Examining the Factor Structure of the Anxiety Sensitivity Index-3 in a Turkish Sample: The Factor Structure of the Anxiety Sensitivity Index-3

Abstract

The purpose of the current study was to investigate the factor structure of the Anxiety Sensitivity Index-3 (ASI-3) in a Turkey sample and to determine measurement invariance of the ASI-3 across gender and age groups. Confirmatory factor analysis was performed on four different models to determine the best fit model for the structure. After the best structure was determined, different models were tested for measurement invariance across gender and age groups. To determine the reliability of the ASI-3, the hierarchical omega coefficient and correlations between the scores obtained from different scales for convergent validity were calculated. It has been determined that the bifactor model is the model that best fits the data, and this model shows invariance across gender and age groups. Besides, evidence regarding the reliability and convergent validity of the ASI-3 was also provided in the study. Current findings show that anxiety sensitivity consists of a general factor (anxiety sensitivity) and three independent specific factors (physical, cognitive, and social concerns). It was concluded that the general factor of anxiety sensitivity constitutes a dominant factor and special factors have a relatively low effect on explaining the structure. Considering the dominance of the general factor, it is recommended to use the ASI-3 total score as a measure of general anxiety sensitivity.

Keywords

Anxiety sensitivity bifactor model measurement invariance

Introduction

Anxiety sensitivity (AS) is an important issue in the conceptualization and investigation of anxiety pathology (McNally, 1990). It refers to the degree of belief that an individual’s anxiety symptoms may have harmful psychological, physical, and/or social consequences (Reiss & McNally, 1985). After this concept was introduced in the 1980s, several studies evaluated AS. One of the most widely used instruments to evaluate AS is the 16-item Anxiety Sensitivity Index (ASI) developed by Reiss et al. (1986), who concluded that the AS structure measured using this tool was unidimensional. However, other studies conducted using this scale showed different results, that is, that AS structure varies between two and four factors (Blais et al., 2001; Cox et al., 2001; Peterson & Heilbronner, 1987; Schmidt & Joiner, 2002; Stewart et al., 1997; Taylor et al., 1992; Telch et al., 1989; Wardle et al., 1990). However, there are also studies that arrived at the same findings as Reiss et al. (1986) (Sandin et al., 1996; Taylor et al., 1991, 1992). Zinbarg et al. (1997) concluded that three lower-order factors (physical concerns, mental incapacitation concerns, and social concerns) related to the factor structure of AS were gathered in one higher-order factor (general AS). Rodriguez et al. (2004) found a similar result and determined that AS has a hierarchical factor structure. Ayvaşık (2000) used exploratory factor analysis and found that the ASI had a four-factor structure. Despite this finding, however, the study concluded that a one-factor structure was more suitable for ASI.

Between 1986 and 2009, the ASI was the most frequently used measure of AS. However, given that AS may be multidimensional and that 16 items may be insufficient to measure it, the ASI was revised twice. Taylor and Cox (1998b) created a 36-item ASI, called the revised ASI (ASI-R) using some items in the ASI (1998a). They found that four lower-order factors were loaded on a single higher-order factor. Other researchers found that the structure of the scale varied between two and four factors (Armstrong et al., 2006; Arnau et al., 2009; Deacon et al., 2003; Zvolensky et al., 2003). Taylor et al. (2007) created the Anxiety Sensitivity Index-3 (ASI-3). As ASI was not developed multidimensionally, the factor structure showed variability, and the number of items in some factors was small. They adhered to the three correlated-factor structures (physical, cognitive, and social concerns) determined by most researchers for AS. Besides, while developing the scale, they also used the items in the ASI-R and created the ASI-3 with 18 items bearing an equal number of items for each factor. The researchers aimed to provide a more valid and reliable tool for AS and to make the results more stable. Taylor et al. (2007) concluded that ASI-3 measures the structure more precisely as it has higher reliability and construct validity when compared to the ASI. Therefore, ASI-3 is the most widely used instrument to assess AS.

Factor structure of the ASI-3

Taylor et al. (2007) proposed a model in which three correlated factors were loaded on a second-order general factor in order to represent the factor structure of ASI-3. Scholars examined the structure of the ASI-3 on clinical and non-clinical samples, and tested the accuracy of the three-factor hierarchical model determined by Taylor et al. (2007) (Cai et al., 2018; Foroughi et al., 2019; Kemper et al., 2012; Petrocchi et al., 2014, Wheaton et al., 2012). However, in some studies where the hierarchical model was determined to fit the data, this result differed slightly from the original study. For example, Kemper et al. (2012) tested the three-factor hierarchical model of the ASI-3, and obtained no exact model fit. They found that there were several recommended modification indices for the cognitive concerns subscale and stated that this result was not because of the misspecification of the model, but rather because of technical aspects of the ASI-3, that is, an overlap in the wording of some items. Therefore, they included these three residual correlations in the model, thus yielding an acceptable fit for the three-factor hierarchical model of the ASI-3. Though Wheaton et al. (2012) used some good fit indices (RMSEA, SRMR, CFI, and TLI)., they could not meet the cut-off criteria for the RMSEA value alone. They concluded that the three-factor model had an acceptable fit in this sample. The results of the studies in which the three-factor hierarchical model of the ASI-3 was tested led the researchers to test the factor structure of ASI-3 using alternative models. Recent studies have found that the ASI-3 is more suitable for the bifactor model (Allan et al., 2015; Ebesutani et al., 2014; Jardin et al., 2018; Osman et al., 2010; Rifkin et al., 2015).

