Network Analysis Applications of networks in Psychology and beyond
Sacha Epskamp University of Amsterdam Department of Psychological Methods
12-05-2014 TNO
Outline
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What is a network?
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What can we do with networks?
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How can we obtain a network structure?
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Example of network analysis on radicalization data
Worry
Insomnia
MD
Fatigue
Concentration
Worry
Insomnia
MD
Fatigue
Concentration
Worry
Insomnia
MD
Fatigue
Concentration
Worry
Insomnia
MD
Fatigue
Concentration
Worry
Insomnia
MD
Fatigue
Concentration
Worry
Insomnia
MD
Fatigue
Concentration
Psychology as a complex system
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Disorders usually first diagnosed in infancy, childhood or adolescence Delirium, dementia, and amnesia and other cognitive disorders Mental disorders due to a general medical condition Substance−related disorders Schizophrenia and other psychotic disorders Mood disorders Anxiety disorders Somatoform disorders Factitious disorders Dissociative disorders Sexual and gender identity disorders Eating disorders Sleep disorders Impulse control disorders not elsewhere classified Adjustment disorders Personality disorders Symptom is featured equally in multiple chapters
http://www.psychosystems.org/
What is a network?
What is a network?
I
A network is a set of nodes connected by a set of edges
Node 1
Edge
Node 2
What is a network?
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A network is a set of nodes connected by a set of edges I
A node represents an entity, this can be anything: I I I
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People Cities Symptoms
An edge represents some connection between two nodes. Again, this can be anything: I I I
Friendship / contact Distance Comorbidity
Anne is friends with Laura:
Anne
Friendship
Laura
Anne is friends with Laura and Roger, but Laura is not friends with Roger:
Anne
Roger
Laura
Networks can be weighted Anne is better friends with met Roger than Laura:
Anne
Roger
Laura
Weights can be signed Anne is friends with Roger and Laura, but Roger and Laura don’t like each other at all!
Anne
Roger
Laura
Networks can be directed Anne likes Laura, but Laura doesn’t like Anne:
Anne
Laura
Networks can model causality If it rains the grass becomes wet:
Rain
Grass wet
If the sprinkler is on the grass also becomes wet:
Rain
Sprinkler
Grass wet
Undirected
Directed
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Unweighted
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What can we do with networks?
What can we do with networks?
Besides providing a interpretable structure of a complex system, we can also use networks to compute unique measures such as: I Distance I
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How fast can symptom A influence symptom B?
Centrality Which symptom is the most important?
Connectivity? I
How well are symptoms connected?
Distance Node A is much further away from node B than node C:
A
B
C
Centrality Node A is much more influential than node B:
B
A
Connectivity The left network is much denser connected than the right one:
Friendship
Friendship
Relationships
Sexual contacts
Networks can be simulated given sufficient information about a population:
Psychopathology as a virus...
How to get a network?
JSS
Journal of Statistical Software May 2012, Volume 48, Issue 4.
http://www.jstatsoft.org/
qgraph: Network Visualizations of Relationships in Psychometric Data Sacha Epskamp
Ang´ elique O. J. Cramer
Lourens J. Waldorp
University of Amsterdam
University of Amsterdam
University of Amsterdam
Verena D. Schmittmann
Denny Borsboom
University of Amsterdam
University of Amsterdam
Abstract We present the qgraph package for R, which provides an interface to visualize data through network modeling techniques. For instance, a correlation matrix can be represented as a network in which each variable is a node and each correlation an edge; by
qgraph
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91
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20
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Neuroticism Extraversion Openness Agreeableness Conscientiousness
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Epskamp, Cramer, Waldorp, Schmittmann, and Borsboom (2012)
Correlations ●
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2
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106
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61
1
79
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226
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17
139
166
52
131
Minimum: 0.25
Cutoff: 0.4
Maximum: 0.77
Neuroticism Extraversion Openness Agreeableness Conscientiousness
Correlation networks
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Correlation networks are useful as a visualization tool
