the qgraph package for network visualizations of ... · qgraph i a r package (cran link) i can be...

The qgraph package for network visualizations ofpsychometric data in R

Sacha Epskamp

University of AmsterdamDepartment of Psychological Methods

AmstRdam

Outline

IntroductionWhat is qgraph?Graphs

Creating graphsInput modesLayout modes

Visualizing statisticsCorrelation matricesFactor loadingsConfirmatory Factor Analysis

Concluding commentsReferences

qgraph

I A R package (CRAN link)

I Can be used to plot various types of graphsI Different from other R packages (e.g. igraph Csardi &

Nepusz, 2006) in:

I Focus on Weighted GraphsI Intended for visualization of data as graphsI Optimized for vector-type image files (e.g. PDF, SVG)

I Aims in qgraph

I Simple inputI Summarize a large amount of statistics without needing data

reduction methods.I Visualize relations between variables

I Main idea: Show variables as nodes, relationships as edges

http://cran.r-project.org/web/packages/qgraph/index.html

qgraph


I Can be used to plot various types of graphs

I Different from other R packages (e.g. igraph Csardi &Nepusz, 2006) in:


I Aims in qgraph





qgraph



Nepusz, 2006) in:


I Aims in qgraph





qgraph



Nepusz, 2006) in:I Focus on Weighted Graphs

I Intended for visualization of data as graphsI Optimized for vector-type image files (e.g. PDF, SVG)

I Aims in qgraph





qgraph



Nepusz, 2006) in:I Focus on Weighted GraphsI Intended for visualization of data as graphs

I Optimized for vector-type image files (e.g. PDF, SVG)

I Aims in qgraph





qgraph



Nepusz, 2006) in:I Focus on Weighted GraphsI Intended for visualization of data as graphsI Optimized for vector-type image files (e.g. PDF, SVG)

I Aims in qgraph





qgraph




I Aims in qgraphI Simple input

I Summarize a large amount of statistics without needing datareduction methods.

I Visualize relations between variables



qgraph




I Aims in qgraphI Simple inputI Summarize a large amount of statistics without needing data

reduction methods.

I Visualize relations between variables



qgraph




I Aims in qgraphI Simple inputI Summarize a large amount of statistics without needing data




Graphs

I A graph is a network that consists of n nodes (or vertices)that are connected with m edges.

I Each edge has a weight indicating the strength of thatconnection

I An edge can be directed (have an arrow) or undirected

Unweighted graph

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Weighted graph

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Directed graph

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Outline





The qgraph() function

I The main function in qgraph is qgraph()

I Most other functions are either wrapping functions usingqgraph() or functions used in qgraph()

I The qgraph() function requires only one argument (adj)

I A lot of other arguments can be specified, but these are alloptional

Usage:

qgraph( adj, ... )

The qgraph() function

I The main function in qgraph is qgraph()I Most other functions are either wrapping functions using

qgraph() or functions used in qgraph()

I The qgraph() function requires only one argument (adj)

I A lot of other arguments can be specified, but these are alloptional

Usage:

qgraph( adj, ... )

The adjacency matrix

I The adj argument is the input. This can be an adjacencymatrix

I An adjacency matrix is a square n by n matrix in which eachelement indicates the relationship between two variables

I Any relationship can be used as long as:

I A 0 indicates no relationshipI Absolute negative values are similar in strength to positive

values

I Examples:

I A 1 indicating a connection (unweighted graphs)I CorrelationsI Regression parametersI Factor loadings

I Adjacency matrices occur naturally in statistics!




I Any relationship can be used as long as:I A 0 indicates no relationship

I Absolute negative values are similar in strength to positivevalues

I Examples:






I Any relationship can be used as long as:I A 0 indicates no relationshipI Absolute negative values are similar in strength to positive

values

I Examples:







values

I Examples:I A 1 indicating a connection (unweighted graphs)

I CorrelationsI Regression parametersI Factor loadings






values

I Examples:I A 1 indicating a connection (unweighted graphs)I Correlations

I Regression parametersI Factor loadings






values

I Examples:I A 1 indicating a connection (unweighted graphs)I CorrelationsI Regression parameters

I Factor loadings






values

I Examples:I A 1 indicating a connection (unweighted graphs)I CorrelationsI Regression parametersI Factor loadings


[,1] [,2] [,3]

[1,] 0 1 1

[2,] 0 0 1

[3,] 0 0 0

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The Big 5

Included is a dataset in which the Dutch translation of a commonlyused personality test, the NEO-PI-R (Costa & McCrae, 1992;Hoekstra, Fruyt, & Ormel, 2003), was administered to 500 firstyear psychology students (Dolan, Oort, Stoel, & Wicherts, 2009).The NEO-PI-R consists of 240 items designed to measure the fivecentral personality factors:

I Neuroticism

I Extroversion

I Agreeableness

I Openess to Experience

I Conscientiousness

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The Big 5

> data(big5)

> str(big5)

num [1:500, 1:240] 2 3 4 4 5 2 2 1 4 2 ...

