Folien 2 ohne Transparenz

Graphiken multivariater Daten
Klassische Graphiken für die Darstellung von 2 Merkmalen:
2*metrisch: Streudiagramm
metrisch+kategorisch: Getrennte Boxplots (Histogramme, . . . )
2*kategorisch: Balkendiagramm (gestapelt oder nebeneinander)
Multivariate Verfahren
Was passiert, wenn wir eine dritte Variable zu einem Streudiagramm
dazunehmen?
Friedrich Leisch
Institut für Statistik
Ludwig-Maximilians-Universität München
metrisch: Streudiagramm-Matrix, Größe oder Farbe der Zeichen, 3d
kategorisch: als Farbe und/oder Zeichentyp
SS 2009, Visualisierung multivariater Daten
Eine vierte Variable? Wir brauchen ein wenig Theorie . . .
Friedrich Leisch, Multivariate Verfahren 2009
Visualisierung von Information
1
Visualisierung von Information
• Das menschliche visuelle System ist hochentwickelt und kann extrem
große Mengen an Information schnell verarbeiten,
• Informationsvermittlung an uns selber
• wurde aber nicht primär
Datenanalyse entwickelt.
• Informationsvermittlung an andere
für
die
Aufgaben
der
• Jagd auf wilde Tiere unterscheidet sich vom
wissenschaftlichen Artikels oder Geschäftsberichtes.
• Verschönerung eines Berichtes
modernen
Lesen
eines
• Es ist wichtig, ein paar Schwächen des menschlichen visuellen
Systems zu kennen.
Friedrich Leisch, Multivariate Verfahren 2009
2
Friedrich Leisch, Multivariate Verfahren 2009
3
Codierungsmöglichkeiten
Winkel und Steigung
20
• Länge, Fläche, Volumen
• Position an (bündig justierten) Achsen
10
• Winkel, Steigung
5
15
• Farbe: Farbton, Sattheit, Schwärzungsgrad
0.0
0.5
1.0
1.5
2.0
2.5
3.0
x
Friedrich Leisch, Multivariate Verfahren 2009
4
Winkel und Steigung
Friedrich Leisch, Multivariate Verfahren 2009
5
Fläche und Volumen
• problematisch für Menschen
• spitze Winkel werden unterschätzt, stumpfe Winkel überschätzt
• Abhängigkeit von Orientierung
• Menschen tendieren dazu, Winkel zu lesen, wenn sie Steigungen
schätzen → Referenzachse wichtig
• der Abstand zwischen 2 Kurven wird in der Regel im rechten Winkel
zur Kurve geschätzt, nicht parallel zur Achse
Friedrich Leisch, Multivariate Verfahren 2009
6
Friedrich Leisch, Multivariate Verfahren 2009
7
Fläche und Volumen
Längen
5
6
• auch schwer zu decodieren
3
4
• stark abhängig von Form:
lang&dünn sieht größer aus als kompakt&konvex
2
• (nicht so starke) Abhängigkeit von Farbe
0
1
• Volumina sind schwer in 2-d zu visualisieren: es ist unklar, wann der
Umriß (= Fläche) die Schätzung des Volumens dominiert.
A
Friedrich Leisch, Multivariate Verfahren 2009
8
Längen
B
C
Friedrich Leisch, Multivariate Verfahren 2009
9
Längen
A
5
4
3
2
1
• für Menschen am einfachsten zu decodieren
• bündig ausgerichtete Achsen besser als frei liegende
B
5
4
3
2
1
• . . . aber nur Längen machen eine Graphik auch unlesbar!
C
5
4
3
2
1
0
1
Friedrich Leisch, Multivariate Verfahren 2009
2
3
4
5
6
7
10
Friedrich Leisch, Multivariate Verfahren 2009
11
Steven’s Gesetz
Farbe
2
x+y
Codierte wahre Werte x1 und x2 resultieren in wahrgenommenen Werten
w(x1) und w(x2) im Verhältnis:
!β
1
x1
x2
x
mit
−1
Wertebereich für β
0.9 – 1.1
0.6 – 0.9
0.5 – 0.8
−2
Attribut
Länge
Fläche
Volumen
0
w(x1)
=
w(x2)
−2
−1
0
1
2
x
Friedrich Leisch, Multivariate Verfahren 2009
12
Farbe
13
Farbe
• Wichtig bei Codierung kategorischer Information.
