S1
Supplemental Materials
Longitudinal Associations Between Social Anxiety Disorder and Avoidant Personality
Disorder: A Twin Study
by F. A. Torvik et al., 2015, Journal of Abnormal Psychology
http://dx.doi.org/10.1037/abn0000124
Table S1
Occurrence and Stability of SAD and AvPD at Wave 1 and Wave 2, Number of Cases
SAD
W1 no
W1 yes
Sum
AvPD
W2 no
W2 yes
Sum
W2 no
W2 yes
Sum
1,358
56
1,414
1,420
21
1,441
35
18
53
25
10
35
1,393
74
1,467
1,445
31
1,476
Note. SAD = Social anxiety disorder. AvPD = Avoidant personality disorder.
Table S2
Co-occurrence of SAD and AvPD at Wave 1 and Wave 2, Number of Cases
Wave 1
No AvPD
AvPD
Sum
Wave 2
No SAD
SAD
Sum
No SAD
SAD
Sum
1,666
51
1,717
1,382
58
1,440
30
14
44
14
17
31
1,696
65
1,761
1,396
75
1,471
Note. SAD = Social anxiety disorder. AvPD = Avoidant personality disorder.
Factor analysis of diagnostic criteria for SAD and AvPD
The diagnostic criteria for SAD and AvPD were analyzed with exploratory factor
analysis (EFA) with oblique geomin rotation and confirmatory factor analysis (CFA). We
Longitudinal associations between SAD and AvPD
S2
used the robust maximum likelihood estimator (MLR) in Mplus 7.3. The criteria were
analyzed as ordered categories. The EFA yielded two factors with eigenvalues clearly above
one, at 5.29 and 3.37, and one factor with an eigenvalue of 1.05. The scree plot is shown in
Figure S1. This suggests the presence of two or three factors. Fit indices for the one-, two-,
and three-factor solutions are provided in Table S3. The AIC improved from the model with
one factor to the model with two factors, and further from two factors to three. The samplesize-adjusted BIC favored the two-factor model compared to one and three factors. The threefactor model lacks theoretical foundation. The statistical indices did not favor the one-factor
model, and the two-factor model has good theoretical foundation and easily interpretable
results. The three-factor solution provided similar results as the two-factor solution, except
that AvPD symptom 1 seemed to fit best within a separate factor, which had no strong
loadings on other items (all below .19). Thus, the EFA suggested a model in which the DSM
criteria for SAD and AvPD loaded on distinct, but correlated factors, with low cross-loadings.
Figure S1. Scree Plot for Exploratory Factor Analysis.
Table S3
Fit Indices for Exploratory (EFA) and Confirmatory Factor Analysis (CFA) for the
Diagnostic Criteria for SAD and AvPD
Longitudinal associations between SAD and AvPD
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AIC
BICSSA
1. One factor
31629.96
31804.64
2. Two factors
31159.84
31372.37
3. Three factors
31130.00
31377.47
4. One factor
31603.68
31778.37
5. Two correlated factors
31193.78
31371.38
6. Bifactor with two group factors
31098.39
31313.84
7. Bifactor with two correlated group factors
31089.80
31308.16
EFA
CFA
Note: SAD = Social anxiety disorder. AvPD = Avoidant personality disorder. AIC = Akaike
Information Criterion. BICSSA = Sample-Size Adjusted Bayesian Information Criterion. EFA
= Exploratory Factor Analysis. CFA = Confirmatory Factor Analysis. Lower values of AIC
and BICSSA indicate better model fit.
Fit indices for the CFAs are shown in Table S3. The model fit was better for the model
with two correlated factors, compared to a one-factor model, suggesting that SAD and AvPD
did not reflect the same latent factors. The SAD and AvPD factors correlated .640 in the twofactor model.
An alternative model is the bifactor model (Jennrich & Bentler, 2012; Reise, Moore, &
Haviland, 2010; Reise, 2012). In this model, all items load on a general factor; in addition, all
SAD items load on a SAD factor and all AvPD items on an AvPD factor. All three latent
factors are orthogonal to each other. The bifactor model (model 6) had better fit than the twofactor model. In the bifactor model, the general factor explained 38.0% of the variance in
Longitudinal associations between SAD and AvPD
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SAD and AvPD items (53.0% of AvPD items and 23.0% of SAD items), whereas the group
factors explained 19.1% of the variance (8.9% of AvPD items and 29.3% of SAD items).
We also tested a bifactor model where the group factors were allowed to correlate
(model 7). This model had the best fit. In this model, the general factor explained 23.6% of
the variance (39.7% of AvPD items and 7.4% of SAD items), whereas the AvPD factor
explained 33.9% of the variance (22.5% of AvPD items and 45.4% of SAD items). The two
group factors correlated .61. It should be noted that bifactor models with correlated group
factors have unclear interpretations and may suggest the presence of unmodeled general
factors (Jennrich & Bentler, 2012; Reise et al., 2010). The implications of this model are
therefore unclear.
