Running head: CFA OF TDI AND STICSA 1. p Factor or Negative Emotionality? Joint CFA of Internalizing Symptomology

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1 Running head: CFA OF TDI AND STICSA 1 p Factor or Negative Emotionality? Joint CFA of Internalizing Symptomology Caspi et al. (2014) reported that CFA results supported a general psychopathology factor, p, as the primary explanation for individual differences in psychopathology symptoms. One conclusion Caspi et al. reached is that p may explain, at least in part, why it has been difficult to identify etiological factors that convey unique risk for specific disorders. Low diagnostic specificity has been a long-standing issue in clinical psychology, particularly in differentiating between internalizing disorders (e.g., Kendler, 2004). Consequently, the purpose of the present study was to apply similar techniques to determine the degree to which individual differences in anxiety and depression may be better explained by a general factor. CFA of the Teate Depression Inventory (TDI; Balsamo et al., 2014) and the State-Trait Inventory of Cognitive and Somatic Anxiety-Trait (STICSA-Trait; Ree et al., 2008) were estimated from the item polychoric correlation matrix using weighted least squares means and variances estimation for a random sample of 694 college students (64.4% female) enrolled in a large public university. Joint CFA of the TDI and STICSA-Trait were performed after confirming the factor structure in each measure independently. Two joint CFA factor models were compared: a) a hierarchical factor model with three first-order factors (i.e., depression, cognitive anxiety, and somatic anxiety) and one second-order general factor, consistent with the notion of an internalizing problems factor, and b) a bifactor model with three orthogonal group factors (i.e., depression, cognitive anxiety, and somatic anxiety) and an orthogonal breadth factor. Conventional criteria for adequate model fit (Hu & Bentler, 1999) and relative fit (Chen, 2007; Cheung & Rensvold, 2002) were applied. Model-based factor reliability and replicability coefficients were also computed (Brunner et al., 2012; Hancock & Mueller, 2001) as well as indices of potential bias introduced from treating the combined TDI and STICSA-Trait items as

2 Running head: CFA OF TDI AND STICSA 2 measuring a single construct (ten Berge & Sočan, 2004; Bonifay et al., 2015; Reise et al., 2013; Sijtsma, 2009). Independent CFAs of each measure resulted in adequate fit for the preferred model (Models 1 and 3); and, the bifactor model exhibited the best fit for the joint CFA (Model 5; see Table 1). Model-based reliability estimates revealed that % of the total variance in TDI and STICSA-Trait scores was due to group factor variance; whereas, general factor variance explained > 50% of individual differences in TDI and STICSA-Trait scores, similar to Caspi et al. (2014). High H indexes for the general, somatic anxiety, and depression factors indicated adequate factor replicability. However, high ECV and PUC values suggest minimal bias would result from applying a unidimensional model to the combined TDI and STICSA-Trait items. Moreover, rather than a p factor or internalizing problems factor per se, we suggest that negative emotionality may better define the breadth factor a suggestion consistent with high negative affect underlying depression and anxiety in models of developmental psychopathology. Session attendees will learn about: (a) the utility of bifactor models in theory development, (b) interpretation of model-based factor coefficients, and (c) implications for a general factor of negative emotionality.

3 Running head: CFA OF TDI AND STICSA 3 References Balsamo, M., Giampaglia, G., & Saggino, A. (2014). Building a new Rasch-based self-report inventory of depression. Neuropsychiatric Disease and Treatment, 10, doi: /ndt.s53425 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 Caspi, A., Houts, R. M., Belsky, D. W., Goldman-Mellor, S. J., Harrington, H., Israel, S., Moffitt, T. E. (2014). The p factor: One general psychopathology factor in the structure of psychiatric disorders? Clinical Psychological Science, 2, doi: / 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 Hancock, G. R., & Mueller, R. O. (2001). Rethinking construct reliability within latent variable systems. In R. Cudek, S. Du Toit, D. Sorbum, and K. G. Joreskog (Eds.,) Structural equation modeling: Present and future (pp ). Lincolnwood, IL: Scientific Software International.

4 Running head: CFA OF TDI AND 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: / Kendler, K. S. (2004). Major depression and generalised anxiety disorder. FOCUS, 2, doi: /foc 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: / 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 TDI AND STICSA 5 Table 1. Fit Statistics for Joint Confirmatory Factor Analyses of the Teate Depression Inventory (TDI) and the State-Trait Inventory of Cognitive and Somatic Anxiety-Trait (STICSA-Trait) for a Sample of 694 College Students χ 2 df CFI SRMR RMSEA 90% CI χ 2 CFI RMSEA Model Independent CFA 1 TDI 1f STICSA-T 1f STICSA-T 2f * Joint CFA 4 TDI and STICSA-T H-O TDI and STICSA-T Bf * Note. Model 1 = one-factor model of the TDI; Model 2 = one-factor model of the STICSA-Trait; Model 3 = two correlated factors model of the STICSA-Trait; Model 4 = higher-order factor model of the combined items of the TDI and STICSA-Trait with three first-order factors (i.e., somatic anxiety, cognitive anxiety, and depression) and a single second-order factor (i.e., negative emotions); Model 5 = bifactor model of the combined items of the TDI and STICSA-Trait with three first-order group factors (i.e., somatic anxiety, cognitive anxiety, and depression) and a single first-order breadth factor (i.e., negative emotions); 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; χ 2 = change in chi-square value; CFI = change in CFI; RMSEA = change in RMSEA.

6 Running head: CFA OF TDI AND STICSA 6 Table 2. Sources of Variance for the Joint Confirmatory Factor Analysis of the Teate Depression Inventory (TDI) and the State-Trait Inventory of Cognitive and Somatic Anxiety-Trait (STICSA-Trait) Estimated from a Bifactor Model NE Cognitive Somatic Depression Item b Var b Var b Var b Var h 2 u 2 STICSA STICSA STICSA STICSA STICSA STICSA STICSA STICSA STICSA STICSA STICSA STICSA STICSA STICSA STICSA STICSA STICSA STICSA STICSA STICSA STICSA TDI TDI TDI TDI TDI Table 2. (Continued)

7 Running head: CFA OF TDI AND STICSA 7 NE Cognitive Somatic Depression Item b Var b Var b Var b Var h 2 u 2 TDI TDI TDI TDI TDI TDI TDI TDI TDI TDI TDI TDI TDI TDI TDI TDI % Total variance % Common variance ω/ω s ω h /ω hs H PUC.640 Note. b = standardized loading of item on factor; Var = percent of variance explained in the item; h 2 = communality; u 2 = uniqueness; 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. % Common variance provides the percentage of explained common variance (ECV).

8 Running head: CFA OF TDI AND STICSA 8 Somatic Anxiety Cognitive Anxiety Depression 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 D 1 D 2 D 3 D 4 D 5 D 6 D 7 D 8 D 9 D 10 D 11 D 12 D 13 D 14 D 15 D 16 D 17 D 18 D 19 D 20 D 21 Negative Emotions Figure 1. Path model for the bifactor model of the joint CFA of the Teate Depression Inventory (TDI) and the State-Trait Inventory of Cognitive and Somatic Anxiety-Trait (STICSA-Trait) for a sample of 694 college students. Standardized factor loadings were omitted for space considerations and can be found in Table 2. A1,2,3 k = STICSA-Trait items; D1,2,3 k = TDI items. STICSA-Trait items 2, 6, 7, 8, 12, 14, 15, 18, 20, and 21 measure somatic anxiety symptoms and STICSA-Trait items 3, 4, 5, 9, 10, 11, 13, 16, 17, and 19 measure cognitive anxiety symptoms (Ree et al., 2008).