• Kann nur wenige Intervalle quantitativer Information darstellen.
• Starke Abhängigkeit vom Ausgeabemedium (Papier, Art des
Monitors, . . . )
• Potentielle Probleme bei schwarz-weiß Druck und Kopien.
• Großer Flächen voll saturierter Farben überlasten die Retina.
• Eine Sammlung von Farbschemata ist verfügbar auf http://
colorbrewer.org (oder R Paket ColorBrewer).
Friedrich Leisch, Multivariate Verfahren 2009
Friedrich Leisch, Multivariate Verfahren 2009
14
YlOrRd
YlOrBr
YlGnBu
YlGn
Reds
RdPu
Purples
PuRd
PuBuGn
PuBu
OrRd
Oranges
Greys
Greens
GnBu
BuPu
BuGn
Blues
Set3
Set2
Set1
Pastel2
Pastel1
Paired
Dark2
Accent
Spectral
RdYlGn
RdYlBu
RdGy
RdBu
PuOr
PRGn
PiYG
BrBG
Friedrich Leisch, Multivariate Verfahren 2009
15
Rangordnung Perzeptionsaufgaben
Rangordnung Perzeptionsaufgaben
Cleveland/McGill:
Position entlang gemeinsamer Achsen
Position entlang identischer, justierter Achsen
Länge
Winkel / Steigung
Fläche
Volumen
Farbton — Sattheit — Schwärzungsgrad
16
17
Mache alle Daten sichtbar
●
●●
0.8
●
0.6
• Verwende Codierungschema vom Anfang der Liste
• Vermeide Flächen und Volumina (Steven’s Law zeigt Verzerrung)
• Vermeide Farben für quantitative Daten (aber verwende Sie für
kategorische Variablen!)
• Vermeide optische Illusionen (3d, unruhige Füllmuster, . . . ).
• Vermeide große Flächen saturierter Farben.
• Verwende bei Panels gemeinsame Achsen und Referenzlinien als
optische Anker.
• Sortiere Werte nach Werten statt einem externen Kriterium (wie
dem Alphabet), dieses kann in Tabellen benutzt werden.
• Überlade die Daten nicht zu stark mit Annotation (Text, Pfeile, . . . ).
x[,2]
Tipps für effektive Graphiken
Friedrich Leisch, Multivariate Verfahren 2009
0.4
Friedrich Leisch, Multivariate Verfahren 2009
0.2
1.
2.
3.
4.
5.
6.
7.
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0.4
0.6
0.8
x[,1]
Friedrich Leisch, Multivariate Verfahren 2009
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Friedrich Leisch, Multivariate Verfahren 2009
19
Mache alle Daten sichtbar
1.0
1.0
Mache alle Daten sichtbar
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0.0
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0.6
0.8
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0.6
x[,2]
0.4
0.2
0.0
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x[,2]
0.6
0.8
●
0.0
1.0
0.2
0.4
0.6
0.8
1.0
x[,1]
x[,1]
Friedrich Leisch, Multivariate Verfahren 2009
20
Sortiere nach Werten
Friedrich Leisch, Multivariate Verfahren 2009
21
Sortiere nach Werten
driving_properties
character
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●
power
clarity
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quality
comfort
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technology
concept
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consumption
reliability
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sporty
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driving_properties
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safety
economy
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comfort
handling
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handling
interior
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economy
model_continuity
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consumption
power
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styling
quality
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interior
reliability
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resale_value
reputation
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resale_value
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concept
safety
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model_continuity
service
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space
reputation
●
clarity
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sporty
●
space
styling
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●
character
technology
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●
0.1
0.2
Friedrich Leisch, Multivariate Verfahren 2009
0.3
0.4
0.5
0.6
0.1
0.7
22
0.2
Friedrich Leisch, Multivariate Verfahren 2009
0.3
0.4
0.5
0.6
0.7
23
Bsp: Zweitstimmen Bundestagswahl 2005
Streudiagramm-Matrix
●
●
> summary(btw05)
SPD
Min.
