NETWORK ANALYSIS

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?

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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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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



Verena D. Schmittmann

Denny Borsboom



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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Neuroticism Extraversion Openness Agreeableness Conscientiousness

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Epskamp, Cramer, Waldorp, Schmittmann, and Borsboom (2012)

Correlations ●

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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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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

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A predicts C and B, but C better

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C predicts A, and B via A

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B predicts A, and C via A

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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

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Cpr

Ede

Xss

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Xli

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Age

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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

T

!"#$%&%! + "' (')$*'%+ "+ (+)$*' + ... + #!

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

uncertainty

col_dep

uncertainty

superiority

distance identification

sym_threat

injustice

disconnected

real_threat

identification

in_dep

in_dep

superiority sym_threat

own_violent

own_violent

injustice real_threat

distance

disconnected

muslim_violence

anxiety anxiety

illegitemacy

muslim_violence

illegitemacy

Equivalent models

col_dep

col_dep

uncertainty

col_dep

uncertainty

illegitemacy

superiority

superiority

distance

uncertainty

real_threat

identification

in_dep

identification

sym_threat

injustice

disconnected

identification


own_violent

in_dep

sym_threat

in_dep own_violent

anxiety

own_violent

disconnected

muslim_violence

injustice injustice disconnected

real_threat

distance

anxiety

illegitemacy

col_dep

illegitemacy

muslim_violence

anxiety

real_threat

muslim_violence

illegitemacy

col_dep

illegitemacy

superiority

uncertainty

identification

sym_threat

injustice

disconnected

real_threat

distance

anxiety

illegitemacy

superiority

uncertainty

sym_threat

identification

in_dep

sym_threat

in_dep anxiety

col_dep superiority

uncertainty

identification

distance

in_dep

own_violent

injustice

anxiety

own_violent

disconnected

muslim_violence

own_violent


muslim_violence

muslim_violence

real_threat

real_threat

distance

distance

Equivalent models

uncertainty

illegitemacy

illegitemacy

identification

sym_threat

superiority

muslim_violence

col_dep

uncertainty

col_dep

disconnected

distance

injustice

uncertainty

real_threat

disconnected

own_violent

superiority

injustice

identification

uncertainty

col_dep sym_threat

real_threat

sym_threat

superiority

muslim_violence


col_dep

distance

uncertainty

in_dep

own_violent

sym_threat

own_violent

identification

own_violent

in_dep

in_dep

injustice superiority

col_dep

real_threat

distance

injustice

identification

real_threat

disconnected

own_violent

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distance

in_dep

identification

in_dep injustice

real_threat

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distance

muslim_violence

disconnected

anxiety

illegitemacy

illegitemacy

anxiety

col_dep

uncertainty

identification

sym_threat

injustice

disconnected

col_dep

muslim_violence

illegitemacy

anxiety

anxiety

muslim_violence

illegitemacy

col_dep

muslim_violence

superiority

uncertainty

illegitemacy

identification

distance

superiority

in_dep

distance

uncertainty uncertainty

col_dep

real_threat illegitemacy

real_threat

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own_violent

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own_violent

identification

in_dep

sym_threat

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in_dep

in_dep

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superiority own_violent

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col_dep

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sym_threat

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real_threat

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muslim_violence

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anxiety

col_dep

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sym_threat

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distance

illegitemacy

disconnected

col_dep

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injustice

col_dep

muslim_violence

illegitemacy

col_dep

uncertainty

identification

sym_threat

injustice

disconnected

col_dep

illegitemacy

identification

sym_threat

superiority

superiority

in_dep


uncertainty

own_violent identification

identification

superiority real_threat

distance

anxiety

illegitemacy

in_dep

superiority

in_dep

sym_threat

sym_threat

in_dep

injustice

disconnected

real_threat

distance

in_dep own_violent


real_threat own_violent

distance

anxiety

own_violent

disconnected

muslim_violence

injustice

own_violent

distance

injustice

muslim_violence

anxiety

real_threat

anxiety muslim_violence

disconnected

muslim_violence

illegitemacy

muslim_violence

illegitemacy

anxiety

illegitemacy

distance

Equivalent models illegitemacy

uncertainty

illegitemacy

col_dep

illegitemacy

identification

sym_threat

injustice

uncertainty

col_dep

col_dep

col_dep

injustice

uncertainty

sym_threat

identification

identification

in_dep

real_threat

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col_dep

uncertainty

superiority

own_violent

injustice

disconnected

sym_threat

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own_violent

injustice

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anxiety

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muslim_violence

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distance

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sym_threat

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illegitemacy

muslim_violence

muslim_violence

uncertainty

col_dep

distance

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distance

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own_violent

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superiority

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muslim_violence

identification

sym_threat

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muslim_violence

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sym_threat

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sym_threat superiority

disconnected

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anxiety

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own_violent

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identification

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in_dep uncertainty

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col_dep

superiority

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in_dep

anxiety

superiority

identification

muslim_violence

anxiety

uncertainty

col_dep



superiority

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anxiety muslim_violence muslim_violence