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But correlations are not easily interpreted as networks due to many spurious connections A partial correlation network, in which you display the correlations conditional on all other variables in the network, is easier interpretable:
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I
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Two nodes are connected if and only if there is covariance between those nodes that can not be explained by any other variable in the network
Such a network is called a Markov Random Field
Markov Random Fields
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A specific type of network is called a Markov Random Field
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Undirected networks with the property that a node is independent of all other nodes given its neighbors (connected nodes)
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Interpretable
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High predictive power
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If data is assumed normal these are called Gaussian random fields or Partial correlation matrices
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If the data is binary these are called the Ising model
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Typically we want to estimate a sparse structure, which we can do using a LASSO penalty
Markov Random Fields
A
C
I
A predicts C and B, but C better
I
C predicts A, and B via A
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B predicts A, and C via A
I
B and C are independent given A
B
A. Correlation network
●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● Oun
Ocr
Hsi
Oaa
Efe
Oin
Ean
Hmo
Ede
Hga
Ese
Hfa
Cdi
Xss
Cpr
Cpe
Apa
Xli
Xsb
Cor
Age
Xso
Afo
Afl
B. Partial Correlation network
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Oun
Oin
Efe
Oaa
Ede
Hmo
Ean
Ocr
Xss
Hga
Ese
Xli
Hsi
Hfa
Xsb
Cpr
Xso
Cor
Cpe
Afo
Cdi
Afl
Apa
Age
C. Adaptive lasso network
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Oin
Oaa
Cor
Ocr
Oun
Cpe
Cdi
Ean
Cpr
Ede
Xss
Ese
Xli
Apa
Efe
Xso
Xsb
Hfa
Afl
Hga
Age
Hsi
Afo
Hmo
Paper by Giulio Costantini, Sacha Epskamp, Denny Borsboom, Marco Perugini, René Mõttus, Lourens J. Waldorp & Angelique O. J. Cramer submitted
# Load packages: library("qgraph") library("parcor") # Read data: Data <- read.csv("HEXACOfacet.csv") # Plot correlations: qgraph(cor(Data), layout = "spring") # Plot partial correlations: qgraph(cor(Data), layout = "spring", graph = "concentration") # Plot LASSO network: adls <- adalasso.net(Data) network <- as.matrix(forceSymmetric(adls$pcor.adalasso)) qgraph(network, layout = "spring")
Partial correlations (using adaptive lasso)
Paper by Jolanda J. Kossakowski, Jacobien M. Kieffer, Sacha Epskamp & Denny Borsboom in preparation
Zooming in: Physical Functioning en Item 2
Three datasets
Figure: Left: AMC cancer. Middle: NKI cancer. Right: NKI healthy.
Ising Network fal
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Paper by Claudia D. van Borkulo, Denny Borsboom, Sacha Epskamp Tessa F. Blanken, Lynn Boschloo, Robert A. Schoevers & Lourens J. Waldorp submitted
Individual networks
C
P
E
F
D
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H
Bringmann, L.,Vissers, N., Wichers, M., Geschwind, N., Kuppens, P., Peeters, F., Borsboom, D., & Tuerlinckx, F. (2013). A network approach to psychopathology: New insights into clinical longitudinal data. PLoS ONE. Wednesday, October 2, 13
A subject over time...
Example of network analysis in Radicalization
Determinants of Radicalization of Islamic Youth in the Netherlands: Personal Uncertainty, Perceived Injustice, and Perceived Group Threat Bertjan Doosje∗ University of Amsterdam
Annemarie Loseman and Kees van den Bos Utrecht University
In this study among Dutch Muslim youth (N = 131), we focus on the process of radicalization. We hypothesize that this process is driven by three main factors: (a) personal uncertainty, (b) perceived injustice, and (c) perceived group threat. Using structural equation modeling, we demonstrate that personal uncertainty, perceived injustice, and group-threat factors are important determinants of a radical belief system (e.g., perceived superiority of Muslims, perceived illegitimacy of Dutch authorities, perceived distance to others, and a feeling of being disconnected from society). This radical belief system in turn predicts attitudes toward violence by other Muslims, which is a determinant of own violent intentions. Results are discussed in terms of the role of individual and group-based determinants of radicalization.
Radicalization example
Doosje, Loseman, and Bos (2013) investigated the process of radicalization of Dutch youth. They looked at possible determinants for adopting a radical beliefs system, which in turn can cause the basis for violent attitudes. An oversimplified version of their model is: Determinants → Radical beliefs system → Violent attitudes To test this model they measured several constructs in 131 Islamic youths in the Netherlands.