:0.1885
1st Qu.:0.2959
Median :0.3361
Mean
:0.3427
3rd Qu.:0.3883
Max.
:0.5586
LINKE
Min.
:0.02275
1st Qu.:0.03866
Median :0.04888
Mean
:0.08870
3rd Qu.:0.07176
Max.
:0.35536
UNION
Min.
:0.1104
1st Qu.:0.2881
Median :0.3432
Mean
:0.3507
3rd Qu.:0.4045
Max.
:0.6048
GRUENE
Min.
:0.02619
1st Qu.:0.05664
Median :0.07195
Mean
:0.08060
3rd Qu.:0.09818
Max.
:0.22769
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FDP
Min.
:0.04565
1st Qu.:0.08095
Median :0.09679
Mean
:0.09769
3rd Qu.:0.11241
Max.
:0.16630
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0.3
0.2
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0.6
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Friedrich Leisch, Multivariate Verfahren 2009
0.3 0.2 0.3
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OST
WEST
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Scatter Plot Matrix
Friedrich Leisch, Multivariate Verfahren 2009
26
Friedrich Leisch, Multivariate Verfahren 2009
27
3d-Punktwolke
3d-Punktwolke
●
LINKE
●
●
●
●
●●
● ●● ●●
●●●● ●
●●●● ● ●●
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● ● ●●
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●
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● ●
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●
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●
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LINKE
OST
WEST
●
●
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● ●● ●
●
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●
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UNION
UNION
SPD
Friedrich Leisch, Multivariate Verfahren 2009
28
3d-Punktwolke
SPD
Friedrich Leisch, Multivariate Verfahren 2009
29
Parallele Koordinaten
Ein mächtiges Werkzeug um mehr als 3 Variablen darzustellen:
OST
WEST
• parallele Achsen für jede Variable
• einzelne Variablen entweder mit gemeinsamer Skalierung oder jede
normalisiert
LINKE
LINKE
• Vorteil: mit etwas Übung auch bei höherer Dimension gut lesbar
UNION
SPD
UNION
• Nachteil: Abhängigkeit von Reihenfolge der Variablen, Korrelationen
nur zwischen benachbarten Variablen ablesbar.
SPD
Bei vielen Datenpunkten ist Transparenz oder Aufteilung auf mehrere
Panels hilfreich.
Friedrich Leisch, Multivariate Verfahren 2009
30
Friedrich Leisch, Multivariate Verfahren 2009
31
Parallele Koordinaten
1.0
●
●
PK: Geraden
Max
1.0
●
Max
●
●
●
0.8
0.8
●
●
●
●
0.6
0.6
●
y
y
●
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●
0.4
0.4
●
●
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●
0.2
0.2
●
●
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●
0.0
●
0.0
●
●
Min
0.0
0.2
0.4
0.6
0.8
1.0
Min
x
0.0
y
0.2
0.4
0.6
x
1.0
x
y
x
Friedrich Leisch, Multivariate Verfahren 2009
32
PK: Geraden
1.0
0.8