The results of the two bifactor models are shown in Table S4. The bifactor model may
be interpreted in different ways. First, it is possible that the group factors of the bifactor
model reflect methodological variance associated with the two different interviews. The
interpretation that the group factors reflect method variance seems implausible in the present
analyses, because the AvPD items do not uniformly load on this potential method factor. In
addition, the general factor showed higher loadings for the AvPD items than for SAD items,
which is inconsistent with the view that AvPD is primarily a more severe form of SAD.
Second, the bifactor model may have a substantive interpretation where a general
psychopathological factor influences the symptoms directly in addition to the disorder factors.
Third, good fit does not necessarily imply that the bifactor model is true. In a simulation
study, Morgan, Hodge, Wells, and Watkins (2015) found that model's fit indices were biased
toward favoring bifactor models when data were generated from a true higher-order structure.
Longitudinal associations between SAD and AvPD
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Table S4
Factor Loadings From Bifactor Models 6 (Bifactor With Two Orthogonal Group Factors)
and 7 (Bifactor With Two Correlated Group Factors). Standardized Model Results.
Model 6
Model 7
Estimate
p
Estimate
p
Avoid 1
.79
< .001
.59
.011
Avoid 2
.85
< .001
.59
.032
Avoid 3
.67
< .001
.45
.031
Avoid 4
.80
< .001
.50
.073
Avoid 5
.67
< .001
.83
< .001
Avoid 6
.68
< .001
.78
< .001
Avoid 7
.61
< .001
.58
< .001
CD20S
.62
< .001
.40
.032
CD22S
.47
< .001
.24
.187
CD23
.45
< .001
.27
.075
CD25
.41
< .001
.20
.230
CD24D
.28
< .001
.26
< .001
CD29
.52
< .001
.23
.347
CD25P
.53
< .001
.25
.289
Avoid 1
.15
.060
.53
.041
Avoid 2
.12
.478
.64
.012
G by
AvPD by
Longitudinal associations between SAD and AvPD
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Avoid 3
.05
.526
.49
.008
Avoid 4
.05
.738
.64
.004
Avoid 5
.53
< .001
.21
.541
Avoid 6
.48
< .001
.28
.405
Avoid 7
.27
.005
.33
.182
CD20S
.55
< .001
.73
< .001
CD22S
.49
< .001
.65
< .001
CD23
.38
< .001
.53
< .001
CD25
.52
< .001
.64
< .001
CD24D
.25
< .001
.31
.001
CD29
.66
< .001
.81
< .001
CD25P
.78
< .001
.89
< .001
SAD by
Note. SAD = Social anxiety disorder. AvPD = Avoidant personality disorder. Avoid 1 ... 7 =
diagnostic criteria for AvPD according to DSM-IV. CD20S … CD25P = section and number
of questions in the Composite International Diagnostic Interview (CIDI). Two-tailed p-values.
AvPD and SAD group factors correlate .61 in model 7.
In order to determine whether the group factors merely reflect methodological
variance, we tested whether they correlated with something substantive. We chose alcohol use
disorder (AUD), which was available at Wave 1 and Wave 2 as a single ordinal variable (no
AUD, subthreshold AUD, full AUD). We added this variable to the bifactor model without
correlations (model 6). In this model, AUD does not load on the g factor, but AUD is allowed
to correlate with the group factors for SAD and AvPD. If the group factors were merely
method factors, the correlations should be close to zero. However, the model-estimated
Longitudinal associations between SAD and AvPD
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correlation between the latent SAD group factor and AUD was .55 (p < .001), and the
correlation between the latent AVPD group factor and AUD was −.33 (p = .090). Thus, the
group factors are most likely not merely reflecting methodological issues.
In conclusion, the analysis suggested a model in which the DSM-IV criteria for SAD
and AvPD loaded on distinct, but correlated factors, with low cross-loadings. The CFA
supported the conclusion that SAD and AvPD do not reflect the same latent factors. The
bifactor model had the best fit, but does not suggest that the differences between SAD and
AvPD are merely due to methodological issues.
Attrition analyses
The prevalence of full SAD at Wave 1 was 3.6% (53 of 1465) among individuals who
participated at Wave 2, and 4.0% (12 of 302) among dropouts. Neither full SAD (OR = 0.91,
95% CI [0.48, 1.72], p = .760) or subthreshold SAD (OR = 0.98, 95% CI [0.65, 1.47], p =
.916) was statistically significantly related to continued participation. The prevalence of full
AvPD at Wave 1 was 2.4% (35 of 1467) among individuals who participated at Wave 2, and
3.3% (10 of 303) among dropouts. AVPD diagnosis was not significantly related to continued
participation (OR = 0.71, 95% CI [0.35, 1.46], p = .359). However, subthreshold symptoms of
AvPD were associated with lower rates of participation at Wave 2 (OR = 0.92, 95% CI [0.84,
0.99], p = .033). Zygosity was also related to dropout. Whereas 85.8% (774 of 902) of MZs
participated at Wave 2, the rate among DZs was 79.7% (697 or 875) (OR = 0.65, 95% CI
[0.50, 0.83], p = .001). The polychoric correlation between SAD and AvPD traits was 0.51
(95% CI [0.36, 0.65]) among individuals who dropped out from the study and 0.49 (95% CI
[0.42, 0.56]) among those who continued to participate in the study.
Longitudinal associations between SAD and AvPD
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