Radical belief system: I
Perceived illegitimacy of authorities
I
Perceived in-group superiority
I
Perceived distance to other people
I
Perceived societal disconnectedness
Determinants: I
Personal uncertainty
I
Perceived injustice
I
Perceived group threat
Background variables: I
In-group identification
I
individualistic relative deprivation
I
collective relative deprivation
1. Identification 2. Ind. Rel. Depri. 3. Col. Rel. Depri. 4. Int. Anxiety 5. Symbolic Threat 6. Realistic Threat 7. Per. Em. Uncertain. 8. Perc. Proc. Injustice 9. Perc. Illegitimacy 10. Perc. Ingr. Super. 11. Distance 12. Disconnected 13. Moslim Violence 14. Violent Intentions
4.56 2.39 3.31 − 0.20 3.46 3.10 2.84 2.38 2.37 3.26 2.32 2.79 2.89 2.08
SD
1
0.85 – 0.81 0.92 0.17 0.76 0.88 0.67 0.68 0.02 0.93 0.66 0.96 1.06 0.91
2
3
− .19* .08 – .49* –
4
5
6
7
8
9
10
11
12
13
14
− .25* .36* .11 –
.42* .23* .54* .01 –
.07 .50* .62* .15 .64* –
.08 .21* .26* .19* .21* .27* –
− .06 .50* .38* .21* .24* .34* .10 –
− .28* .25* .21 .35* .07 .16 .08 .15 –
.09 .12 .31* .08 .39* .35* .29* .01 .22* –
− .17 .17 .18* .22* .01 .19* .18 .03 .17* .34* –
− .25* .21* .09 .26* .04 .14 .00 .23* .35* .08 .08 –
− .04 .12 .20* .18* .17 .26* .30* .04 .35* .53* .44* .24* –
− .07 .09 .10 .14 − .01 .16 .14 .06 .24* .30* .39* .00 .47* –
Determinants of Radicalization of Islamic Youth in the Netherlands
Table 1. The Means, Standard Deviations, and Inter-Correlations of All the Constructs M
Note. 2 = Individual Relative Deprivation, 3 = Collective Relative Deprivation, 4 = Intergroup Anxiety, 5 = Symbolic Threat, 6 = Realistic Threat, 7 = Personal Emotional Uncertainty, 8 = Perceived Procedural Injustice, 9 = Perceived Illegitimacy, 10 = Perceived Ingroup Superiority. *p < .05.
595
Correlations The qgraph package can be used to visualize correlations as a network (Epskamp et al., 2012):
12 4
11 9
1 14 13 2
10
3 7
8
6
5
1: In−group Identification 2: Individual Deprivation 3: Collective Deprivation 4: Intergroup Anxiety 5: Symbolic Threat 6: Realistic Threat 7: Personal Emotional Uncertainty 8: Perceived Injustice 9: Perceived Illegitimacy authorities 10: Perceived In−group superiority 11: Distance to Other People 12: Societal Disconnected 13: Attitude towards Muslim Violence 14: Own Violent Intentions
To test the hypothesized model, Doosje et al. (2013) used Structural Equation Modelling (SEM). SEM is a powerful modeling framework that has been one of the main focuses of Psychometrics for decades. In essence, it can be seen as confirmatory testing a network of observed and unobserved variables where typically is assumed that: I
All paths are directed and indicate linear effects
I
All variables are assumed normally distributed
I
The network is acyclic
596
Doosje, Loseman, and van den Bos
Background Variables
Determinants
.26
.33 R2=.40
.35
Individual Deprivation
Symbolic Threat
.53
-.21 .29 .37
.23 R2=.43
Collective Deprivation
Realistic Threat
.51
.16
R2=.16
Perceived Illegitimacy Authorities
R2=.18
Perceived In-group Superiority
.18 .36 .28
R2=.07
Personal Emotional Uncertainty
.23
Distance to Other People
R2=.39
Attitude towards Muslim Violence .15 .35
R2=.05
.26
R2=.26 .25
Own Violent Intentions
R2=.05
.41 .17
Violent Intentions
Intergroup Anxiety
-.18 In-group Identification
Radical Belief System
R2=.17
R2=.27
Perceived Injustice
.21
Societal DisConnected
Fig. 1. Final structural equation model. All paths are significant. R2 = % variance explained.
Interpreting SEM results
SEM can be used to test if the data rejects a theorized model. But care should be taken in that a fitting SEM model does not mean the model is correct. Many equivalent models could fit the data just as well.