The bifactor model was first proposed by Holzinger and Swineford (1937) to examine cognitive abilities. However, it came to be used in the investigation of many psychological structures over time. The bifactor model provides useful information to understand the structure of the test and interpret different scores correctly Canivez, 2016). It has a set of special factors and a general factor.

Λ = (\begin{matrix} * & * & 0 \\ * & * & 0 \\ * & * & 0 \\ * & 0 & * \\ * & 0 & * \\ * & 0 & * \end{matrix})

The first column in Λ shows the general factor. The other columns show the special (group) factors. Asterisks (*) denote items with free factor loadings, and 0 denotes items with expected factor loadings of 0. Each item has only two free loading parameters, usually in the general factor and one specific factor. In this model, the general factor is assumed to be orthogonal to the specific ones. That is, bifactor models include a single general factor that reflects the common variance among all items and specific factors, which are orthogonal ones that reflect the variance between item clusters (Reise, 2012). The overall factor represents the broad structure measured. Group factors represent narrower structures.

In studies where the bifactor model was tested for the ASI-3, AS, and physical, cognitive, and social concerns were considered the general and special factors, respectively. These studies determined that the bifactor model provided better results than did the hierarchical model that was introduced during the development of the ASI-3 (Allan et al., 2015; Ebesutani et al., 2014; Jardin et al., 2018; Osman et al., 2010; Rifkin et al., 2015).

For example, Osman et al. (2010) found that there is a general AS factor that explains 50% of the variance in scores. They found that AS explained a significant variance beyond the variance values explained by any of the sub-factors (physical concerns, 6.11%, cognitive concerns, 7.68%, and social concerns, 7.38%) and that the ASI-3 was unidimensional because many items loaded more strongly on the general factor rather than relevant specific ones. When these results are combined with the fact that in the bifactor analysis many items load more strongly on the general AS factor than on the specific ones, the researchers concluded that the ASI-3 is unidimensional. Ebesutani et al. (2014) determined that the bifactor model provided better results for the ASI-3 and thus claimed that AS should be classified as a unidimensional structure. Figure 1 presents the bifactor model tested in these studies.

Figure 1.

The bifactor model for the ASI-3.

Purpose of the study

The current study has theoretical and practical importance. With the COVID-19 pandemic, the psychological health of adults has become a very important issue. The accurate interpretation of these psychological measures requires the effective testing of scale constructs. However, different studies that have examined the dimensionality of AS have presented different findings. Thus, it is essential to examine this issue further. The verification of an established model for a dataset may not always be sufficient. As more than one model can yield valid results in explaining the relationships between variables, there must be evidence for the model through which the results representing the variables studied are best arrived at (Şimşek, 2007). This study was carried out with the aim of enabling future research to ascertain the validity and reliability of the scale Reise et al. (2010, p. 2) stated that for complex measures with controversial factor structures, a bifactor latent structure would be a better alternative than unidimensional, correlated-traits, and second-order structures, which are commonly used. The current study addresses the gaps in existing research on the factor structure of the ASI-3 for a Turkish sample. The ASI-3 bifactor models have been adapted to suit different samples such as those from the USA, South Korea, and Italy (Ebesutani et al., 2014, 2016). The scale has not been adapted to suit a Turkish sample thus far. Scales like the ASI-3, which are used widely in different cultures should be renewed in line with updated research. The results arrived should be discussed comparatively. Testing the bifactor model will enable the assessment of whether the ASI-3 factors offer incremental value beyond the general factor, and facilitates the empirical review of the usefulness of constructing subscales. This study can contribute toward the interpretation of the ASI-3 scores. Examining the structure of AS can support researchers who study the pathology of different anxiety and mood disorders. Repeating the psychometric properties of ASI-3 in line with new recommendations in the literature will help interpret the scores obtained from the scale more accurately.

