Running head: CFA OF STICSA 1. Model-Based Factor Reliability and Replicability of the STICSA

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1 Running head: CFA OF STICSA 1 Model-Based Factor Reliability and Replicability of the STICSA The State-Trait Inventory of Cognitive and Somatic Anxiety (STICSA; Ree et al., 2008) is a new measure of anxiety symptoms for adolescents and adults. The structure of the scale has been cross-validated in samples of college students (Roberts et al., 2016; Seng et al., 2015), middle-aged older adults (Balsamo et al., 2015), and adult psychiatric outpatients receiving treatment for anxiety disorders (Grös et al., 2007). The STICSA is gaining popularity among researchers (e.g., Elwood et al., 2012) as a psychometrically sound measure of anxiety. However, the dimensionality of the scale has not been evaluated using modern methods of factor reliability and replicability estimation (Reise, 2012). Consequently, the purpose of the present study was to fill this gap in the literature by using bifactor modeling techniques to further evaluate the multidimensionality of the scale. CFA of the STICSA were estimated from the item polychoric correlation matrix using weighted least squares means and variances estimation for a random sample of 642 college students (64.3% female) enrolled at a large public university. Participants were administered the STICSA-Trait and STICSA-State in a counterbalanced order. Three factor models were compared for each version of the scale: a one factor model and a two-correlated factors model as per Ree et al. (2008); and, a bifactor model with two orthogonal group factors (i.e., cognitive anxiety and somatic anxiety) and an orthogonal general breadth factor. Conventional criteria to determine adequate model fit and relative fit were applied (Chen, 2007; Cheung & Rensvold, 2002; Hu & Bentler, 1999). In addition, model-based factor reliability and replicability coefficients were computed from the bifactor model (Brunner et al., 2012) as well as indices of bias that could potentially be introduced by forcing a unidimensional model (a one factor model

2 Running head: CFA OF STICSA 2 of anxiety) to the multidimensional dataset (ten Berge & Sočan, 2004; Bonifay et al., 2015; Reise et al., 2013; Sijtsma, 2009). Fit statistics for all factor models are contained in Table 1. The two correlated factors model (Models 2 and 5) fit better than the one factor model for both the STICSA-State and the STICSA-Trait. In addition, the bifactor model (Models 3 and 6) fit both versions of the scale equally well. Model-based factor reliability estimates indicated that general factor variance explained > 50% of the variance in cognitive anxiety and somatic anxiety scores on both versions of the scale; whereas, variance in the cognitive anxiety and somatic anxiety factors explained % and % of variance in corresponding STICSA scores, respectively. The high H index on the general and somatic anxiety factors for both versions of the scale indicates adequate factor replicability across studies. However, high ECV and PUC values for the general factor on the STICSA-State and STICSA-Trait indicate minimal bias would result from interpreting the STICSA as a unidimensional measure of anxiety. Session attendees will learn about: (a) the utility of bifactor models in scale development, (b) interpretation of model-based factor reliability and replicability coefficients, and (c) the implications for measuring anxiety symptoms.

3 Running head: CFA OF STICSA 3 References Balsamo, M., Innamorati, M., Van Dam, N. T., Carlucci, L., & Saggino, A. (2015). Measuring anxiety in the elderly: Psychometric properties of the state trait inventory of cognitive and somatic anxiety (STICSA) in an elderly Italian sample. International Psychogeriatrics, 27, doi: /s Bonifay, W. E., Reise, S. P., Scheines, R., & Meijer, R. R. (2015). When are multidimensional data unidimensional enough for structural equation modeling? An evaluation of the DETECT multidimensionality index. Structural Equation Modeling: A Multidisciplinary Journal, 22, doi: / Brunner, M., Nagy, G., & Wilhelm, O. (2012). A tutorial on hierarchically structured constructs. Journal of Personality, 80, doi: /j x Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling, 14, doi: / Cheung, G. W., & Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 9, doi: /s sem0902_5 Elwood, L. S., Wolitzky-Taylor, K., & Olatunji, B. O. (2012). Measurement of anxious traits: a contemporary review and synthesis. Anxiety, Stress and Coping, 25, doi: / Grös, D. F., Antony, M. M., Simms, L. J., & McCabe, R. E. (2007). Psychometric properties of the State-Trait Inventory for Cognitive and Somatic Anxiety (STICSA): Comparison to the State-Trait Anxiety Inventory (STAI). Psychological Assessment, 19, doi: /