Equivalent model
illegitemacy muslim_violence
uncertainty
col_dep sym_threat superiority
own_violent
identification
injustice disconnected
in_dep real_threat
distance
anxiety
Equivalent models
col_dep
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illegitemacy
Equivalent models
col_dep
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Equivalent models
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injustice
real_threat
muslim_violence
superiority
anxiety
illegitemacy
identification
muslim_violence
illegitemacy
col_dep
illegitemacy
illegitemacy
injustice
sym_threat
own_violent
anxiety
distance
identification
muslim_violence
sym_threat
col_dep
uncertainty
identification
col_dep
real_threat
distance
uncertainty
superiority
sym_threat
sym_threat
superiority
muslim_violence
injustice
illegitemacy
anxiety
uncertainty
anxiety
col_dep
disconnected
uncertainty
superiority
sym_threat
uncertainty disconnected
disconnected
injustice
real_threat
distance
in_dep
injustice
disconnected
own_violent
injustice
col_dep
distance injustice
disconnected
distance
disconnected
uncertainty
distance
muslim_violence
muslim_violence
distance real_threat
own_violent
in_dep
identification
col_dep uncertainty
distance injustice
distance
uncertainty
disconnected
disconnected
injustice own_violent
anxiety
col_dep
own_violent
own_violent
illegitemacy own_violent
injustice
in_dep
own_violent
muslim_violence
illegitemacy
disconnected
superiority
anxiety
col_dep
col_dep
distance injustice
own_violent
sym_threat
identification
uncertainty own_violent
own_violent
injustice
distance real_threat
anxiety
anxiety
muslim_violence
illegitemacy
disconnected
own_violent
anxiety
col_dep
anxiety
col_dep uncertainty
uncertainty
identification
illegitemacy illegitemacy
distance
disconnected
col_dep
muslim_violence
illegitemacy
anxiety
disconnected
uncertainty real_threat
own_violent
distance
anxiety
muslim_violence
sym_threat
disconnected
in_dep
col_dep
real_threat
muslim_violence
illegitemacy
anxiety
illegitemacy
illegitemacy
identification
injustice
in_dep
disconnected
anxiety
muslim_violence
illegitemacy
muslim_violence
illegitemacy
muslim_violence
col_dep uncertainty own_violent
injustice
superiority
sym_threat
in_dep
identification
injustice
disconnected
superiority sym_threat
uncertainty
col_dep identification
muslim_violence
illegitemacy
illegitemacy
muslim_violence
illegitemacy
injustice identification
in_dep
anxiety
distance
identification
anxiety
illegitemacy
identification
distance real_threat
real_threat
own_violent
real_threat
anxiety
muslim_violence
muslim_violence
illegitemacy
own_violent
distance
in_dep
disconnected
in_dep
anxiety
anxiety muslim_violence
illegitemacy
identification
injustice
superiority sym_threat
injustice
anxiety muslim_violence
sym_threat
distance
superiority
real_threat
distance
uncertainty
superiority
real_threat
uncertainty
real_threat
superiority
illegitemacy
superiority
illegitemacy
superiority sym_threat
in_dep
sym_threat
illegitemacy
muslim_violence
in_dep
in_dep
muslim_violence
in_dep
superiority
real_threat
in_dep
real_threat
in_dep
anxiety
superiority
in_dep
real_threat
sym_threat
in_dep
in_dep
sym_threat
anxiety
illegitemacy
anxiety
col_dep
identification
anxiety
col_dep
identification
muslim_violence
identification
muslim_violence
identification
identification
in_dep sym_threat
muslim_violence
illegitemacy
disconnected
anxiety
illegitemacy illegitemacy
col_dep
own_violent
injustice
sym_threat
own_violent
anxiety
distance
illegitemacy
col_dep
own_violent
sym_threat
own_violent
anxiety
distance
illegitemacy
col_dep
sym_threat
own_violent
anxiety
distance
distance
injustice
sym_threat
disconnected
injustice
disconnected
injustice
disconnected
col_dep
disconnected
injustice
in_dep illegitemacy
injustice
in_dep
superiority
injustice
superiority
uncertainty
in_dep
injustice
in_dep
uncertainty
superiority
uncertainty
in_dep
injustice
in_dep
distance
identification
identification
disconnected
identification
in_dep
real_threat
real_threat
sym_threat
identification identification
disconnected
disconnected
muslim_violence
col_dep identification
disconnected
muslim_violence
in_dep
real_threat
distance
real_threat
illegitemacy
anxiety
muslim_violence
illegitemacy
anxiety
col_dep
real_threat
own_violent
own_violent
own_violent
distance
muslim_violence
real_threat
disconnected
disconnected
real_threat
