Mardia’s test showed that data is not multivariate normal, g1p = 34.23, χSkew = 1243.78, p < .001; g2p = 281.09, ZKurtosis = 8.53, p < .001; χSMSkew = 1263.08, p < .001. Sample size was considered adequate for factorial analysis.
Factorial Validity
Bartlett's test of sphericity was significant, 𝜒²(105) = 599.93, p < .001, and the KaiserMeyerOlkin Measure of Sampling Adequacy (KMO) analysis returned a value of .81 for the overall matrix, and values between .65 and .96 for all variables. Both indicators support factor analysis as a useful approach to the data.
Parallel analysis with unweighted leastsquares estimator (ULS) indicated that three factors should be retained (see Figure 1). However, only two principal factor eigenvalues reached values greater than 1 or .7 (old and new Keiser Criterion, respectively). Moreover, Hull method with CFI and RMSEA, and lower bound of RMSEA 90% CI, also support a twofactor retention. Given these results and the conceptual framework surrounding the bifactorial structure of the original scale, a twofactor solution was extracted.
An EFA with Promax rotation using ULS estimator was performed. Factor loadings and respective R2, Uniqueness and Complexity by factor are shown in Table 1.
Table 1 Factor loadings and respective R2, uniqueness and complexity values.


Factor






F1(PI)

F2(GA)

R2

Uniqueness

Complexity

CL Ratio

Q1

0.09

0.68

0.43

0.57

1.0

7.6

Q2

0.43LL

0.31

0.38

0.62

1.8

1.4CL

Q3

0.15

0.57

0.29

0.71

1.1

3.8

Q4

0.01

0.60

0.37

0.63

1.0

60

Q5

0.55

0.30

0.28

0.72

1.6

1.8CL

Q6

0.44LL

0.04

0.21

0.79

1.0

11

Q7

0.01

0.68

0.47

0.53

1.0

68

Q8

0.84

0.13

0.64

0.36

1.1

6.5

Q9

0.01

0.41LL

0.17

0.83

1.0

41

Q10

0.58

0.22

0.47

0.53

1.3

2.6

Q11

0.00

0.57

0.33

0.67

1.0

57

Q12

0.70

0.01

0.49

0.51

1.0

70

Q13

0.19

0.38LL

0.23

0.77

1.5

2CL

Q14

0.59

0.07

0.38

0.62

1.0

8.4

Q15

0.05

0.59

0.37

0.63

1.0

11.8

Note: Items corresponding to each factor are listed according to the strength of their factor loading. PI=Perceived Infectability; GA=Germ Aversion; CL Ratio=Primary/Secondary Loading; LL=Loading below 0.5; CL=CrossLoading.

The twofactor solution accounted for 37% of the variance, with the PI factor explaining 18% and the GA factor 19% of the variance. The interfactor correlation was .35. Interestingly, this factorial solution mimics the twofactor solution expected and postulated in the literature (e.g., 8), with the highest loading of each item saturated in the theoretically correct factor.
Items Q2, Q6, Q9 and Q13 registered low loadings for the sample size (< .50) and some also showed crossloadings with complexity and/or CL ratio values above those recommended (35,36). Despite an acceptable primary loading, item Q5 showed inadequate complexity and CL ratio, evidencing crossloading. An average EFA with different oblique rotation models was performed to ensure elimination decision. Visual analysis of loadings distribution suggested an absence of major fluctuations (see Figure 2). Although visually adequate, the ratio between loadings in item Q5 is still below the recommended (< .03; 36).
Furthermore, two Polytomous Item Response Theory analysis using generalized partial credit model  one for each factor  were performed (see Table 2). Results showed that the five aforementioned items reached discrimination values below the acceptable (≥ .70; 37), suggesting that they are not good at discriminating the latent trait and, therefore, supporting their removal.
Table 2 Results of the PIRT analysis using Generalized Partial Credit Model per factor


