Network Visualizations of Relationships inPsychometric Data and Structural Equation
ModelsUsing the qgraph package for R
Sacha Epskamp
University of AmsterdamDepartment of Psychological Methods
IMPS 2013
Look at your data...
var 1
−4 0 2 4
0.37 −0.26
−4 0 4
0.14 0.25
−6 −2 2
−0.26 0.23
−4 0 2
0.52 0.28
−4 0 4
−4
02
4
−0.46
−4
04
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var 2 −0.17 0.24 0.39 −0.35 0.29 0.26 0.17 −0.29
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var 3 −0.40 −0.29 0.23 −0.33 −0.29 −0.29
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var 5 −0.42 0.38 0.33 0.25
−4
04
−0.33
−6
−2
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var 6 −0.24 −0.37 −0.32 0.34
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Simulated data
Simulated data
1
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1 2 3 4 5 6 7 8 9 10
Simulated data
2
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2 4 6 8 10
−1.0
−0.5
0.0
0.5
1.0
Real data example
Included in qgraph is a dataset in which the Dutch translationof a commonly used personality test, the NEO-PI-R (Costa &McCrae, 1992; Hoekstra, de Fruyt, & Ormel, 2003), wasadministered to 500 first year psychology students (Dolan,Oort, Stoel, & Wicherts, 2009). The NEO-PI-R consists of 240items designed to measure the five central personality factors:
I NeuroticismI ExtroversionI AgreeablenessI Openness to ExperienceI Conscientiousness
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
O73O78O83O88O93O98O103O108O113O118O123O128O133O138O143O148O153O158O163O168
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
C125
C130C135
C140C145
C150C155
C160C165
C170C175
C180C185
C190C195
C200C205C210C215C220C225C230C235C240
N
E
O
A
C
Neuroticism correlations
N1N6
N11N16N21N26N31N36N41N46N51N56N61N66N71N76N81N86N91N96
N101N106N111N116N121N126N131N136N141N146N151N156N161N166N171N176N181N186N191N196N201N206N211N216N221N226N231N236
N1
N6
N11
N16
N21
N26
N31
N36
N41
N46
N51
N56
N61
N66
N71
N76
N81
N86
N91
N96
N10
1N
106
N11
1N
116
N12
1N
126
N13
1N
136
N14
1N
146
N15
1N
156
N16
1N
166
N17
1N
176
N18
1N
186
N19
1N
196
N20
1N
206
N21
1N
216
N22
1N
226
N23
1N
236
Neuroticism correlations
N1N6
N11N16N21N26N31N36N41N46N51N56N61N66N71N76N81N86N91N96
N101N106N111N116N121N126N131N136N141N146N151N156N161N166N171N176N181N186N191N196N201N206N211N216N221N226N231N236
N1N6N11N16N21N26N31N36N41N46N51N56N61N66N71N76N81N86N91N96N101N106N111N116N121N126N131N136N141N146N151N156N161N166N171N176N181N186N191N196N201N206N211N216N221N226N231N236
−1.0
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0.5
1.0
Big 5 correlations
N
E
O
A
C
N E O A C
−1.0
−0.5
0.0
0.5
1.0
I When extended to the amount of variables commonly usedin tests:
I Scatterplot and ellipse visualizations become unreadableI Heatmaps plots do better, but only show trends
I Very hard, if not impossible, to see important violations oftrends
I We need another way to look at our data
The Network Approach
Basic idea:I Nodes represent variables