The present investigation used confirmatory factor analytic (CFA) techniques to examine the factor structure of the ASI-3 by testing several alternative models as suggested by previous research (Allan et al., 2015; Ebesutani et al., 2014; Jardin et al., 2018; Osman et al., 2010; Petrocchi et al., 2014). The one-factor, two-factor (physical concerns, social concerns + cognitive concerns, see Zvolensky et al., 2003), three correlated factors, and bifactor models were tested. A second-order model (three dimensions plus a common higher-order AS factor) was not tested in this study because a single higher-order factor and three lower-order factors produce the same goodness of fit as a three-factor model in which the factors are freely intercorrelated. A similar approach has been followed in the literature for this model (Ebesutani et al., 2014).

Whether the model that best represents the factor structure of the ASI-3 provides measurement invariance across gender and age groups was also tested using multiple-group confirmatory factor analysis. Scale reliability was calculated with the hierarchical omega coefficient because it is the most suitable coefficient for evaluating the reliability of the bifactor model. Finally, the convergent validity of the scale was examined with the correlations between the measurements of the structures associated with AS and the ASI-3.

Method

Participants

The participants were Turkish residents. The sample was non-clinical. Data were collected from 448 people in all. As this study was conducted based on the completion of the ASI-3, there were no missing data. However, after the extreme value control of the dataset, the data of 6 participants were excluded, leaving the total at 442 (M_age = 25.91, SD = 7.031, Range:18–50). Of these, 73.1% of the participants were female (M_age = 24.80, SD = 6.625, Range: 18–50) and 26.9% were male (M_age = 28.93, SD = 7.240, Range: 18–48). Most participants were aged between 18 and 31 years and they were from a middle-class socioeconomic background (85.1%).

Instruments

Personal information form

It contains several items related to variables such as gender and age variables to be used in the measurement invariance analysis of the study.

The Anxiety Sensitivity Index-3 (ASI-3)

The ASI-3 with 18 items developed by Taylor et al. (2007) was used to evaluate AS. In the ASI-3, participants are asked to indicate the extent to which they are concerned about the possible negative consequences of anxiety-related symptoms (e.g., “It scares me when my heart beats rapidly”). The ASI-3 has three factors: physical, cognitive, and social concerns. Each item on the ASI-3 should be rated on a 5-point Likert-type scale ranging from 0 (very little) to 4 (very much). The higher the score, the more severe the AS level. Taylor et al. (2007) determined that the ASI-3 is a psychometrically valid tool after working with large samples with different characteristics. Mantar et al. (2010) adapted the ASI-3 to suit the Turkish context. In their study, after exploratory factor analysis, the ASI-3 was found to have a three-factor structure, including physical, cognitive, and social concerns. The ASI-3 showed high internal consistency (α = .93). The test-retest reliability was .64, and it was statistically significant.

The anxiety and depression structures have been measured and discussed together in most studies (Brown et al., 1997; Mahmoud et al., 2012; Mantar et al., 2010; Yılmaz et al., 2017). Owing to the intersection of both structures (Türkçapar, 2004), the other scales applied to the participants were the CES-Depression Scale and the Depression Anxiety Stress Scale.

The Center for Epidemiologic Studies Depression Scale (The CES-D)

The CES-D is a 20-item scale developed by Radloff (1977) to measure depression. The answers are scored on a 4-point Likert scale that ranges from 0 (never-rarely) to 3 (mostly-usually). Items 4, 8, 12, and 16 of the scale are scored in reverse. The scores that can be obtained from the scale are in the range of 0 to 60 points. Higher scores on the scale indicate that depression may also be higher. Tatar and Saltukoğlu verified the validity and reliability of the Turkish scale in 2010. Exploratory factor analysis presented four factors explaining 49.9% of the total variance. The internal consistency coefficient was α = .89, the Guttman split-half reliability of the test was r = .89, and the two-week test-retest reliability coefficient was r = .69.

In the current study, a four-factor hierarchical model was tested for the CES-D, as Tatar and Saltukoglu (2010) stated, that the subdimensions were unrelated to each other, and it was determined that the fit indices were good (CFI = .995, GFI = .991, RMSEA = .044). Besides, the internal consistency coefficients for the negative affect factor, positive affect factor, somatic symptoms factor, and interpersonal problems factor of the scale were calculated as .88, .82, .80, and .72, respectively.

The Depression Anxiety Stress Scales – 21 (DASS-21)

DASS-21 was developed by Lovibond and Lovibond (1995). A short form of the DASS-21 was developed by Brown et al. (1997). It has individual subscales comprising seven items each to measure the dimensions of depression, stress, and anxiety. Each item is scored on a 4-point scale ranging from 0 (did not apply to me at all) to 3 (applied to me very much or most of the time). Higher scores indicate more frequent symptomatology. The scale was adapted to suit the Turkish context by Yılmaz et al. (2017). The confirmatory factor analysis confirmed the three-factor structure in the form of anxiety, depression, and stress, and high alpha coefficients (.81, .82, .76, respectively) and omega (.81, .82, .76, respectively) were obtained for these factors. The current study tested the three-factor structure of the scale. The fit indices were good (CFI = .983, GFI = .982, RMSEA = .068). The internal consistency coefficient of the DASS-21 was .81, .85, and .79 for the anxiety, depression, and stress factors, respectively.