disconnected
superiority
sym_threat
own_violent
anxiety
distance
superiority
real_threat
distance
in_dep
illegitemacy
col_dep
uncertainty
illegitemacy
col_dep
uncertainty
in_dep
muslim_violence
sym_threat
illegitemacy
anxiety
superiority
disconnected
uncertainty
superiority
sym_threat
uncertainty
in_dep
injustice
sym_threat
disconnected
sym_threat
identification
injustice
distance
identification
col_dep
own_violent
own_violent
real_threat
identification
in_dep
distance
col_dep
muslim_violence
sym_threat
disconnected
in_dep identification
muslim_violence
in_dep
in_dep
sym_threat
in_dep
illegitemacy
muslim_violence
illegitemacy
injustice
injustice
col_dep
muslim_violence
col_dep uncertainty
disconnected
own_violent
uncertainty
real_threat
disconnected
real_threat
own_violent
own_violent
uncertainty
distance
in_dep
distance sym_threat
distance
in_dep
superiority
real_threat identification identification
in_dep
uncertainty
injustice
uncertainty
col_dep
sym_threat
in_dep
disconnected
in_dep
identification
superiority
sym_threat
identification
identification
sym_threat
superiority
anxiety
injustice
illegitemacy
anxiety
col_dep
disconnected
in_dep
uncertainty
col_dep muslim_violence
in_dep
illegitemacy
in_dep disconnected
anxiety
real_threat
disconnected
injustice
disconnected
col_dep
distance
real_threat
distance
injustice
disconnected
illegitemacy
illegitemacy
muslim_violence
col_dep
muslim_violence
anxiety illegitemacy
sym_threat
anxiety
injustice
col_dep
own_violent
distance real_threat
anxiety
real_threat
muslim_violence
identification
muslim_violence
illegitemacy
sym_threat
superiority
distance superiority
muslim_violence
identification muslim_violence
illegitemacy
illegitemacy
disconnected
uncertainty
distance
identification
uncertainty illegitemacy
distance real_threat
injustice disconnected
anxiety
injustice
col_dep
own_violent
real_threat
sym_threat
superiority
uncertainty
muslim_violence
identification
muslim_violence
col_dep
illegitemacy
disconnected
uncertainty
own_violent disconnected
injustice
superiority
superiority
illegitemacy
sym_threat
muslim_violence
disconnected
injustice
col_dep
muslim_violence
real_threat
superiority sym_threat
superiority
anxiety
in_dep
illegitemacy
injustice
injustice
disconnected
distance
injustice
superiority
identification
superiority
illegitemacy
col_dep
anxiety col_dep
own_violent
uncertainty
anxiety
muslim_violence
real_threat
distance
sym_threat
uncertainty
uncertainty
in_dep
disconnected
sym_threat illegitemacy
injustice own_violent
distance disconnected
in_dep in_dep
real_threat
sym_threat
in_dep
anxiety
in_dep
identification
disconnected
illegitemacy
distance
col_dep
own_violent
uncertainty uncertainty
sym_threat illegitemacy
disconnected
in_dep
anxiety
real_threat muslim_violence
in_dep
real_threat
own_violent
real_threat
injustice
anxiety
col_dep
illegitemacy
col_dep
own_violent
superiority sym_threat
injustice
in_dep
anxiety
muslim_violence
identification
sym_threat
superiority
muslim_violence
identification
muslim_violence
anxiety
in_dep
identification
disconnected
disconnected
uncertainty disconnected
injustice distance
own_violent
superiority
uncertainty
own_violent
anxiety sym_threat
injustice
identification
injustice
real_threat
muslim_violence
uncertainty
injustice
anxiety
own_violent
real_threat
in_dep
disconnected
distance real_threat
in_dep
anxiety
muslim_violence
col_dep
muslim_violence
illegitemacy
col_dep
anxiety
injustice
uncertainty
illegitemacy
superiority real_threat
col_dep
sym_threat
identification
injustice
real_threat
superiority
disconnected
uncertainty
injustice
identification
col_dep
col_dep distance uncertainty
anxiety
uncertainty superiority
injustice
muslim_violence
sym_threat
distance
illegitemacy
identification
disconnected
superiority
sym_threat
identification
uncertainty
col_dep distance
injustice
disconnected
uncertainty
in_dep superiority
sym_threat
in_dep
illegitemacy
col_dep
illegitemacy
superiority
own_violent illegitemacy
own_violent
anxiety
col_dep
col_dep distance
injustice
uncertainty
own_violent
distance
muslim_violence
superiority
identification
anxiety
in_dep
muslim_violence
illegitemacy
anxiety
col_dep
distance
muslim_violence
superiority uncertainty
own_violent
distance
sym_threat
superiority
distance real_threat
distance distance
own_violent
real_threat
superiority
own_violent disconnected
injustice
uncertainty