I Possible to vary in color, shape, size and label to indicatedifferent statistics
I Edges represent relationshipsI Green edges indicate positive relationshipsI Red edges indicate negative relationshipsI The wider and more saturated an edge, the stronger the
absolute relationship
0.5
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1
2
34
5
6
7
89
10
11
12
1314
15
16
17
1819
20
21
22
2324
25
26
27
2829
30
31
32
3334
35
36
37
3839
40
41
42
4344
45
46
47
4849
50
51
52
5354
55
56
57
5859
60
61
62
6364
65
66
67
6869
70
71
72
7374
75
76
77
7879
80
81
82
8384
85
86
87
8889
90
91
92
9394
95
96
97
9899
100
101
102
103104
105
106
107
108109
110
111
112
113114
115
116
117
118119
120
121
122
123124
125
126
127
128129
130
131
132
133134
135
136
137
138139
140
141
142
143144
145
146
147
148149
150
151
152
153154
155
156
157
158159
160
161
162
163164
165
166
167
168169
170
171
172
173174
175
176
177
178179
180
181
182
183184
185
186
187
188189
190
191
192
193194
195
196
197
198199
200
201
202
203204
205
206
207
208209
210
211
212
213214
215
216
217
218219
220
221
222
223224
225
226
227
228229
230
231
232
233234
235
236
237
238239
240
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NeuroticismExtraversionOpennessAgreeablenessConscientiousness
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NeuroticismExtraversionOpennessAgreeablenessConscientiousness
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1
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6
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10
11
12
13
14
15
16
17
18
19
20
21
22
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2627
28
29
30
31
32
33
34
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59
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68
69
70
71
72
73
74
75
7677
78
79
80
81
82
83
84
85
86
87
88
89
90
9192
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116 117
118
119
120
121
122
123
124
125
126
127
128
129130
131
132
133
134
135
136
137
138
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140
141
142
143
144
145
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149
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172
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220
221222
223
224
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229
230
231
232
233
234
235
236
237
238
239240
Implied correlations
λ11(y) λ21
(y) λ31(y)
θ11(ε) θ22
(ε) θ33(ε)
ψ11
y1 y2 y3
η1
CFA modelσ1
2
σ21σ31
σ22σ32σ3
2
y1
y2y3
Covariance structure
Implied correlations
λ11(y) λ21
(y) λ31(y)
θ11(ε) θ22
(ε) θ33(ε)
ψ11
y1 y2 y3
η1
CFA modelλ11
2 ψ11 + ε1
λ21λ11ψ11λ31λ21ψ11
λ212 ψ11 + ε2λ31λ21ψ11λ31
2 ψ11 + ε3
y1
y2y3
Implied covariance structure
Implied correlations
Σ = ΛΨΛ> +Θ σ21 σ12 σ13
σ21 σ22 σ23
σ31 σ32 σ23
=
λ1λ2λ3
[ψ11] [λ1 λ2 λ3
]+
θ11 0 00 θ22 00 0 θ33
=
λ21ψ11 + θ11 λ1λ2ψ11 λ1λ3ψ11λ2λ1ψ11 λ2
2ψ11 + θ22 λ2λ3ψ11λ3λ1ψ11 λ3λ2ψ11 λ2
3ψ11 + θ33
Implied correlations
ψ can be set to 1 without loss of information.