- attr(*, "dimnames")=List of 2

..$ : NULL

..$ : chr [1:240] "N1" "E2" "O3" "A4" ...

The Big 5

> cor(big5)[1:15, 1:3]

N1 E2 O3

N1 1.000000e+00 -0.1855271104 0.095361021

E2 -1.855271e-01 1.0000000000 0.082879486

O3 9.536102e-02 0.0828794862 1.000000000

A4 -1.388302e-01 0.2639947325 -0.077486908

C5 -6.958419e-02 0.0433073349 -0.019451268

N6 1.901235e-01 -0.1144449337 0.052585940

E7 -8.556772e-02 0.1968042360 -0.001360255

O8 3.599480e-02 0.0380351107 0.143715099

A9 3.775956e-02 0.0918642940 -0.147722360

C10 7.113742e-02 -0.1250087306 0.005001674

N11 3.491657e-01 -0.1085540815 0.072827947

E12 -2.680803e-01 0.0456805867 -0.003996781

O13 9.768583e-02 -0.0002757219 0.218802592

A14 4.512596e-05 0.1133985066 0.009208309

C15 5.859827e-03 0.0988472658 -0.051836728

> qgraph(cor(big5), minimum = 0.2)

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> data(big5groups)

> qgraph(cor(big5), groups = big5groups, minimum = 0.2)

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NeuroticismExtraversionOpennessAgreeablenessConscientiousness

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Fruchterman-Reingold layout (20 iterations)

> data(big5groups)

> Q <- qgraph(cor(big5), groups = big5groups,

+ minimum = 0.2, layout = "spring")

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> Q <- qgraph(Q, legend = FALSE)

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> Q <- qgraph(Q, vsize = 2, borders = FALSE,

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> Q <- qgraph(Q, overlay = TRUE)

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> qgraph(Q, transparency = T, bg = T, bgcontrol = 5,

+ filetype = "png", filename = "bg", res = 144,

+ width = 7, height = 7)

Outline





Association

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Significance

> qgraph(cor(big5), Q, graph = "sig")

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p < 0.05p < 0.01p < 0.001p < 1e−04

Factor loadings

I A factor loadings matrix can be visualized usingqgraph.loadings()

I There are two wrapper functions that perform an analysis andsend the results to qgraph.loadings():

I qgraph.efa() performs an exploratory factor analysis (EFA)using stats:::factanal

I qgraph.pca() performs a principal component analysis (PCA)using psych:::principal (Revelle, 2010)

I These functions use a correlation or covariance matrix as input

Factor loadings: EFA

> qgraph.efa(big5, 5, groups = big5groups,

+ rotation = "promax", minimum = 0.2, cut = 0.4,

+ vsize = c(1, 15), borders = FALSE, asize = 0.07,

+ esize = 4, vTrans = 200)

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Neuroticism

Extraversion

Conscientiousness

Agreeableness

Openness

Factor loadings: EFA crossloadings

> qgraph.efa(big5, 5, groups = big5groups,



+ esize = 4, vTrans = 200, crossloadings = TRUE)

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Factor loadings: PCA

> qgraph.pca(cor(big5), 5, groups = big5groups,



+ esize = 4, vTrans = 200)

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Confirmatory Factor Analysis

I qgraph.cfa() can be used to fit a simple confirmatory factormodel

I Each variable loads on only one factorI Factors are correlatedI Scaling by fixing first loading of each factor to 1

I This can be done with the sem (Fox, 2006) or lavaan(Rosseel, 2011) packages

I Returns a "sem" or lavaan object

I Results can be send to qgraph.sem() or qgraph.lavaan()for a full report



I Each variable loads on only one factor

I Factors are correlatedI Scaling by fixing first loading of each factor to 1






I Each variable loads on only one factorI Factors are correlated

I Scaling by fixing first loading of each factor to 1






I Each variable loads on only one factorI Factors are correlatedI Scaling by fixing first loading of each factor to 1