Procedures and data analysis

Ethical approval was granted by a university ethics committee. The data were collected for approximately three months using Google Forms. Participants were sent a link to answer the scales, and their consent was obtained. The time taken to answer the scales online was approximately 15 minutes.

Preliminary analyses and reliabilities

Data screening and descriptive analyses were performed using SPSS 24 (IBM Corp, 2016). The mean, standard deviation, and internal consistency coefficients for each subscale and the total scale were calculated.

Alternative models

Alternative models were tested using the weighted least square mean and variance adjusted (WLSMV) estimator available in Mplus Version 7, as it is recommended to use WLSMV as the method of estimation for ordered-categorical data (Flora & Curran, 2004; O’Connell et al., 2008).

To determine the factor structure of the ASI-3, first, 18 items of the ASI-3 were modeled under a single factor as AS (Figure 2(a)). Next, the 18 items were used to establish two correlated-factor models, namely the physical (6 items) and social/cognitive (12 items) (Figure 2(b)) concerns factor models (PC and S/CC, respectively). After this, the 18 items were used to establish three correlated-factor models, namely the physical (6 items), cognitive (6 items), and social (6 items) (Figure 2(c)) concerns factor models (PC, CC, and SC, respectively). Finally, for the bifactor model, AS general factor and PC, CC, and SC sub-factors were considered special factors (Figure 1).

Figure 2.

Testing model for the ASI-3 (a) one-factor model; (b) two-factor (correlated traits) model; (c) three-factor (correlated traits) model.

The goodness of fit of the models was evaluated based on the chi-square test. An insignificant chi-square value indicates a good model fit. However, as the $χ^{2}$ statistic is restrictive especially in large samples and in cases with more items per factor, different indices were used for model fit. Comparative Fit Index (CFI), Tucker-Lewis Index (TLI), Root Mean Square Error of Approximation (RMSEA), and weighted root mean square residual (WRMR) were used The recommended cut-off points for these indices were used (good fit: CFI > .97, TLI > .97, RMSEA < .05; acceptable fit: CFI > .95, TLI > .95, RMSEA < .08) (Schermelleh-Engel et al., 2003). For the WRMR, a cut-off value close to 1.00 is considered suitable (Finney et al., 2006). The fit indices obtained for each model were compared. Besides, CFI differences (ΔCFI) (Cheung & Rensvold, 2002) of the bifactor and other models were examined. If this difference was less than .010, there was no difference between the two models compared in terms of fit statistics. However, if they exceed .010, the more restricted model was used. ΔCFI is highly recommended as the main criterion in comparing the bifactor models, as the χ² difference tests are affected by the sample size (Chen, 2007; Cheung & Rensvold, 2002).

Measurement invariance

The invariance of the factor structure of ASI-3 was examined with the lavaan package (Rosseel et al., 2017) in the R program. Theta parameterization was also used. This parameterization is recommended as it allows for the residual variance estimation of latent structure and independence test of metric and scalar invariance, which is useful for multi-group analysis (Muthén & Muthén, 2012).

After the best model was determined, the first CFAs were examined separately by age and gender. Then, the configural invariance model was examined to check whether the same number of factors and the item-factor loading patterns were consistent across groups. In the next as data for the ASI-3 are in the ordered-categorical structure, metric and scale invariance models are tested simultaneously in measurement invariance studies with such data (see Ebesutani et al., 2014; Jardin et al., 2018). At this stage, factor loadings for metric invariance and item thresholds for scale invariance were equal across the groups.

The CFI and RMSEA results obtained from both the configural and the metric and scale invariance models were compared. A CFI difference of under .010 and RMSEA difference of under .015 implied invariance between the groups. The significance of the WLSMV $χ^{2}$ differences (Δ $χ^{2})$ of the models was also tested, and p < .05 was taken as the criterion.

The coefficient omega hierarchical and explained common variance

The coefficient omega hierarchical (omegaH or ω_H) is a useful model-based reliability index (Reise et al., 2010) when the data are properly represented by the bifactor structure. The coefficient omegaH estimates the variance ratio in total scores that can be attributed to a single general factor and thus treats the variability in scores because of specific factors as a measurement error (McDonald, 1999; Reise et al., 2013; Zinbarg et al., 2006). First ω_H was calculated (the total score variance that can be associated with the variation of a single latent variable common to all items in a scale). Second, the coefficient omega hierarchical subscale (omegaHS or ω_HS) was calculated. OmegaHS is an index of the reliability of the subscale score after taking into account the general factor (Reise et al., 2013). It is generally preferred that this coefficient be greater than .50.

