We show how to estimate a Cronbach's alpha reliability coefficient in Stata after running a principal component or factor analysis. Alpha evaluates to what extent items measure the same underlying content when the items are combined into a scale or used for latent variable. Stata allows for testing the reliability coefficient (alpha) of a scale only when all items receive homogenous weights. We present a user-written program that computes reliability coefficients when implementation of principal component or factor analysis shows heterogeneous item loadings. We use data on management practices from Bloom and Van Reenen (2010) to explain how to implement and interpret the adjusted internal consistency measure using afa.
Sufficient conditions for mean square convergence of factor predictors in common factor analysis are given by Guttman, by Williams, and by Schneeweiss and Mathes. These conditions do not hold for confirmatory factor analysis or when an error variance equals zero (Heywood cases). Two sufficient conditions are given for the three basic factor predictors and a predictor from rotated principal components analysis to converge to the factors of the model for confirmatory factor analysis, including Heywood cases. For certain model specifications the conditions are necessary. The conditions are sufficient for the existence of a unique true factor. A geometric interpretation is given for factor indeterminacy and mean square convergence of best linear factor prediction.
MULTIFILE
Objective: To examine the underlying factor structure and psychometric properties of the Assessment of Self-management in Anxiety and Depression (ASAD) questionnaire, which was specifically designed for patients with (chronic) anxiety and depressive disorders. Moreover, this study assesses whether the number of items in the ASAD can be reduced without significantly reducing its precision. Methods: The ASAD questionnaire was completed by 171 participants across two samples: one sample comprised patients with residual anxiety or depressive symptoms, while the other consisted of patients who have been formally diagnosed with a chronic anxiety or depressive disorder. All participants had previously undergone treatment. Both exploratory (EFA) and confirmatory factor analyses (CFA) were conducted. Internal consistency and test–retest reliability were also assessed. Results: Both EFA and CFA indicated three solid factors: Seeking support, Daily life strategies and Taking ownership [Comparative Fit Index = 0.80, Tucker Lewis Index = 0.78, Root Mean Square Error of Approximation = 0.09 (CI 0.08–1.00), Standardized Root Mean Square Residual = 0.09 ($2 = 439.35, df = 168)]. The ASAD was thus reduced from 45 items to 21 items, which resulted in the ASAD-Short Form (SF). All sub-scales had a high level of internal consistency (> a = 0.75) and test–retest reliability (ICC > 0.75). Discussion: The first statistical evaluation of the ASAD indicated a high level of internal consistency and test–retest reliability, and identified three distinctive factors. This could aid patients and professionals’ assessment of types of self-management used by the patient. Given that this study indicated that the 21-item ASAD-SF is appropriate, this version should be further explored and validated among a sample of patients with (chronic or partially remitted) anxiety and depressive disorders. Alongside this, to increase generalizability, more studies are required to examine the English version of the ASAD within other settings and countries.