> names(big5groups) <- strtrim(names(big5groups),

+ 1)

> names(big5) <- 1:ncol(big5)

> fit <- qgraph.cfa(cov(big5), nrow(big5),

+ big5groups, pkg = "lavaan", opts = list(se = "none"),

+ vsize.man = 1, vsize.lat = 6, edge.label.cex = 0.5)

> print(fit)

Lavaan (0.4-8) converged normally after 161 iterations

Number of observations 500

Estimator ML

Minimum Function Chi-square 60838.192

Degrees of freedom 28430

P-value 0.000

Confirmatory Factor Analysis> pdf("big5cfaModel%03d.pdf", width = 7, height = 7,

+ onefile = FALSE)

> qgraph.lavaan(fit, filetype = "", include = 1:7,

+ vsize.man = 1, vsize.lat = 6, edge.label.cex = 0.5,

+ residSize = 0.1, groups = big5groups,

+ titles = FALSE)

> dev.off()

pdf

2

> pdf("big5cfaRes%03d.pdf", width = 14, height = 7,

+ onefile = FALSE)

> qgraph.lavaan(fit, filetype = "", include = 8:12,

+ vsize.man = 1, vsize.lat = 6, edge.label.cex = 0.5,

+ residSize = 0.1, groups = big5groups,

+ titles = FALSE, minimum = 0.15)

> dev.off()

pdf

2

Model

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N56N61

N66N71

N76N81

N86N91

N96N101

N106N111

N116

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E232

E237

O3O8

O13O18

O23O28

O33O38

O43O48

O53O58

O63O68


O173O178

O183O188

O193O198

O203O208

O213O218

O223O228

O233O238

A4A9

A14

A19

A24

A29

A34

A39

A44

A49

A54

A59

A64

A69

A74

A79

A84

A89

A94

A99

A104

A109

A114

A119

A124

A129

A134

A139

A144

A149

A154

A159

A164

A169

A174

A179

A184

A189

A194

A199

A204

A209

A214

A219

A224

A229

A234

A239

C5

C10

C15

C20

C25

C30

C35

C40

C45

C50

C55

C60

C65

C70

C75

C80

C85

C90

C95

C100

C105

C110

C115

C120

C125C130

C135C140

C145C150

C155C160

C165C170

C175C180

C185C190

C195C200C205C210C215C220C225C230C235C240

N

E

O

A

C

Results

10.651.140.830.021.040.90.541.33−0.060.350.451.080.31.220.810.221.031.010.360.50.710.180.530.970.410.580.83−0.110.751.090.450.910.310.40.60.630.651.350.640.240.431.050.691.030.40.661.04

11.571.52−0.990.451.581.441.631.221.180.7510.811.071.070.780.681.861.270.640.991.950.391.441.180.950.751.891.091.921.770.360.670.130.671.71.181.341.010.570.851.340.861.651.221.590.721.29

11.470.760.270.780.520.780.840.680.780.90.381.040.980.340.270.520.170.941.310.620.710.550.350.991.690.620.310.440.330.410.960.410.440.740.40.671.670.40.290.520.10.610.790.980.460.770.33

11.161.260.870.940.340.831.510.490.450.450.680.860.870.950.540.950.540.440.970.580.710.640.650.580.460.540.410.680.480.61.410.260.721.040.860.861.380.710.610.660.550.610.90.870.690.740.03

10.540.781.271.540.94−0.41.481.111.681.631.190.981.491.331.31.180.670.971.170.591.671.791.010.671.120.80.761.340.80.990.740.531.161.561.210.630.141.291.070.950.621.721.251.080.962.130.88

0.950.640.740.780.970.620.610.720.710.780.950.420.830.80.731.290.960.780.510.91.080.910.950.610.70.560.730.550.520.83

0.610.97

0.620.77

1.50.420.781.110.560.870.890.340.840.99

0.60.870.760.470.660.910.810.590.90.970.660.631.10.641.450.520.411.02

10.951.060.9

0.760.6

0.920.7

1.280.750.31

1.020.65

0.460.340.5

0.451.4

0.831.05

1.450.26

0.550.52

0.740.75

1.161.28

0.450.79

0.930.411.060.410.580.980.680.621.030.730.760.680.490.630.760.70.691.410.40.671.011.10.70.880.740.991.280.560.750.80.390.771.220.820.890.660.390.761.010.350.950.760.470.850.610.860.470.960.860.980.570.790.690.810.690.60.80.77