4 Running head: CFA OF STICSA 4 Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6, doi: / Ree, M. J., French, D., MacLeod, C., & Locke, V. (2008). Distinguishing cognitive and somatic dimensions of state and trait anxiety: Development and validation of the State-Trait Inventory for Cognitive and Somatic Anxiety (STICSA). Behavioural and Cognitive Psychotherapy, 36. doi: /s Reise, S. P., Scheines, R., Widaman, K. F., & Haviland, M. G. (2013). Multidimensionality and structural coefficient bias in structural equation modeling: A bifactor perspective. Educational and Psychological Measurement, 73, doi: / Reise, S. P. (2012). The rediscovery of bifactor measurement models. Multivariate Behavioral Research, 47, doi: / Roberts, K. E., Hart, T. A., & Eastwood, J. D. (2016). Factor structure and validity of the State- Trait Inventory for Cognitive and Somatic Anxiety. Psychological Assessment, 28, doi: /pas Seng, T. C., Wei, L. J., Yan, L. M., Yee, P. J., & Ying, T. T. (2015). Validation of the State-Trait Inventory for Cognitive and Somatic Anxiety in a sample of Malaysian undergraduates. Presented at the USM International Conference on Social Sciences. Sijtsma, K. (2009). On the use, the misuse, and the very limited usefulness of Cronbach s alpha. Psychometrika, 74, doi: /s ten Berge, J. M. F., & Sočan, G. (2004). The greatest lower bound to the reliability of a test and the hypothesis of unidimensionality. Psychometrika, 69, doi: /bf

5 Running head: CFA OF STICSA 5 Table 1. Fit Statistics for Confirmatory Factor Analyses of the State-Trait Inventory of Cognitive and Somatic Anxiety (STICSA) for a Sample of 642 College Students χ 2 df CFI SRMR RMSEA 90% CI CFI RMSEA Model STICSA-State 1 STICSA-State 1f STICSA-State 2f STICSA-State bifactor STICSA-Trait 4 STICSA-Trait 1f STICSA-Trait 2f STICSA-Trait bifactor Note. Model 1 = one factor model of the STICSA-State; Model 2 = two correlated factors model of the STICSA-State; Model 3 = bifactor model of the STICSA-State with two orthogonal group factors (i.e., cognitive anxiety and somatic anxiety) and one orthogonal general breadth factor; Model 4 = one factor model of the STICSA-Trait; Model 5 = two correlated factors model of the STICSA-Trait; Model 6 = bifactor model of the STICSA-Trait with two orthogonal group factors (i.e., cognitive anxiety and somatic anxiety) and one orthogonal general breadth factor; χ 2 = chi-square test statistic; df = degrees of freedom; CFI = comparative fit index; SRMR = root mean square residual; RMSEA = root mean square error of approximation; 90% CI = 90% confidence interval of the root mean square error of approximation; CFI = change in the CFI; RMSEA = change in the RMSEA.

6 Running head: CFA OF STICSA 6 Table 2. Sources of Variance for the Bifactor Model of the State-Trait Inventory of Cognitive and Somatic Anxiety-State Scale (STICSA-State) for a Sample of 642 College Students General Cognitive anxiety Somatic anxiety Item b Var b Var b Var h 2 u 2 STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S STICSA-S % Total variance % Common variance (ECV) ω/ω s ω h /ω hs H PUC.524

7 Running head: CFA OF STICSA 7 Note. b = standardized loading of item on factor; Var = percent of variance explained in the item; h 2 = communality; u 2 = uniqueness; ECV = explained common variance; ω = omega coefficient; ω s = omega subscale coefficient; ω h = omega hierarchical coefficient; ω hs = omega hierarchical subscale coefficient; H = H index of factor replicability; PUC = percentage of uncontaminated correlations.

8 Running head: CFA OF STICSA 8 Table 3. Sources of Variance for the Bifactor Model of the State-Trait Inventory of Cognitive and Somatic Anxiety-Trait Scale (STICSA-Trait) for a Sample of 642 College Students General Cognitive anxiety Somatic anxiety Item b Var b Var b Var h 2 u 2 STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T STICSA-T % Total variance % Common variance (ECV) ω/ω s ω h /ω hs H PUC.524

9 Running head: CFA OF STICSA 9 Note. b = standardized loading of item on factor; Var = percent of variance explained in the item; h 2 = communality; u 2 = uniqueness; ECV = explained common variance; ω = omega coefficient; ω s = omega subscale coefficient; ω h = omega hierarchical coefficient; ω hs = omega hierarchical subscale coefficient; H = H index of factor replicability; PUC = percentage of uncontaminated correlations.

10 Running head: CFA OF STICSA 10 Somatic Anxiety Cognitive Anxiety A 1 A 2 A 3 A 4 A 5 A 6 A 7 A 8 A 9 A 10 A 11 A 12 A 13 A 14 A 15 A 16 A 17 A 18 A 19 A 20 A 21 Negative Emotions Figure 1. Path model for the bifactor model of the State-Trait Inventory of Cognitive and Somatic Anxiety (STICSA) for a sample of 642 college students. Standardized factor loadings were omitted for space considerations and can be found in Tables 2 (STICSA- State) and Table 3 (STICSA-Trait). A1,2,3 k = STICSA items. Items 1, 2, 6, 7, 8, 12, 14, 15, 18, 20, and 21 measure somatic anxiety and items 3, 4, 5, 9, 10, 11, 13, 16, 17, and 19 measure cognitive anxiety.