λ21 + θ11 λ1λ2 λ1λ3λ2λ1 λ2
2 + θ22 λ2λ3λ3λ1 λ3λ2 λ2
3 + θ33
Implied correlations
I The single factor model implies a very distinct correlationalpattern:
I Two variables are correlated highly if, and only if, they bothload strongly on the factor
I Because of this, if one factor underlies, for example, fourvariables, and we know there are strong correlationsbetween two pairs of variables, then all other correlationsbetween these four variables must be strong as well
I Multiple factors do not change this as long as there are nocrossloadings
Implied correlations
y1 y2 y3 y4 y5 y6 y7 y8 y9 y10
η1 η2
Implied correlations
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21
22
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2627
28
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31
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43
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55
56
57
58
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60
61
62
63
64
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66
67
68
69
70
71
72
73
74
75
7677
78
79
80
81
82
83
84
85
86
87
88
89
90
9192
93
94
95
96
97
98
99
100
101
102
103
104
105
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107
108
109
110
111
112
113
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116 117
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129130
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176
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180
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195
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205
206
207
208
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210
211
212
213
214
215
216217
218
219
220
221222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239240
Factor loadings: EFA
1
23
4 5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
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48
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50
51
52
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56
57
58
59
60
61
62
63
64
65
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69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
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205
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208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
Neuroticism
Extraversion
Conscientiousness
Agreeableness
Openness
Factor loadings: EFA crossloadings
1
23
4 5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
Neuroticism
Extraversion
Conscientiousness
Agreeableness
Openness
CFA model
N1 N6 N11 N16 N21 N26 N31 N36N41
N46N51
N56N61
N66N71
N76N81
N86
N91
N96
N101
N106
N111
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
O13
O18
O23
O28
O33O38
O43O48
O53O58
O63O68
O73O78
O83O88O93O98O103O108O113O118O123O128O133O138O143O148O153O158
O163O168
O173O178
O183O188
O193O198
O203O208
O213
O218
O223
O228
O233
O238
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
C125
C130
C135
C140
C145
C150
C155
C160C165
C170C175
C180C185
C190C195
C200C205
C210 C215 C220 C225 C230 C235 C240
N
E
O
A
C
Correlations
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717273747576
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97 98 99100
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119120121122
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4546
47 48
49 50 5152
5354
55
56
57
58
59
60
61
62
63
64
65
66
6768
6970
717273747576
7778
79
80
81
82
83
84
85
86
87
88
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90
9192
9394
95 96
97 98 99100
101
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103
104
105
106
107
108
109
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111
112
113
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117118
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123124
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141142
143 144145 146147
148149
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qgraph
I qgraph is a network plotting package aimed atautomatically visualizing fully connected weightednetworks
I Can be used for many other kinds of networks as wellI qgraph objects can be exported to igraph objectsI Support for following classes:
I "principal" (psych)I "loadings" (stats)I "factanal" (stats)I "graphNEL" (Rgraphviz)I "pcAlgo" (pcalg)I ("bn" (bnlearn))I ("bn.strength" (bnlearn))
I Easy to use!
Graphical options
Graph by Claudia van Borkulo
fal slewak
hyp
sad
irr
anx
rmo
mod
qmo
app
wei
con
sel
fut
sui
int
eneple
sexslo
resach
bod
pan
dig
sen
par
semPlotCurrently supported SEM software packages:
I lavaanI semI OpenMx (RAM only)I MPlus (using MplusAutomation)I LISREL (using LisrelToR)
Other R functions:I lm
I factanal
I principal
Supported modelling frameworks:I lavaanI LISREL matrix modelI RAM matrix modelI Mplus matrix model
semPlot
Holzinger and Swineford (1939) CFA example:
1.00 0.55 0.73 1.00 1.11 0.93 1.00 1.18 1.08
0.55 1.13 0.84 0.37 0.45 0.36 0.80 0.49 0.57
0.81 0.98 0.38
0.41
0.26
0.17
x1 x2 x3 x4 x5 x6 x7 x8 x9
vsl txt spd
semPlot
Holzinger and Swineford (1939) CFA example:
x1 x2 x3 x4 x5 x6 x7 x8 x9
vsl txt spd
semPlotBased on output file from Little (in press).