The ECV statistic can also be used to quantify general factor importance. A high value of ECV indicates that the model has a strong general latent dimension rather than latent subdimensions. As tests of ECV calculation using various datasets suggest that data with ECV < 0.70 are multidimensional, they were thus decomposed into multiple scales (O'Connor Quinn, 2014).

Convergent validity

The ASI-3 scores of the CES-D and the DASS-21 were used for convergent validity. Relationships between scales in general and their sub-factors were analyzed using the Pearson correlation coefficient. Correlation coefficients above .40 were accepted as sufficient for convergent validity (Kaasa et al., 1995).

Findings

Preliminary analyses and reliabilities

The mean and standard deviation values for the ASI-3 subscales and the total scale score were calculated in terms of both the whole group and the subgroups of the gender and age variables used in the measurement invariance. The internal consistency coefficients for the ASI-3 subscales and the total scale score were also examined. Table 1 presents the findings.

Table 1.

Descriptive statistics of the ASI-3.

Scale/Subscale	M_w (SD)	M_m (SD)	M_younger (SD)	M_older (SD)	M_t (SD)	α
Social concerns	14.450 (5.347)	14.810 (5.324)	14.240 (5.357)	15.290 (5.234)	14.550 (5.337)	.782
Physical Concerns	15.250 (5.968)	15.000 (5.752)	15.260 (5.987)	15.010 (5.721)	15.190 (5.905)	.849
Cognitive Concerns	13.790 (5.328)	12.740 (5.103)	13.620 (5.165)	13.240 (5.572)	13.510 (5.283)	.816
Total Scale	43.492 (14.023)	42.546 (13.975)	43.115 (14.120)	43.535 (13.756)	43.238 (14.001)	.902

M_w: mean for women, Mean_m: mean for men, Mean_younger: mean for participants aged 18–31 years old, Mean_older: mean for participants aged 31 and over, Mean_t: mean for all participants, SD: standard deviation, α: internal consistency coefficient.

The findings in Table 1 show that the mean of the ASI-3 total scores for women is higher than that for men. The mean of the ASI-3 total scores for older adults is slightly higher than that for younger adults. Values above .70 are considered good for internal consistency estimates (George & Mallery, 2003). Thus, it can be said that the internal consistency coefficients for each subscale and total scale were sufficient.

Alternative models

Table 2 presents the fit indices obtained by CFA for the bifactor and other comparison models.

Table 2.

Fit statistics of the alternative for the ASI-3.

Model	χ²	df	CFI	TLI	RMSEA [90% CI]	WRMR	ΔCFI
Bifactor Model	336.152***	117	.970	.960	.065 [.057; .073]	1.013	–
One-Factor (Unidimensional) Model	1062.628***	135	.871	.854	.125 [.118; .132]	2.075	.099
Two-Factor (Correlated Traits) Model (PC, S/CC)	729.820***	134	.917	.905	.100 [.093; .107]	1.661	.053
Three-Factor (Correlated Traits) Model	522.043***	132	.946	.937	.082 [.074; .089]	1.344	.024

Note. CFI: comparative fit index; TLI: Tucker Lewis index; RMSEA: root mean square error of approximation; WRMR: weighted root mean square residual; ΔCFI: difference among CFIs between the bifactor model and the associated competing model.

***

p < .001.

Table 2 shows that the model fit of the one-factor model is weak because of CFI and TLI < .95, RMSEA > .10, and WRMR > 1.00. When the two-factor model was applied to the dataset, a small improvement was seen in the fit indices. In the model established on the three-factor, fit indices came closer to acceptable values. However, the bifactor model met the criteria of the relevant fit indices and gave the best results (χ² (117,442) = 336.152, p < .001, CFI = .970, TLI = .960, RMSEA = .065 [90% CI: .057 – .073], WRMR = 1.013). Although the acceptable value of 1.00 for WRMR was not met, the value that emerged was very close. The bifactor model also had the best fit, as the small size of the index indicated a better fit. Under all conditions, the differences between the bifactor model and the CFI values of the other models were greater than .010, and the ΔCFIs were significant.

Table 3 presents the standardized factor loadings obtained from the bifactor model. Item loadings for the bifactor model, the general AS factor, were generally high and positive for all items (|λ| = .257 to .806, M = .597). All items (except item 6) loaded saliently (greater than .32) and significantly on the general AS factor. The factor loadings of all items defined in the social concern factor, which is one of the special ones, are significant and positive (|λ| = .166 to .588, M = .427). However, there are also some items (Items 1 and 17) with factor loadings that are smaller than the accepted cut-off point. A similar situation emerged for the physical concern factor. Except for items 4 and 15, factor loadings of all items were positive, significant, and salient (|λ| = .266 to .746, M = .452). However, the cognitive factor was not well defined (|λ| = .072 to .589, M = .267), as some items within this factor presented insignificant and negative loadings. These items are 10, 14, 16, and 18. Ghisi et al. also found that these four items presented unexpected results in their respective factors.