Item

a

b1

b2

b3

b4

b5

b6

PI

Q8

1.923

1.291

0.412

0.555

0.648

1.405

2.168

Q10

1.113

0.902

1.497

0.326

2.984

0.719

2.37

Q12

1.007

3.341

0.347

0.101

0.368

1.232

2.045

Q14

0.7

2.772

0.5

0.219

1.044

2.667

1.377

Q2

0.562

1.256

1.656

0.281

1.997

3.852

1.318

Q6

0.425

0.963

3.325

0.416

2

6.297

1.44

Q5

0.31

3.701

0.189

0.637

2.211

0.023

2.199










GA

Q1

1.234

1.891

1.952

1.419

1.734

0.749

0.476

Q7

1.093

0.284

1.034

0.75

1.149

2.399

3.239

Q15

0.513

0.298

0.961

0.659

2.148

3.051

0.839

Q4

0.465

1.704

0.273

0.247

0.689

0.237

1.611

Q11

0.449

1.279

0.417

1.284

2

2.384

0.837

Q3

0.422

2.268

0.802

0.348

1.044

0.262

0.067

Q13

0.386

3.475

0.881

1.476

0.234

1.961

4.371

Q9

0.234

1.348

0.674

0.614

0.395

0.104

1.327

Note: a = discrimination ability; PI=Perceived Infectability; GA=Germ Aversion.
A CFA with WLSMV was used to confirm the 10items bifactorial structure obtained from the EFA. Results revealed an acceptable global adjustment, χ2(34) = 46.68; CFI = .93; TLI = .91; RMSEA = .05, RMSEA 90% CI [.00, .09]; SRMR = .07. Moreover, all items reached high factor weights and appropriate individual reliabilities on latent variables (see Figure 3).
Several CFAs were also compared to verify the factor structure that best fits the data. Apart from the original factor structure, and considering the cultural proximity, structure models from two Spanish studies assessing the psychometric properties of the PVD were tested with our sample. All models are present in Table 3.
Table 3 Confirmatory Factor Analysis for all the models tested.


Model 1

Model 2.1 Original

Model 2.2
Spain1

Model 2.3
Portugal

Model 3.1
Spain2

Model 3.2
Portugal

Model 4.1
Spain2

Model 4.2
Portugal

One Factor
PVD
(all items)

Two Factors
PI & GA
(all items)

Two Factors
PI & GA
(w/o reverse items)

Two Factors
PI & GA
(w/o items Q2, Q5, Q6, Q9 and Q13)

One Factor
PI
(all items)

One Factor
PI
(w/o items Q2, Q5 and Q6)

One Factor
GA
(all items)

One Factor
GA
(w/o items Q9 and Q13)

χ2;
p(df)

237.68; p<.001(90)

147.43; p<.001(89)

34.57; p=.12(26)

46.68; p=.07(34)

35.97; p=.001(14)

11.57; p<.01(2)

17.51; p=.62(20)

5.375; p=.80(9)

CFI

.50

.80

.95

.93

.84

.88

1.00

1.00

TLI

.42

.77

.93

.91

.76

.63

1.02

1.04

RMSEA (90%CI)

.11 (.09, .13)

.07 (.05, .09)

.05 (0, .09)

.05 (0, .09)

.11 (.07, .15)

.19 (.09, .30)

0 (0, .06)

0 (0, .06)

SRMR

.12

.09

.06

.07

.08

.07

.04

.03

Loadings
Range

(.13 to .62)

PI (.28 to .75)
GA (.42 to .70)

PI (.47 to .83)
GA (.41 to .69)

PI (.63 to .75)
GA (.52 to .70)

(.41 to .78)

(.61 to .79)

(.40 to .69)

(.55 to .67)

Items
below
0.5

Q3, Q5, Q6, Q8, Q9, Q12, Q13, Q14

PI – Q5, Q6
GA – Q3, Q9

PI – Q6
GA – Q9


Q5


Q9, Q13


Note: WLSMV was used as an estimator for all models. PI=Perceived Infectability; GA=Germ Aversion; Spain1 = Study by Magallares and colleagues (39); Spain2 = Study by Díaz and collaborators (40).