Friedrich Leisch, Multivariate Verfahren 2009
33
PK: Geraden
Max
●
1.0
Max
●
●
●
●
●
●
●
●
●
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●
0.8
0.8
●
●
●
●
●
●
●
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●
●
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●
0.6
0.6
●
●
●
●
●
●
●
y
y
●
●
0.4
0.4
●
●
●
●
0.2
0.2
●
●
●
●
0.0
0.0
●
Min
0.0
0.2
0.4
0.6
0.8
1.0
Min
x
0.0
y
x
Friedrich Leisch, Multivariate Verfahren 2009
0.2
0.4
0.6
0.8
1.0
x
y
x
34
Friedrich Leisch, Multivariate Verfahren 2009
35
PK: Geraden
1.0
PK: Geraden
Max
●
Max
1.0
●
●
●
●
●
0.8
●
0.8
●
●
●
●
●
●
●
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●
0.6
●
0.6
●
●
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●
y
y
●
●
0.4
0.4
●
●
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●
●
●
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●
0.2
0.2
●
●
●
●
●
●
●
●
●
0.0
●
0.0
●
Min
0.0
0.2
0.4
0.6
0.8
1.0
Min
x
0.0
y
0.2
0.4
0.6
x
36
PK: Geraden
Max
1.0
●
●
●
●
●
37
Max
●
●
●
●
●
●
●
●
●
●
●
●
y
Friedrich Leisch, Multivariate Verfahren 2009
●
●
x
PK: Kreis
1.0
●
1.0
x
Friedrich Leisch, Multivariate Verfahren 2009
●
●
0.8
●
0.8
0.8
●
●
●
●
●●
●
●
●
●
●
●
0.6
●
0.6
●
●
●
●
●
●
y
●
y
●
●
●
●
●
0.4
0.4
●
●
●
●
●
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●
0.2
0.2
●
●
●
●
●
●
●
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●
0.0
0.0
●
●
●
●
●
●
Min
0.0
0.2
0.4
0.6
0.8
1.0
Min
x
0.0
y
x
Friedrich Leisch, Multivariate Verfahren 2009
0.2
0.4
0.6
0.8
1.0
x
y
x
38
Friedrich Leisch, Multivariate Verfahren 2009
39
PK: Halbkreis
1.0
●
●
●
●
PK: Halbkreis
Max
●
Max
1.0
●
●
●
●
●
●
●
●
●
0.8
0.8
●
●
●
●
●
●
●
0.6
0.6
●
●
●
●
●
y
y
●
●
●
0.4
0.4
●
●
●
●
●
●
●
0.2
0.2
●
●
●
●
●
●
●
●
●
●
0.0
●
0.0
●
●
●
●
Min
0.0
0.2
0.4
0.6
0.8
1.0
Min
x
0.0
y
0.2
0.4
0.6
x
0.8
1.0
x
y
x
Friedrich Leisch, Multivariate Verfahren 2009
40
PK: Unkorreliert
Friedrich Leisch, Multivariate Verfahren 2009
41
PK: Cluster
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Friedrich Leisch, Multivariate Verfahren 2009
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Friedrich Leisch, Multivariate Verfahren 2009
43
PK: Cluster
PK: Zusammenfassung
Vorteile: • Achsen werden parallel verteilt, Platz wird effizient
ausgenutzt
• Viele Variablen auf einen Blick – Vergleich von Profilen
• Geometrische Eigenschaften im d-dimensionalen übersetzen sich
in 2-dimensionale Ansicht
• Ordnung auf Variablen wird unterstützt
Max
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Nachteile: • Strukturen nur bei benachbarten Variablen sichtbar
• Ohne interaktives Sortieren und Skalieren für explorative Analyse
schlecht geeignet (nächste Woche)
• Stärkeres Overplotting als bei Streudiagramm
• Bei d Variablen gibt es d! Permutationen.