Table 3.

The standardized regression coefficients obtained from the bifactor model.

Items	General AS	Social	Physical	Cognitive
i1	.257 (.047)	.166 (.060)
i6	.527 (.037)	.502 (.042)
i9	.606 (.034)	.510 (.041)
i11	.463 (.041)	.588 (.043)
i13	.566 (.035)	.544 (.043)
i17	.597 (.035)	.251 (.049)
i3	.586 (.036)		.402 (.045)
i4	.567 (.036)		.266 (.047)
i7	.651 (.031)		.455 (.039)
i8	.531 (.039)		.746 (.034)
i12	.619 (.033)		.552 (.038)
i15	.637 (.037)		.293 (.054)
i2	.606 (.041)			.369 (.069)
i5	.696 (.035)			.589 (.110)
i10	.707 (.030)			−.072 (.050)
i14	.567 (.036)			−.159 (.054)
i16	.752 (.027)			−.127 (.052)
i18	.806 (.026)			−.285 (.059)

Note. Italic ones show non-significant standardized regression coefficients p > 0.05. The standard errors are presented in the parentheses.

Most items had higher factor loadings in the general factor, rather than in the special factors. Therefore, it can be said that the general factor contributed to the factor structure of the scale and that the bifactorial representation was beneficial. The factor loadings for special factors were rather low, especially for the cognitive concerns factor.

Measurement invariance of the ASI-3 bifactor model across gender and age groups

Table 4 presents all the steps in the examination of the measurement invariance of the ASI-3 bifactor model across gender and age groups. First, single-sample solutions of the ASI-3 bifactor model were checked and the bifactor model presented good fit values for both female (n = 323) and male (n = 119). Later, it was determined that the model tested for the configural invariance of the bifactor model over all participants also showed a good fit to the data (CFI = .996, TLI = .994, RMSEA = .040). Thus, it can be said that the same number and pattern of factors were arrived at in both gender groups. The fit indices obtained in the next model in which equal factor loadings and item threshold parameters were tested presented good results. It also met the criterion for ΔCFI < .010 and ΔRMSEA < .015. The results show that the chi-square difference test was not statistically significant (Δχ² = 93.219, df = 82, p > .05). This finding suggests that after constraining the factor loadings and item threshold parameters to remain equal between men and women, the model fit did not change substantially. Thus, the constrained model fits the data equally well.

Table 4.

Measurement invariance results of the ASI-3 bifactor model across gender and age groups.

Group	Model	n	χ² (df)	CFI	TLI	RMSEA	Δχ² (Δdf)	ΔRMSEA	ΔCFI
Gender	Women	323	210.680 (117)***	.979	.972	.058	–	–	–
	Men	119	164.091 (117)***	.993	.991	.040	–	–	–
	Configural invariance	442	315.661 (234)***	.996	.994	.040	–	–	–
	Metric / Scalar invariance	442	415.012 (316)***	.995	.995	.038	93.919 (82)	.002	.001
Age	Younger	313	203.666*** (117)	.995	.993	.049	–	–	–
	Older	129	176.061 (117)***	.994	.992	.063	–	–	–
	Configural invariance	442	344.321 (234)***	.994	.993	.046	–	–	–
	Metric / Scalar invariance	442	525.362 (316)***	.989	.990	.055	134.58 (82)***	−.009	.005

Note. χ²: WLSMV chi square; df: Degrees of freedom; CFI: comparative fit index; TLI: Tucker-Lewis index; RMSEA: root mean square error of approximation; Δ since previous model; Δχ²: chi square difference test for WLSMV estimation; ΔRMSEA: difference among RMSEAs between configural invariance and metric/scalar invariance models. ΔCFI: difference among CFIs between configural invariance and metric/scalar invariance models.

***

p < .001.

The fit indices of the ASI-3 bifactor model in Table 4 show that good fit values were obtained for both groups, namely those in the 18–30 years age range (n = 313) and those aged above 31 years (n = 129). The model that was tested for the configural invariance of the bifactor model over all participants also fit the data well (CFI = .994, TLI = .993, RMSEA = .046). Therefore, it can be said that the same number and pattern of factors were arrived at among the differentage groups. The fit indices obtained in the next model in which equal factor loadings and item threshold parameters were tested presented good results. It also met the criterion ΔCFI < .010 and ΔRMSEA < .015. However, the chi-square difference test was statistically significant (Δχ² = 134.58, df = 82, p < .001). Considering the sensitivity of the chi-square as mentioned earlier and the need to meet the other two criteria, it was assumed that invariance was achieved at this stage. Therefore, factor loadings and item threshold parameters did not change between age groups.

