tobacco_N
tobacco_Y
Dim 1 (42.51%)
Dim 2 (35.14%)
●
−4 −2 0 2 4
−10 −5 0 5 10
Multiple imputation using Procrustes
Dim 1 (49.31%)
Dim 2 (28.59%)
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3 4 6 5
7 9 8
11 12 10 14 13
15 16 17
18 19
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21 22 23
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25 26 27
28
29 30
31
32 33
34
35 36 37 38
39 40 41
42
43 44
45 46 47 48
49 50 51
52 53 54
55 56
58 57
59 60
62 61
63 64
65
66
67 68
69 70 71
72 74 73
75 76
77 79 78
80 81 82
83
84
85 86
87 88
89 90
91 92 93 94
96 95 97 98 99
100
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−1.0 −0.5 0.0 0.5 1.0
−2 −1 0 1 2
Variable representation
Dim 1 (49.31%)
Dim 2 (28.59%)
age
weight size
alcohol
●