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Friedrich Leisch, Multivariate Verfahren 2009
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Bsp PK: gemeinsame Skala
Friedrich Leisch, Multivariate Verfahren 2009
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Bsp PK: getrennte Skala
LINKE
LINKE
FDP
FDP
GRUENE
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UNION
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SPD
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Min
Friedrich Leisch, Multivariate Verfahren 2009
Max
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Friedrich Leisch, Multivariate Verfahren 2009
Max
47
Bsp PK: Korrelationen
Bsp PK: Korrelationen
Min
Max
OST
Min
WEST
LINKE
LINKE
UNION
SPD
SPD
Max
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Friedrich Leisch, Multivariate Verfahren 2009
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Bsp PK: Korrelationen
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Friedrich Leisch, Multivariate Verfahren 2009
Min
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Brandenburg
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Hamburg
UNION
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Rheinland−Pfalz
Saarland
FDP
GRUENE
UNION
0.1
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Min
Berlin
GRUENE
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Max
Bayern
FDP
0.2 0.3
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49
Bsp PK: Sortierung alphabetisch
Baden−Wuerttemberg
0.4
WEST
UNION
Min
0.5
Max
OST
SPD
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LINKE
Sachsen−AnhaltSchleswig−Holstein Thueringen
FDP
GRUENE
UNION
Scatter Plot Matrix
SPD
Min
Friedrich Leisch, Multivariate Verfahren 2009
50
Max
Min
Friedrich Leisch, Multivariate Verfahren 2009
Max
51
Median pro Bundesland
Bsp PK: Sortierung nach Median Union
Min
SPD UNION GRUENE FDP LINKE
Baden-Wuerttemberg
0.31 0.39
0.10 0.12 0.04
Bayern
0.26 0.51
0.07 0.09 0.03
Berlin
0.35 0.23
0.14 0.08 0.12
Brandenburg
0.36 0.20
0.05 0.07 0.27
Bremen
0.43 0.23
0.14 0.08 0.08
Hamburg
0.39 0.29
0.16 0.09 0.06
Hessen
0.35 0.32
0.10 0.12 0.05
Mecklenburg-Vorpommern 0.32 0.29
0.04 0.06 0.24
Niedersachsen
0.44 0.32
0.07 0.09 0.04
Nordrhein-Westfalen
0.39 0.35
0.07 0.10 0.05
Rheinland-Pfalz
0.34 0.37
0.07 0.12 0.05
Saarland
0.33 0.30
0.06 0.08 0.18
Sachsen
0.24 0.30
0.04 0.10 0.23
Sachsen-Anhalt
0.33 0.25
0.04 0.08 0.27
Schleswig-Holstein
0.38 0.37
0.08 0.10 0.04
Thueringen
0.30 0.26
0.04 0.08 0.27
LINKE
Max
Min
Max
Brandenburg
Bremen
Berlin
Sachsen−Anhalt
Hamburg
Saarland
Sachsen
Hessen
Min
Max
Thueringen
Mecklenburg−Vorpommern
FDP
GRUENE
UNION
SPD
LINKE
NiedersachsenNordrhein−Westfalen
FDP
GRUENE
UNION
SPD
Schleswig−HolsteinRheinland−Pfalz
Baden−Wuerttemberg
LINKE
Bayern
FDP
GRUENE
UNION
SPD
Min
Friedrich Leisch, Multivariate Verfahren 2009
52
Bsp PK: Sortierung nach Median Linke
Min
Bayern
LINKE
Max
Min
Max
Min
Max
Min
Max
Friedrich Leisch, Multivariate Verfahren 2009
53
Sterne und Segmente
Max
Baden−WuerttembergNiedersachsen Schleswig−HolsteinRheinland−Pfalz
Nordrhein−Westfalen
FDP
Sterne: Ein Polygonzug für jede Beobachtung, Radien der Eckpunkte
entsprechen Werte der Variablen.
GRUENE
UNION
SPD
Hessen
LINKE
Hamburg
Bremen
Berlin
Saarland
Sachsen
FDP
Segmente: Bessere Variante des Tortendiagramms. Winkel der Segmente konstant, Radien variabel.