real_threat
identification
real_threat
illegitemacy own_violent
injustice
anxiety
col_dep
uncertainty
own_violent
distance
col_dep
superiority
distance
real_threat
identification
muslim_violence
muslim_violence
illegitemacy
illegitemacy
anxiety
col_dep
uncertainty
own_violent
real_threat
anxiety own_violent
disconnected
injustice
uncertainty
distance
real_threat
disconnected
muslim_violence
illegitemacy illegitemacy
uncertainty
sym_threat
sym_threat illegitemacy
anxiety col_dep
superiority uncertainty
muslim_violence
distance
real_threat
muslim_violence
identification
muslim_violence
identification
sym_threat illegitemacy
own_violent disconnected
injustice superiority uncertainty muslim_violence
distance
superiority
anxiety
col_dep
in_dep muslim_violence
identification
sym_threat
own_violent
superiority uncertainty muslim_violence
muslim_violence
distance
in_dep
in_dep muslim_violence
col_dep
disconnected
injustice own_violent
superiority uncertainty
uncertainty
sym_threat
anxiety anxiety
col_dep
disconnected
injustice
superiority
real_threat
muslim_violence
superiority
sym_threat
sym_threat
illegitemacy
col_dep
own_violent
uncertainty uncertainty identification
superiority
sym_threat
superiority
identification
own_violent disconnected
injustice
real_threat
real_threat identification
sym_threat
identification
anxiety
anxiety col_dep
superiority
injustice
own_violent
distance real_threat
illegitemacy
identification
illegitemacy disconnected
col_dep
distance uncertainty
in_dep sym_threat
illegitemacy
identification
sym_threat
illegitemacy disconnected
injustice own_violent
uncertainty
sym_threat
superiority
identification
muslim_violence
anxiety disconnected
injustice
col_dep
sym_threat
sym_threat
injustice
sym_threat
injustice
injustice own_violent
uncertainty
disconnected
in_dep
own_violent
distance real_threat
identification
distance real_threat
own_violent
own_violent
anxiety
col_dep
distance
in_dep
superiority
anxiety
col_dep
own_violent
injustice sym_threat
uncertainty
col_dep
disconnected
uncertainty
own_violent
col_dep
disconnected
own_violent
injustice
distance
identification own_violent
distance
distance
identification
col_dep
identification
uncertainty
identification
uncertainty
uncertainty
col_dep
col_dep
real_threat
superiority
real_threat
anxiety
uncertainty
superiority
muslim_violence
illegitemacy
real_threat superiority
in_dep injustice
in_dep
anxiety
in_dep
distance
sym_threat
anxiety
in_dep
in_dep
identification
col_dep
in_dep
disconnected
identification
disconnected
identification
in_dep
superiority
in_dep
own_violent
injustice
own_violent
in_dep
in_dep
injustice
anxiety
own_violent
in_dep
uncertainty
disconnected
injustice
sym_threat
illegitemacy
distance
muslim_violence
superiority
anxiety
distance
muslim_violence
real_threat
uncertainty
col_dep
real_threat
disconnected
injustice
in_dep
uncertainty
disconnected
distance
uncertainty
superiority
sym_threat
col_dep
sym_threat
col_dep
disconnected
col_dep disconnected
uncertainty
col_dep
injustice
uncertainty
distance own_violent
own_violent
identification
sym_threat
distance
real_threat
in_dep
anxiety
uncertainty
muslim_violence
col_dep
identification
identification
disconnected
col_dep
col_dep
disconnected
injustice
own_violent
own_violent
real_threat
distance
superiority
injustice
real_threat
sym_threat
anxiety
in_dep
illegitemacy
identification
sym_threat
identification
identification
identification
muslim_violence
sym_threat
superiority
identification
anxiety
col_dep
identification
in_dep
in_dep
injustice uncertainty
real_threat
distance
distance
uncertainty
disconnected
in_dep
illegitemacy
anxiety
disconnected
distance
superiority
real_threat
col_dep
own_violent
injustice
real_threat
in_dep
distance
disconnected
disconnected
real_threat
muslim_violence
col_dep
col_dep real_threat
own_violent
injustice real_threat disconnected
own_violent
col_dep
injustice
col_dep
in_dep injustice
uncertainty
own_violent
uncertainty disconnected
own_violent
col_dep
in_dep
disconnected
uncertainty
muslim_violence
distance distance
uncertainty
distance
identification
own_violent
superiority
real_threat superiority
anxiety
real_threat
distance
illegitemacy
anxiety muslim_violence
illegitemacy
superiority muslim_violence
sym_threat
anxiety
illegitemacy muslim_violence
anxiety
sym_threat
anxiety
illegitemacy muslim_violence
injustice
disconnected
in_dep
disconnected