The coefficient omega hierarchical

As a result of the omega coefficient analysis performed based on the bifactor model of the ASI-3, the coefficient omega (ω) estimates for the total scale score was .95, which was very high. The omega hierarchical coefficient was ωH = .84 for the general AS factor, and .34, .01, and .35 for the PC, CC, and SC factors, respectively. The omega hierarchical coefficients for the sub-factors calculated by eliminating the effect of the general dimension are low. Based on this, when the effects of all other sub-factors and the general factor are subtracted from the former, it can be said that the effect of the relevant sub-factor on the change in the ASI-3 scores was low. The values for group factors were less than .50, suggesting that these factors should not be interpreted independently (Reise, 2012).

For the bifactor model, the ECV for the general and group factors for PC, CC, and SC were .67, .15, .06, and .12, respectively. Therefore, the ECV value was lower than .70 for the general factor. It can be said that the ASI-3 is multidimensional, and that the group factors contribute a small part of the variance among the ASI-3 items. However, these findings support the presence of a strong general AS factor.

Convergent validity

The relationships between the total score of AS, which is the general factor determined for the ASI-3, and the CES-D and the DASS-21 scores were calculated using the Pearson correlation coefficient. These results are presented in Table 5.

Table 5.

Convergent validity coefficients of the ASI-3 total scale and subscales.

Scale	ASI	ASI-PC	ASI-SC	ASI-CC	CES-D
ASI	–
ASI-PC	.86**	–
ASI-SC	.81**	.50**	–
ASI-CC	.87**	.65**	.58**	–
CES-D	.49**	.35**	.39**	.52**	–
DASS-21	.54**	.43**	.38**	.57**	.80**

Note. ASI: Anxiety Sensitivity Index-3 total scale; ASI-PC: Anxiety Sensitivity Index-3 physical concerns subscale; ASI-SC: Anxiety Sensitivity Index-3 social concerns subscale; ASI-CC: Anxiety Sensitivity Index-3 cognitive concerns subscale; CES-D: The Center for Epidemiologic Studies Depression Scale; DASS-21:Depression Anxiety Stress Scales.

p < .01.

Table 5 presents the correlations between the ASI-3, ASI-3 subscales, and the CES-D and the DASS-21. The ASI-3 subscales score was strongly correlated with the ASI-3 total scale score (range = .81 to .87). The three ASI-3 subscales were moderately correlated (range= .50 to .65). The ASI-3 total and the subscales scores were moderately correlated with the CES-D total scale score (range = .35 to .52). The cognitive concerns factor was more related to the CES-D than to the other factors. The ASI-3 total scale and the subscales scores were moderately correlated with the DASS-21 total scale score (range = .38 to .57). The cognitive concerns factor was also more related to the DASS-21 than to the other factors.

Discussion

This study sought to determine the factor structure of the ASI-3, which was developed by Taylor et al. (2007), and to examine the measurement invariance of this determined bifactor structure across gender and age groups. As mentioned before, this scale is used quite frequently in AS studies in many countries and has strong results in terms of validity and reliability. However, arriving at different results regarding the structure measured by the scale has led researchers to re-examine this issue with different approaches (Allan et al., 2015; Ebesutani et al., 2014; 2016; Osman et al., 2010; Volarov et al., 2017). The findings of these studies support the bifactor structure, which includes the three factors of physical, cognitive, and social concerns as determined by Taylor et al. (2007), but which is different from the structure determined by the original study. In these studies, it was stated that the bifactor model formed by the group factor of these three factors and the general factor as AS is more suitable for the structure measured by the ASI-3. Based on these suggestions, this study examined whether the ASI-3, adapted into Turkish by Mantar et al. (2010) coincides with these current findings. If a structure is evaluated using a tool that does not measure the same feature in different cultures, its interpretation will differ (Irvine & Carroll, 1980).

Data collected from a non-clinical study group were used in this study. The models tested in the study are as follows: (a) the one-factor model (unidimensional) that includes all items of the scale to determine the factor structure of the ASI-3; (b) two-factor model that includes physical concerns and social/cognitive concerns factors; (c) the bifactor model that includes the gneral AS factor and three special factors (the physical, cognitive and social concerns).Fit indices of each model were examined through CFA. The bifactor model represented the factor structure of the ASI-3 best. It represents a single general factor (AS) and sub-factors (physical, cognitive, and social concerns) that are orthogonal to each other (uncorrelated). However, many studies have confirmed the three-related factor model for the factor structure of the ASI-3, as suggested by Taylor et al. (2007) (Foroughi et al., 2019; Kemper et al., 2012; Petrocchi et al., 2014; Wheaton et al., 2012). Although the results of the three-related factor models in this study can be interpreted as acceptable, the bifactor model gives the best-fit indices. Ebesutani et al. (2014) stated that the relationship between sub-factors is discussed in the field and more research is needed in the future to solve this problem. As this current study is technical, comments were made only on the statistics that were revealed.