GRUENE
UNION
SPD
Mecklenburg−Vorpommern
Thueringen
LINKE
Sachsen−Anhalt
Brandenburg
FDP
GRUENE
UNION
SPD
Min
Max
Min
Friedrich Leisch, Multivariate Verfahren 2009
Max
54
Friedrich Leisch, Multivariate Verfahren 2009
55
Sternendiagramm
Bayern
Baden−Wuerttemberg
Hessen
Sternendiagramm: Variablen standardisiert
Brandenburg
Berlin
Bayern
Hamburg
Baden−Wuerttemberg
Bremen
Mecklenburg−Vorpommern
Nordrhein−Westfalen
Niedersachsen
Rheinland−Pfalz
Saarland
Hessen
Brandenburg
Berlin
Hamburg
Bremen
Mecklenburg−Vorpommern
Nordrhein−Westfalen
Niedersachsen
Rheinland−Pfalz
UNION
UNION
GRUENE
Sachsen−Anhalt
Sachsen
GRUENE
SPD
Thueringen
Schleswig−Holstein
Sachsen−Anhalt
Sachsen
FDP
SPD
Thueringen
Schleswig−Holstein
FDP
LINKE
Friedrich Leisch, Multivariate Verfahren 2009
LINKE
56
Segmentdiagramm ganzer Kreis
Friedrich Leisch, Multivariate Verfahren 2009
Bayern
Baden−Wuerttemberg
Brandenburg
Berlin
Brandenburg
Berlin
Bremen
Hessen
Mecklenburg−Vorpommern
Nordrhein−Westfalen
Niedersachsen
Rheinland−Pfalz
GRUENE
UNION
SPD
Sachsen−Anhalt
Sachsen
Thueringen
Saarland
Saarland
UNION
Sachsen
Hamburg
Bremen
Hamburg
Mecklenburg−Vorpommern
Nordrhein−Westfalen
Hessen
Niedersachsen
Rheinland−Pfalz
Sachsen−Anhalt
57
Segmentdiagramm Halbkreis
Baden−Wuerttemberg
Bayern
Saarland
Thueringen
Schleswig−Holstein
SPD
FDP
LINKE
GRUENE
Schleswig−Holstein
LINKE
FDP
Friedrich Leisch, Multivariate Verfahren 2009
58
Friedrich Leisch, Multivariate Verfahren 2009
59
Segmentdiagramm: Variablen standardisiert
Bayern
Baden−Wuerttemberg
Hessen
Brandenburg
Berlin
Chernoff-Gesichter
Baden−Wuerttemberg
Bayern
Berlin
Brandenburg
Bremen
Hamburg
Hessen
Mecklenburg−Vorpommern
Index
Index
Index
Index
Niedersachsen
Nordrhein−Westfalen
Rheinland−Pfalz
Saarland
Index
Index
Index
Index
Sachsen
Sachsen−Anhalt
Schleswig−Holstein
Thueringen
Index
Index
Index
Index
Index
Index
Index
Index
Hamburg
Bremen
Mecklenburg−Vorpommern
Nordrhein−Westfalen
Niedersachsen
Rheinland−Pfalz
Saarland
UNION
SPD
Sachsen−Anhalt
Sachsen
Thueringen
GRUENE
Schleswig−Holstein
LINKE
FDP
Friedrich Leisch, Multivariate Verfahren 2009
60
Mosaikdiagramme
61
Bsp: Alkohol und WM 2006
• Darstellung der Interaktionen zwischen 2 oder mehr kategorischen
Merkmalen.
• Interessierende Nullhypothese: Unabhängigkeit
• Visualisierung über Gitterlinien und Farbe nach signierten PearsonResiduen (Wurzel der Summanden im χ2-Test)
Friedrich Leisch, Multivariate Verfahren 2009
Friedrich Leisch, Multivariate Verfahren 2009
62
Bevölkerungsrepräsentativ quotierte Umfrage der Größe n = 1008 von
Anfang Juni 2006 zum Thema Fußball-WM und Alkoholgenuß: Wie
schauen Sie sich die Spiele der deutschen Nationalmannschaft an?
schaue gar nicht
schaue ohne Alkohol
schaue mit Alkohol
keine Angabe
Maenner Frauen
83
142
150
204
260
168
0
1
Quelle: innofact.com
Friedrich Leisch, Multivariate Verfahren 2009
63
Bsp: Alkohol und WM 2006
250
500
Bsp: Alkohol und WM 2006
200
schaue gar nicht
schaue ohne Alkohol
schaue mit Alkohol
keine Angabe
0
0
50
100
100
200
150
300
400
keine Angabe
schaue mit Alkohol
schaue ohne Alkohol
schaue gar nicht
Maenner
Frauen
Maenner
Friedrich Leisch, Multivariate Verfahren 2009
64
Friedrich Leisch, Multivariate Verfahren 2009
400
65
Bsp: Alkohol und WM 2006
250
Bsp: Alkohol und WM 2006
Frauen
Maenner
Frauen
0
0
100
50
100
200
150
300
200
Frauen
Maenner
schaue gar nicht
schaue gar nicht
schaue ohne Alkohol schaue mit Alkohol
Friedrich Leisch, Multivariate Verfahren 2009
schaue ohne Alkohol
schaue mit Alkohol
keine Angabe
keine Angabe
66
Friedrich Leisch, Multivariate Verfahren 2009
67
Balkendiagramme
Mosaikdiagramme
Je nach Typ können unterschiedliche Variablen leichter miteinander
verglichen werden:
• Flächenproportionale Darstellung der Zeilen und Spalten einer
Kontingenztafel.