injustice
anxiety
uncertainty own_violent
col_dep own_violent
injustice
own_violent
real_threat
superiority
injustice
own_violent
superiority
disconnected
illegitemacy
uncertainty
real_threat
sym_threat
illegitemacy
distance
superiority
superiority
muslim_violence
anxiety
muslim_violence
illegitemacy
sym_threat
superiority illegitemacy
uncertainty sym_threat
distance
injustice
anxiety
col_dep
own_violent
real_threat
muslim_violence
illegitemacy
muslim_violence
distance
identification
superiority
distance
muslim_violence
illegitemacy
real_threat
sym_threat
identification
in_dep
identification
injustice
uncertainty
own_violent disconnected
injustice
uncertainty
sym_threat
uncertainty
col_dep
anxiety col_dep
anxiety col_dep
own_violent
superiority
superiority muslim_violence
sym_threat
illegitemacy
sym_threat
superiority
identification
muslim_violence
illegitemacy
in_dep
disconnected
illegitemacy
distance
distance
anxiety
superiority muslim_violence
muslim_violence
sym_threat
illegitemacy
muslim_violence
injustice
in_dep identification
real_threat
disconnected disconnected
superiority
illegitemacy
in_dep
identification
disconnected
sym_threat
identification
uncertainty
sym_threat
anxiety distance
sym_threat superiority
identification
anxiety
muslim_violence
illegitemacy
muslim_violence
muslim_violence
illegitemacy
sym_threat illegitemacy
own_violent
uncertainty
own_violent
injustice
col_dep
sym_threat illegitemacy
own_violent
distance real_threat
superiority
sym_threat
in_dep
anxiety illegitemacy
real_threat
identification
uncertainty
superiority
superiority
anxiety muslim_violence
illegitemacy
in_dep
uncertainty
real_threat
real_threat
muslim_violence
superiority
in_dep
real_threat
distance
anxiety
distance
identification
anxiety muslim_violence
sym_threat
illegitemacy muslim_violence
injustice
identification
in_dep
superiority
anxiety
muslim_violence
distance
real_threat
injustice
in_dep
own_violent
own_violent
identification
real_threat
in_dep
sym_threat
own_violent
injustice
distance
in_dep own_violent
identification
superiority
anxiety
uncertainty
distance
in_dep real_threat
real_threat
distance
superiority
illegitemacy
disconnected
own_violent
anxiety
sym_threat identification
muslim_violence
muslim_violence
sym_threat
col_dep
injustice
in_dep
injustice
disconnected
real_threat
in_dep
distance
in_dep identification
own_violent
superiority uncertainty
muslim_violence
anxiety
sym_threat
uncertainty
col_dep uncertainty
sym_threat
disconnected
injustice own_violent
superiority uncertainty
distance
superiority real_threat superiority
sym_threat
disconnected
col_dep
identification
col_dep disconnected
real_threat
col_dep
anxiety
col_dep
disconnected
injustice real_threat
distance distance
illegitemacy
distance
injustice disconnected
anxiety
col_dep disconnected
injustice
real_threat
superiority
muslim_violence
illegitemacy
uncertainty
injustice
identification
anxiety
injustice
uncertainty
own_violent
distance muslim_violence
superiority
superiority
illegitemacy
sym_threat
illegitemacy
illegitemacy
own_violent
identification
own_violent
injustice
uncertainty uncertainty
muslim_violence
superiority
real_threat sym_threat
superiority
anxiety
illegitemacy
illegitemacy
own_violent
col_dep uncertainty
disconnected
real_threat
distance
muslim_violence
illegitemacy
own_violent
sym_threat
col_dep
illegitemacy
in_dep
col_dep
anxiety
injustice
col_dep uncertainty
uncertainty superiority sym_threat muslim_violence
illegitemacy
real_threat
identification
muslim_violence
real_threat
col_dep
own_violent
distance real_threat
anxiety
uncertainty
muslim_violence
uncertainty
disconnected
distance injustice
identification
own_violent
superiority
illegitemacy
anxiety anxiety
identification
identification
col_dep own_violent illegitemacy
injustice
col_dep
identification
sym_threat
own_violent
real_threat disconnected
own_violent
distance
identification
anxiety
anxiety
muslim_violence
identification
disconnected
distance
superiority
sym_threat
anxiety identification
identification
real_threat
sym_threat
identification
sym_threat
disconnected
superiority
sym_threat
uncertainty
muslim_violence
illegitemacy
sym_threat
in_dep
anxiety
real_threat
sym_threat
superiority
anxiety illegitemacy
sym_threat
illegitemacy
anxiety
real_threat
distance
own_violent
superiority
muslim_violence
anxiety
superiority
superiority
real_threat
distance