1.14 1.14 1.39 1.41 2.48 2.91 1.25 0.88 0.66 1.86 1.71 1.99 1.17 0.83 1.27 1.53
0.60
0.48
0.49
0.480.55
0.72
ANSWER1 ANSWER2 ANSWER3 ANSWER8 ANSWER4 ANSWER5 ANSWER6 ANSWER9 ANSWER16 ANSWER10 ANSWER11 ANSWER12 ANSWER7 ANSWER13 ANSWER14 ANSWER15
WITHDRAW SELFCARE COMPLIAN ANTISOCI
Within
0.59 0.56 0.82 0.76 1.34 1.57 0.92 0.59 0.40 0.94 0.87 1.09 0.67 0.51 0.90 1.05
0.83
0.71
0.78
0.730.77
0.85
0.14 0.17 0.30 0.46 0.80 0.11 0.200.23 0.19 0.13 0.23 0.21 0.13 0.20 0.180.34
ANSWER1 ANSWER2 ANSWER3 ANSWER8 ANSWER4 ANSWER5 ANSWER6 ANSWER9 ANSWER16 ANSWER10 ANSWER11 ANSWER12 ANSWER7 ANSWER13 ANSWER14 ANSWER15
BWITHDRA BSELFCAR BCOMPLIA BANTISOC
Between
semPlot
Y1 Y2 Y3 Y4 Y5 Y6
Y7 Y8 Y9 Y10 Y11 Y12
F1 F2
F3 F4
1 1 1 1 1 1
1 1 1 1 1 1
Y1 Y2 Y3 Y4 Y5 Y6
Y7 Y8 Y9
Y10 Y11 Y12
F1 F2
F3
F4
1 1 1 1 1 1
1 1 1
1 1 1
semPlot
Y1 Y2 Y3 Y4 Y5 Y6
Y7 Y8 Y9 Y10 Y11 Y12
F1 F2
F3
F4
1 1 1 1 1 1
1 1 1 1 1 1
Y1Y2Y3 Y4Y5Y6
Y7
Y8
Y9
Y10 Y11 Y12
F1 F2
F3
F4
111 111
1
1
1
1 1 1
semPlotModel by Janneke de Kort
θ11(ε) θ22
(ε) θ33(ε) θ44
(ε)
θ55(ε) θ66
(ε) θ77(ε) θ88
(ε)
ψ55
ψ175
ψ66
ψ186
ψ77
ψ197
ψ88
ψ208
ψ99
ψ219
ψ1010
ψ2210
ψ1111
ψ2311
ψ1212
ψ2412
ψ1717 ψ1818 ψ1919 ψ2020
ψ2121 ψ2222 ψ2323 ψ2424
β101
β141
β112
β152
β123
β163
β15
β65
β26
β76
β37
β87
β48
β19
β109
β210
β1110
β311
β1211
β412
β213
β2213
β314
β2314
β415
β2415
β1317
β1817
β1418
β1918
β1519
β2019
β1620
β1321
β2221
β1422
β2322
β1523
β2423
β1624
IQ11 IQ12 IQ14IQ13
IQ21 IQ22 IQ24IQ23
A11 A12 A13 A14
E11 E12 E13 E14
A21 A22 A23 A24
E21 E22 E23 E24
Concluding comments
qgraph:I Paper in JSS: http://www.jstatsoft.org/v48/i04I Stable versions on CRAN:
cran.r-project.org/package=qgraphI developmental version on Github:
https://github.com/SachaEpskamp/qgraph
semPlot:I Paper in preparationI Stable versions on CRAN:
cran.r-project.org/package=semPlotI developmental version on Github:
https://github.com/SachaEpskamp/semPlotI More info on my website: sachaepskamp.com
And more...
Netherlands: Germany:
Thank you for your attention!
References
Costa, P. T., & McCrae, R. R. (1992). Neo personality inventoryrevised (neo pi-r). Psychological Assessment Resources.
Dolan, C., Oort, F., Stoel, R., & Wicherts, J. (2009). TestingMeasurement Invariance in the Target Rotated MultigroupExploratory Factor Model. Structural Equation Modeling:A Multidisciplinary Journal, 16(2), 20.
Hoekstra, H., de Fruyt, F., & Ormel, J. (2003).Neo-Persoonlijkheidsvragenlijsten: NEO-PI-R, NEO-FFI[Neo personality questionnaires: NEO-PI-R, NEO-FFI].Lisse: Swets Test Services.
Holzinger, K. J., & Swineford, F. (1939). A study in factoranalysis: The stability of a bi-factor solution.Supplementary Educational Monographs.
Little, J. (in press). Multilevel confirmatory ordinal factoranalysis of the life skills profile-16. PsychologicalAssessment, xx.