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identification

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muslim_violence

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col_dep

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col_dep

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col_dep

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anxiety sym_threat

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col_dep

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uncertainty

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identification

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anxiety

own_violent

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col_dep


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uncertainty real_threat

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in_dep in_dep

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col_dep sym_threat

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col_dep

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col_dep

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in_dep

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col_dep

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col_dep

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sym_threat

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superiority

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own_violent

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col_dep

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in_dep

in_dep injustice

sym_threat

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col_dep

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col_dep

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col_dep

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identification

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muslim_violence

muslim_violence

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col_dep

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identification

col_dep

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injustice

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muslim_violence

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distance

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distance

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col_dep

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in_dep

col_dep

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muslim_violence muslim_violence

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in_dep own_violent

disconnected

own_violent

distance

muslim_violence

disconnected

sym_threat

sym_threat

anxiety

distance

anxiety

sym_threat

superiority

Equivalent models in_dep

in_dep

in_dep

in_dep

in_dep

anxiety identification

identification

anxiety

col_dep

identification

col_dep

illegitemacy disconnected

in_dep anxiety

identification

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col_dep

illegitemacy

in_dep

in_dep


col_dep

identification

identification

col_dep illegitemacy

illegitemacy

identification

muslim_violence

illegitemacy

illegitemacy

col_dep

anxiety

anxiety uncertainty

illegitemacy

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muslim_violence

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col_dep

illegitemacy

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illegitemacy

in_dep anxiety

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identification

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illegitemacy


identification

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col_dep

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disconnected

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own_violent

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distance

own_violent

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distance

own_violent

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own_violent

uncertainty

col_dep

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own_violent

col_dep

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uncertainty

own_violent

col_dep

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own_violent

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uncertainty

own_violent

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distance

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distance


muslim_violence

uncertainty

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muslim_violence

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muslim_violence

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muslim_violence

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distance

superiority

real_threat

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muslim_violence

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distance uncertainty

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col_dep

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col_dep

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muslim_violence

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col_dep

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col_dep

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col_dep

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col_dep

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uncertainty

uncertainty

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col_dep

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injustice

own_violent

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col_dep own_violent

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real_threat

own_violent

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muslim_violence

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muslim_violence

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anxiety


sym_threat

anxiety

illegitemacy

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own_violent

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own_violent

injustice

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muslim_violence

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superiority

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col_dep

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distance injustice

own_violent

sym_threat

identification


own_violent

injustice


anxiety

anxiety

muslim_violence

illegitemacy

disconnected

own_violent

anxiety

col_dep

anxiety

col_dep uncertainty

uncertainty

identification


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


uncertainty


muslim_violence

illegitemacy

illegitemacy