When the coefficient hierarchical omega, which is the proposed reliability coefficient for bifactor models, are analyzed, while a very high value is calculated for the AS general factor, these values are low for special factors. This finding is similar to those of studies that have calculated the coefficient omega hierarchical for the bifactor structure of the ASI-3 (Ebesutani et al., 2014; Jardin et al., 2018; Osman et al., 2010). This shows that the variability in the measured AS structure is mostly caused by the AS general factor. ECV values also support this result. Osman et al. (2010), and Ebesutani et al. (2014), stated that these results indicate that the latent structure measured using the ASI-3 can be considered largely one-dimensional. As stated in Jardin et al. (2018), although the evidence for the bifactor model of the ASI-3 suggests that the ASI-3 structure is multidimensional, the general findings obtained in the study are that the ASI-3 is primarily a one-dimensional structure.

Although the factor loadings obtained from the bifactor model comprise significant and generally sufficient values for the AS general factor, this is different especially for the cognitive concerns factor. This result is quite similar to those of some previous studies (Ebesutani et al., 2016). Ebesutani et al. (2016) established a modified bifactor model that included only physical and social factors. They took into account this situation of cognitive concerns factor in their study with the ASI-3. There is a need for research that can reveal the structure of AS more clearly. Even the development of a new measurement tool that provides more stable results regarding this structure can be considered a need. In the study that adapted the scale to suit the Turkish context, the original structure was not fully provided (Mantar et al., 2010). Items 1 and 17, which led to this situation, presented insufficient results in terms of standardized regression coefficients in which the bifactor structure was tested.

Another issue addressed in the study is the examination of the bifactor model, which gives the best-fit values in terms of measurement invariance. Most studies that have examined the measurement invariance of the ASI-3 through the bifactor model using different samples and subgroups (such as ethnicity, gender, age) concluded that the bifactor model of the ASI-3 was generalizable across different groups Ebesutani et al., 2014; Jardin et al., 2018; Fergus et al., 2017). In the current study, the measurement invariance results by gender and age were similar to those mentioned above. In other words, the bifactor model showed that genders and age groups are equal in terms of factor patterns and loadings, and item thresholds in the current study. These results show that scores from the bifactor model are directly comparable between these groups.

The correlation analysis performed for the convergent validity of the ASI-3 showed that there are generally moderate and significant relationships between the scores obtained from this and other scales. A moderate relationship was found between the ASI-3 and the CES-D total scores. These results are similar to those of studies reporting the relationships between the scores obtained from both scales Kemper et al., 2012; Lim & Kim, 2012; Stanley et al., 2018). As in other studies, the cognitive concerns factor had the highest correlation between the subscales of ASI-3 and the CES-D total score Kemper et al., 2012; Lim & Kim, 2012; Wheaton et al., 2012). There is a moderate and significant relationship between the ASI-3 and the DASS-21 total scores. This result coincides with those of the extant literature (Cai et al., 2018; Maack et al., 2018; Toth & Jokić-Begić, 2020). Besides, as in other studies, the correlation between cognitive anxiety, one of the subscales of ASI-3, and DASS-21 total score was found to be higher (Melli et al., 2018; Olthuis et al., 2014). Thus, it can be said that there is sufficient evidence for the convergent validity of the ASI-3.

Limitations and directions for future research

In this study, the factor structure of the ASI-3 was examined cross-sectionally. A longitudinal study design can be used to examine how the AS structure performs over time in future research. Validity analyses of the ASI-3 were examined in the literature using clinical and non-clinical study groups (Escocard et al., 2009; Kemper et al., 2012; Osman et al., 2010; Wheaton et al., 2012). This study was conducted on a non-clinical study group alone. It is necessary to examine whether the same factor structure occurs for AS by using samples that include participants with clinically high levels of mood and anxiety disorders. The participants were mostly young adults and women. The measurement invariance of the ASI-3 can be examined over groups that are more balanced in terms of gender and age. Another way to enhance the validity of the ASI-3 bifactor model is to test the measurement invariance according to clinical and non-clinical groups.

Conclusion

The results of this study show that the factor structure of the scale is more suitable for a bifactor structure. All three factors of ASI-3 (physical, social, and cognitive factors) were loaded at a high level in the general factor. The cognitive concern factor, which is one of the special factors, is inadequately defined when compared to the other two. The omega coefficient for the general factor was high. Considering the dominance of the general factor, the ASI-3 total score may be used as a measure of general AS. ASI-3 provides measurement invariance across gender and age variables. The scale shows convergent validity. Thus, the ASI-3 is a reliable and valid assessment tool despite its limitations.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Esin Yılmaz Koğar

Author Biography

Esin Yılmaz Koğar works as a researcher at the Department of Educational Sciences, Faculty of Education, Niğde Ömer Halisdemir University, Niğde, Turkey. Her research interests include item response theory models, factor analysis, differential item functioning, psychology of adults and students, test development, and large scale assessments.

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