Models 1, 2.1 and 3.1 obtained inadequate global and local adjustment values. Models 2.2 and 4.1, on the other hand, obtained acceptable values of global adjustment, but inappropriate local adjustment values. The remaining three models (i.e., 2.3, 3.2 and 4.2) reached acceptable values of global and local adjustments. Considering the conceptual framework and the original structure of the PVD, the bifactorial model obtained from the EFA (i.e., model 2.3) was adopted (see Additional file 1 for the original and final Portuguese version of the scale).
Convergent and discriminant validity of PVD factors
The Average Variance Extracted (AVE) and Composite Reliability (CR) values for both factors were as follows: AVEPI = .41, AVEGA = .33, CRPI > .79, CRGA > .74. While these AVE values are below those that are usually regarded as adequate (38), Fornell and Larcker (34) state that if the AVE values are less than .5, but the CR values are higher than .6, convergent validity of the construct is still considered adequate. Furthermore, both CR values are greater than .7, supporting the notion of an appropriate construct reliability. Thus, convergent validity of PVD factors was confirmed.
Furthermore, both AVE values were above the square of the correlation between the two factors (.12), indicating only 12.3% of common information between them and confirming the discriminant validity of the twofactor model (34).
Convergent and discriminant validity of the scale
Regarding convergent validity, as shown in Table 4, both PVD subscales significantly correlated with DPSSR subscales, MOCI, MMPIHs and NEOFFI Neuroticism, while DSR total score, Core Disgust and Contaminationbased Disgust subscales only correlated with GA. Furthermore, DPSSR Disgust Propensity subscale and MOCI correlated more strongly with GA, and MMPIHs with PI, as predicted.
Table 4 Polychoric Correlation Matrix among study variables.


Variables

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

PVD

















1. Perceived Infectability

(.82)
















2. Germ Aversion

.27***

(.82)















DPSSR

















3. Disgust Propensity

.25**

.34***

(.85)














4. Disgust Sensitivity

.29***

.22*

.50***

(.87)













DSR

















5. Core Disgust

.04

.28***

.31***

.40***

(.81)












6. Animalreminder Disgust

.02

.11

.20*

.39***

.68***

(.82)











7. Contaminationbased

.12

.41***

.16

.25**

.54***

.37***

(.581)










8.Total

.00

.28***

.28***

.43***

.93***

.86***

.66***

(.89)









MOCI

















9.Total

.39***

.42***

.43***

.35***

.18*

.12

.25**

.20*

(.86)








SQR15

















10. Total

.12

.09

.38***

.27**

.30***

.18*

.15

.27**

.37***

(.89)







MMPI  Hs

















11. Total

.32***

.23**

.41***

.27**

.13

.14

.10

.15

.52***

.29***

(.94)






NEOFFI

















12. Neuroticism

.26**

.17*

.32***

.35***

.20*

.12

.11

.18*

.54***

.37***

.57***

(.88)





13. Extraversion

.15

.11

.10

.01

.06

.11

.07

.06

.24**

.08

.25**

.45***

(.84)




14. Openness

.02

.02

.07

.17*

.07

.12

.07

.10

.11

.23**

.14

.21*

.27**

(.632)



15. Agreeableness

.21**

.07

.17

.08

.10

.17

.08

.10

.24*

.10

.27*

.20*

.26**

.22*

(.80)


16. Conscientiousness

.08

.24**

.00

.06

.04

.11

.09

.09

.05

.08

.14

.25**

.19*

.09

.14

(.89)

Note: Ordinal alphas are presented in parenthesis on the diagonal axis. ***p<.001; **p<.01; *p < .05; 1Average Polychoric R=.21; 2Nonordinal alpha=.72.
1Average polychoric R = .213; 2Nonordinal alpha = .72

Evidence for discriminant validity was also found as DSR Animalreminder Disgust, SQR15, and NEOFFI Extraversion and Openness subscales did not significantly correlate with PVD factors. Likewise, NEOFFI Agreeableness and Conscientiousness subscales showed low correlations with PI and GA, respectively.
Reliability
Both factors showed good levels of internal consistency (41), Ordinal Cronbach's αPI = .82, G6(smc)PI = .81, Median rPI = .54, Ordinal Cronbach's αGA = .82, G6(smc)GA = .80, Median rGA = .45.