muslim_violence

illegitemacy

injustice identification

in_dep

anxiety

distance

identification

anxiety

illegitemacy

identification


real_threat

own_violent

real_threat

anxiety

muslim_violence

muslim_violence

illegitemacy

own_violent

distance

in_dep

disconnected

in_dep

anxiety


illegitemacy

identification

injustice


injustice


sym_threat

distance

superiority

real_threat

distance

uncertainty

superiority

real_threat

uncertainty

real_threat

superiority

illegitemacy

superiority

illegitemacy


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


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


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


sym_threat

anxiety

injustice

col_dep

own_violent


anxiety

real_threat

muslim_violence

identification

muslim_violence

illegitemacy

sym_threat

superiority


muslim_violence

identification muslim_violence

illegitemacy

illegitemacy

disconnected

uncertainty

distance

identification

uncertainty illegitemacy



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

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



distance disconnected

in_dep in_dep

real_threat

sym_threat

in_dep

anxiety

in_dep

identification

disconnected

illegitemacy

distance

col_dep

own_violent



disconnected

in_dep

anxiety


in_dep

real_threat

own_violent

real_threat

injustice

anxiety

col_dep

illegitemacy

col_dep

own_violent


injustice

in_dep

anxiety

muslim_violence

identification

sym_threat

superiority

muslim_violence

identification

muslim_violence

anxiety

in_dep

identification

disconnected

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


in_dep

anxiety

muslim_violence

col_dep

muslim_violence

illegitemacy

col_dep

anxiety

injustice

uncertainty

illegitemacy


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 distance

own_violent

real_threat

superiority


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


uncertainty

sym_threat


anxiety col_dep


muslim_violence

distance

real_threat

muslim_violence

identification

muslim_violence

identification



injustice superiority uncertainty muslim_violence

distance

superiority

anxiety

col_dep


identification

sym_threat

own_violent

superiority uncertainty muslim_violence

muslim_violence

distance

in_dep


col_dep

disconnected



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


injustice

real_threat

real_threat identification

sym_threat

identification

anxiety

anxiety col_dep

superiority

injustice

own_violent


illegitemacy

identification


col_dep


in_dep sym_threat

illegitemacy

identification

sym_threat



uncertainty

sym_threat

superiority

identification

muslim_violence


injustice

col_dep

sym_threat

sym_threat

injustice

sym_threat

injustice


uncertainty

disconnected

in_dep

own_violent


identification


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


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


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


uncertainty

col_dep

injustice

uncertainty


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


own_violent

col_dep

in_dep

disconnected

uncertainty

muslim_violence

distance distance

uncertainty

distance

identification

own_violent

superiority


anxiety

real_threat

distance

illegitemacy


illegitemacy


sym_threat

anxiety


anxiety

sym_threat

anxiety


injustice

disconnected

in_dep

disconnected

injustice

anxiety


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


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


injustice

uncertainty

sym_threat

uncertainty

col_dep

anxiety col_dep

anxiety col_dep

own_violent

superiority


sym_threat

illegitemacy

sym_threat

superiority

identification

muslim_violence

illegitemacy

in_dep

disconnected

illegitemacy

distance

distance

anxiety


muslim_violence

sym_threat

illegitemacy

muslim_violence

injustice


real_threat

disconnected disconnected

superiority

illegitemacy

in_dep

identification

disconnected

sym_threat

identification

uncertainty

sym_threat

anxiety distance


identification

anxiety

muslim_violence

illegitemacy

muslim_violence

muslim_violence

illegitemacy


own_violent

uncertainty

own_violent

injustice

col_dep


own_violent


superiority

sym_threat

in_dep


real_threat

identification

uncertainty

superiority

superiority


illegitemacy

in_dep

uncertainty

real_threat

real_threat

muslim_violence

superiority

in_dep

real_threat

distance

anxiety

distance

identification


sym_threat


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


own_violent


muslim_violence

anxiety

sym_threat

uncertainty

col_dep uncertainty

sym_threat

disconnected



distance

superiority real_threat superiority

sym_threat

disconnected

col_dep

identification


real_threat

col_dep

anxiety

col_dep

disconnected

injustice real_threat

distance distance

illegitemacy

distance


anxiety


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


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


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


own_violent

distance

identification

anxiety

anxiety

muslim_violence

identification

disconnected

distance

superiority

sym_threat


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


sym_threat

illegitemacy

anxiety

real_threat

distance

own_violent

superiority

muslim_violence

anxiety

superiority

superiority

real_threat

distance

uncertainty



superiority

anxiety

own_violent

sym_threat real_threat

injustice

injustice distance

disconnected

anxiety

col_dep

own_violent


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


Partial correlation network 10 13 14

11

5

1 12 6 7 9 3 8

2

4


Partial correlation network After glasso (Friedman, Hastie, & Tibshirani, 2011):

9

7

14 10 3

13

6 11 5

2 12 8

1

4


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.

Thank you for your attention!

References I Doosje, B., Loseman, A., & Bos, K. (2013). Determinants of radicalization of islamic youth in the netherlands: Personal uncertainty, perceived injustice, and perceived group threat. Journal of Social Issues, 69(3), 586–604. Epskamp, S., Cramer, A. O. J., Waldorp, L. J., Schmittmann, V. D., & Borsboom, D. (2012). qgraph: Network visualizations of relationships in psychometric data. Journal of Statistical Software, 48(4), 1–18. Retrieved from http://www.jstatsoft.org/v48/i04/ Friedman, J., Hastie, T., & Tibshirani, R. (2011). glasso: Graphical lasso- estimation of gaussian graphical models [Computer software manual]. Retrieved from http://CRAN.R-project.org/package=glasso (R package version 1.7)

NETWORK ANALYSIS

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