Gestapelt: primäre Variable
• Modifikation gestapelter Balkendiagramme: Statt Höhe codiert
Breite der Balken die primäre Variable.
Nebeneinander: sekundäre Variable innerhalb der Gruppen der primären
Variablen
• Sekundäre Variable als Stapel innerhalb der Balken der primären
Variablen.
In jedem Fall gibt es eine Asymmetrie zwischen den beiden Variablen.
• Asymmetrie zwischen Variablen weniger stark als bei Balkendiagrammen, kann auch für höherdimensionale Tafeln verwendet werden.
Friedrich Leisch, Multivariate Verfahren 2009
68
Bsp: Alkohol und WM
Friedrich Leisch, Multivariate Verfahren 2009
69
Bsp: Alkohol und WM
schaue gar nicht
1.1
schaue ohne Alkohol
schaue mit Alkohol
keine Angabe
100%
Friedrich Leisch, Multivariate Verfahren 2009
70
Friedrich Leisch, Multivariate Verfahren 2009
71
Bsp: Alkohol und WM
schaue gar nicht
schaue ohne Alkohol
Bsp: Alkohol und WM
schaue mit Alkohol
keine Angabe
schaue ohne Alkohol
schaue mit Alkohol
keine Angabe
Frauen
Frauen
Maenner
Maenner
schaue gar nicht
Friedrich Leisch, Multivariate Verfahren 2009
72
Bsp: Alkohol und WM
schaue ohne Alkohol
schaue mit Alkohol
keine Angabe
Zulassung von Studenten zur Graduate School der Universität Berkeley
1973 für die 6 größten Fakultäten:
<−4 −4:−2 −2:0
0:2
2:4
Maenner
Gender
Male
Female
Standardized
Residuals:
Frauen
Friedrich Leisch, Multivariate Verfahren 2009
73
Bsp: UCB Admissions
>4
schaue gar nicht
Friedrich Leisch, Multivariate Verfahren 2009
74
Admit Admitted Rejected
1198
557
1493
1278
Friedrich Leisch, Multivariate Verfahren 2009
75
Bsp: UCB Admissions
Bsp: UCB Admissions
Gender Dept
Male
A
B
C
D
E
F
Female A
B
C
D
E
F
Admit
Rejected
Pearson
residuals:
4.78
4.00
Male
Admitted
Gender
2.00
0.00
Female
−2.00
−4.00
Admit Admitted Rejected
512
353
120
138
53
22
89
17
202
131
94
24
313
207
205
279
138
351
19
8
391
244
299
317
−5.79
p−value =
< 2.22e−16
Friedrich Leisch, Multivariate Verfahren 2009
76
Bsp: UCB Admissions
Friedrich Leisch, Multivariate Verfahren 2009
77
Bsp: UCB Admissions
Admit
Rejected
Pearson
residuals:
20.2
A
Dept
B
C
D
Friedrich Leisch, Multivariate Verfahren 2009
Admitted
C
D
Rejected
Admit
4.0
2.0
0.0
−2.0
−4.0
D
E
F
Female
C BA
Gender
F E
Dept
Male
B
A
Admitted
−14.0
p−value =
< 2.22e−16
E F
Pearson
residuals:
12.6
4.0
2.0
0.0
−2.0
−4.0
−13.9
p−value =
< 2.22e−16
78
Friedrich Leisch, Multivariate Verfahren 2009
79
Bsp: UCB Admissions
B
Dept
C
D
E
Female
Gender
Male
A
Friedrich Leisch, Multivariate Verfahren 2009
F
Pearson
residuals:
11.5
4.0
2.0
0.0
−2.0
−4.0
−13.9
p−value =
< 2.22e−16
80