0.70.83

0.620.72

0.940.75

0.761.1

0.81.3

0.90.93

0.421.01

0.260.8

0.510.790.4

0.720.680.920.760.610.590.680.280.870.760.510.450.720.480.750.750.630.570.840.570.850.780.90.540.890.490.650.561.090.910.821.040.580.770.620.370.721.02

0.810.47

0.840.73

1.071.480.410.680.770.440.640.40.780.380.760.920.910.670.540.740.730.370.860.470.770.8510.371.121.150.980.590.82

0.41

0.09

0.21

0.2

0.12

−0.11

0.01

−0.04

−0.08

0.04

0.03

0.02

0.04

0

0.03

N1 N6 N11 N16 N21 N26 N31 N36 N41 N46N51

N56N61

N66N71

N76N81

N86N91

N96N101

N106N111

N116

N121

N126

N131

N136

N141

N146

N151

N156

N161

N166

N171

N176

N181

N186

N191

N196

N201

N206

N211

N216

N221

N226

N231

N236

E2

E7

E12

E17

E22

E27

E32

E37

E42

E47

E52

E57

E62

E67

E72

E77

E82

E87

E92

E97

E102

E107

E112

E117

E122

E127

E132

E137

E142

E147

E152

E157

E162

E167

E172

E177

E182

E187

E192

E197

E202

E207

E212

E217

E222

E227

E232

E237

O3O8

O13O18

O23O28

O33O38

O43O48

O53O58

O63O68


O173O178

O183O188

O193O198

O203O208

O213O218

O223O228

O233O238

A4A9

A14

A19

A24

A29

A34

A39

A44

A49

A54

A59

A64

A69

A74

A79

A84

A89

A94

A99

A104

A109

A114

A119

A124

A129

A134

A139

A144

A149

A154

A159

A164

A169

A174

A179

A184

A189

A194

A199

A204

A209

A214

A219

A224

A229

A234

A239

C5

C10

C15

C20

C25

C30

C35

C40

C45

C50

C55

C60

C65

C70

C75

C80

C85

C90

C95

C100

C105

C110

C115

C120

C125C130

C135C140

C145C150

C155C160

C165C170

C175C180

C185C190

C195C200C205C210C215C220C225C230C235C240

N

E

O

A

C

Results

N1 N6 N11 N16 N21 N26 N31 N36 N41 N46N51

N56N61

N66N71

N76N81

N86N91

N96N101

N106N111

N116

N121

N126

N131

N136

N141

N146

N151

N156

N161

N166

N171

N176

N181

N186

N191

N196

N201

N206

N211

N216

N221

N226

N231

N236

E2

E7

E12

E17

E22

E27

E32

E37

E42

E47

E52

E57

E62

E67

E72

E77

E82

E87

E92

E97

E102

E107

E112

E117

E122

E127

E132

E137

E142

E147

E152

E157

E162

E167

E172

E177

E182

E187

E192

E197

E202

E207

E212

E217

E222

E227

E232

E237

O3O8

O13O18

O23O28

O33O38

O43O48

O53O58

O63O68


O173O178

O183O188

O193O198

O203O208

O213O218

O223O228

O233O238

A4A9

A14

A19

A24

A29

A34

A39

A44

A49

A54

A59

A64

A69

A74

A79

A84

A89

A94

A99

A104

A109

A114

A119

A124

A129

A134

A139

A144

A149

A154

A159

A164

A169

A174

A179

A184

A189

A194

A199

A204

A209

A214

A219

A224

A229

A234

A239

C5

C10

C15

C20

C25

C30

C35

C40

C45

C50

C55

C60

C65

C70

C75

C80

C85

C90

C95

C100

C105

C110

C115

C120

C125C130

C135C140

C145C150

C155C160

C165C170

C175C180

C185C190

C195C200C205C210C215C220C225C230C235C240

N

E

O

A

C

Correlations

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

1 2 3 45

67

89101112131415

1617

1819

2021

2223242526272829

3031

3233

34353637383940

4142

4344

4546 47 48

49 50 51 5253

5455

5657

585960616263

6465

6667

6869

7071727374757677

7879

8081

82838485868788

8990

9192

9394 95 96

97 98 99 100101

102103

104

105

106

107

108

109

110

111

112

113

114

115116

117118

119120121122123124

125126

127

128

129

130

131

132

133

134

135

136

137

138

139140

141142

143 144145 146 147148

149150

151

152

153

154

155

156

157

158

159

160

161

162

163164

165166

167168169170171172

173174

175

176

177

178

179

180

181

182

183

184

185

186

187188

189190

191 192

193 194 195196

197198

199

200

201

202

203

204

205

206

207

208

209

210

211212

213214

215216217218219220

221222

223

224

225

226

227

228

229

230

231

232

233

234

235236

237238

239 240

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●●●●●

1 2 3 45

67

89101112131415

1617

1819

2021

2223242526272829

3031

3233

34353637383940

4142

4344

4546 47 48

49 50 51 5253

5455

5657

585960616263

6465

6667

6869

7071727374757677

7879

8081

82838485868788

8990

9192

9394 95 96

97 98 99 100101

102103

104

105

106

107

108

109

110

111

112

113

114