uncertainty
real_threat superiority
disconnected muslim_violence
superiority
anxiety
own_violent
sym_threat real_threat
injustice
injustice distance
disconnected
anxiety
col_dep
own_violent
injustice disconnected
sym_threat
sym_threat
illegitemacy
sym_threat
Interpreting SEM results
I
Direction of causation can often not be inferred
I
Assumption of no cycles is very strict and in psychology often not tenable SEM is very powerful in testing strict theories where the acyclic assumption is met. In more exploratory settings however, using partial correlation networks can be preferred:
I
I I I I
Shows relationships present in the data No equivalent models Naturally cyclic Optimally predicts each node given all others
Correlation network 12 4
11 9
1 14 13 2
10
3 7
8
6
5
1: In−group Identification 2: Individual Deprivation 3: Collective Deprivation 4: Intergroup Anxiety 5: Symbolic Threat 6: Realistic Threat 7: Personal Emotional Uncertainty 8: Perceived Injustice 9: Perceived Illegitimacy authorities 10: Perceived In−group superiority 11: Distance to Other People 12: Societal Disconnected 13: Attitude towards Muslim Violence 14: Own Violent Intentions
Partial correlation network 10 13 14
11
5
1 12 6 7 9 3 8
2
4
1: In−group Identification 2: Individual Deprivation 3: Collective Deprivation 4: Intergroup Anxiety 5: Symbolic Threat 6: Realistic Threat 7: Personal Emotional Uncertainty 8: Perceived Injustice 9: Perceived Illegitimacy authorities 10: Perceived In−group superiority 11: Distance to Other People 12: Societal Disconnected 13: Attitude towards Muslim Violence 14: Own Violent Intentions
Partial correlation network After glasso (Friedman, Hastie, & Tibshirani, 2011):
9
7
14 10 3
13
6 11 5
2 12 8
1
4
1: In−group Identification 2: Individual Deprivation 3: Collective Deprivation 4: Intergroup Anxiety 5: Symbolic Threat 6: Realistic Threat 7: Personal Emotional Uncertainty 8: Perceived Injustice 9: Perceived Illegitimacy authorities 10: Perceived In−group superiority 11: Distance to Other People 12: Societal Disconnected 13: Attitude towards Muslim Violence 14: Own Violent Intentions
Centrality Betweenness
Closeness
Symbolic Threat Societal Disconnected
Perceived Injustice
●
●
●
●
●
●
Perceived Illegitimacy authorities
●
Own Violent Intentions
●
Intergroup Anxiety
●
●
●
Perceived In−group superiority
●
●
●
●
●
●
In−group Identification
●
Individual Deprivation
Collective Deprivation
●
●
●
●
●
Realistic Threat
Attitude towards Muslim Violence
●
●
Personal Emotional Uncertainty
Distance to Other People
Strength
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
0.00 0.25 0.50 0.75 1.00 0.5 0.6 0.7 0.8 0.9 1.00.00 0.25 0.50 0.75 1.00
Shortest path length
In-group Identification Individual Deprivation Collective Deprivation Intergroup Anxiety Symbolic Threat Realistic Threat Personal Emotional Uncertainty Perceived Injustice Perceived Illegitimacy authorities Perceived In-group superiority Distance to Other People Societal Disconnected Attitude towards Muslim Violence Own Violent Intentions
Muslim Violence 16.12 20.10 17.05 Inf 11.44 14.81 10.73 24.83 Inf 3.16 5.70 9.15 0.00 3.77
Violent Intentions 19.89 23.87 20.82 Inf 15.21 18.58 14.50 28.60 Inf 6.93 8.81 12.92 3.77 0.00
Shortest path length
In-group Identification Individual Deprivation Collective Deprivation Intergroup Anxiety Symbolic Threat Realistic Threat Personal Emotional Uncertainty Perceived Injustice Perceived Illegitimacy authorities Perceived In-group superiority Distance to Other People Societal Disconnected Attitude towards Muslim Violence Own Violent Intentions
Muslim Violence 16.12 20.10 17.05 Inf 11.44 14.81 10.73 24.83 Inf 3.16 5.70 9.15 0.00 3.77
Violent Intentions 19.89 23.87 20.82 Inf 15.21 18.58 14.50 28.60 Inf 6.93 8.81 12.92 3.77 0.00
Conclusion
Preliminary network analysis agrees with Doosje et al. (2013) that Perceived In-group superiority, Distance to Other People and to a lesser extent Societal Disconnected are strong predictors for attitudes towards Muslim violence which in turn predicts own violent intents. The fourth element of the radical beliefs system, Perceived Illegitimacy authorities, plays a lesser role in the network. Personal Emotional Uncertainty is the only variable whose predictive power on the violent variables is not mediated by the radical beliefs system.
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