115116

117118

119120121122123124

125126

127

128

129

130

131

132

133

134

135

136

137

138

139140

141142

143 144145 146 147148

149150

151

152

153

154

155

156

157

158

159

160

161

162

163164

165166

167168169170171172

173174

175

176

177

178

179

180

181

182

183

184

185

186

187188

189190

191 192

193 194 195196

197198

199

200

201

202

203

204

205

206

207

208

209

210

211212

213214

215216217218219220

221222

223

224

225

226

227

228

229

230

231

232

233

234

235236

237238

239 240

Outline





Concluding comments

I qgraph is still work in progress

I Plans for the future:

I More wrapper functions for different statistics (e.g. IRT)I More layout modesI Estimating and fitting causal models

I Some things I couldn’t describe...

Concluding comments

I qgraph is still work in progressI Plans for the future:



Concluding comments


I More wrapper functions for different statistics (e.g. IRT)

I More layout modesI Estimating and fitting causal models


Concluding comments


I More wrapper functions for different statistics (e.g. IRT)I More layout modes

I Estimating and fitting causal models


Concluding comments




Layout constraints

Grayscale colors

> Q <- qgraph(cor(big5), minimum = 0.25, cut = 0.4,

+ vsize = 2, groups = big5groups, legend = T,

+ borders = F, vTrans = 200, gray = TRUE)

1

2

34

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89

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5354

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5859

60

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6364

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6869

70

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72

7374

75

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7879

80

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8384

85

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8889

90

91

92

9394

95

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9899

100

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103104

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108109

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113114

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118119

120

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143144

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●

●

●

●

●

NEOAC

●

●

●

●

●

NEOAC

Tooltips

Link

Modelling

ξ

η1 η2 η3

y1 y2 y3 y4 y5 y6 y7

x1 x2 x3

Concluding comments

Thank you for your attention!

ReferencesCosta, P. T., & McCrae, R. R. (1992). Neo personality inventory

revised (neo pi-r). Psychological Assessment Resources.Csardi, G., & Nepusz, T. (2006). The extttigraph software package

for complex network research. InterJournal, ComplexSystems, 1695. Available from http://igraph.sf.net

Dolan, C., Oort, F., Stoel, R., & Wicherts, J. (2009). TestingMeasurement Invariance in the Target Rotated MultigroupExploratory Factor Model. Structural Equation Modeling: AMultidisciplinary Journal, 16(2), 20.

Fox, J. (2006). Structural Equation Modeling With the extttsemPackage in R. Structural Equation Modeling, 13(3),465–486.

Hoekstra, H., Fruyt, F. de, & Ormel, J. (2003).Neo-Persoonlijkheidsvragenlijsten: NEO-PI-R, NEO-FFI [Neopersonality questionnaires: NEO-PI-R, NEO-FFI]. Lisse:Swets Test Services.

Revelle, W. (2010). extttpsych: Procedures for psychological,psychometric, and personality research [Computer softwaremanual]. Evanston, Illinois. Available from http://

personality-project.org/r/psych.manual.pdf (Rpackage version 1.0-93)

Rosseel, Y. (2011). extttlavaan: Latent variable analysis[Computer software manual]. Available fromhttp://CRAN.R-project.org/package=lavaan (Rpackage version 0.4-7)

http://igraph.sf.net

http://personality-project.org/r/psych.manual.pdf

http://personality-project.org/r/psych.manual.pdf

http://CRAN.R-project.org/package=lavaan

the qgraph package for network visualizations of ... · qgraph i a r package (cran link) i can be...

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