In structural equation modeling, application of the root mean square error of approximation (RMSEA), comparative fit index (CFI), and Tucker-Lewis index (TLI) highly relies on the conventional cutoff values developed under normal-theory maximum likelihood (ML) with continuous data. For ordered categorical data, unweighted least squares (ULS) and diagonally weighted least squares (DWLS) based on polychoric correlation matrices have been recommended in previous studies. Although no clear suggestions exist regarding the application of these fit indices when analyzing ordered categorical variables, practitioners are still tempted to adopt the conventional cutoff rules. The purpose of our research was to answer the question: Given a population polychoric correlation matrix and a hypothesized model, if ML results in a specific RMSEA value (e.g., .08), what is the RMSEA value when ULS or DWLS is applied? CFI and TLI were investigated in the same fashion. Both simulated and empirical polychoric correlation matrices with various degrees of model misspecification were employed to address the above question. The results showed that DWLS and ULS lead to smaller RMSEA and larger CFI and TLI values than does ML for all manipulated conditions, regardless of whether or not the indices are scaled. Applying the conventional cutoffs to DWLS and ULS, therefore, has a pronounced tendency not to discover model-data misfit. Discussions regarding the use of RMSEA, CFI, and TLI for ordered categorical data are given.

reliability, coefficient alpha, violation of assumptions, structural equation modeling,

reliability, structural equation modeling, factor analysis of categorical data, reliability of scales with Likert items,

This study examined the symptoms of posttraumatic stress disorder (PTSD), anxiety, and depression among 2,250 adolescents 6 months after the 2008 Wenchuan earthquake in China. Results showed that 15.8%, 40.5%, and 24.5% of participants reported clinical symptoms of PTSD, anxiety, and depression, respectively. Posttraumatic stress disorder, anxiety, and depression were highly comorbid. Risk factors for symptoms of the 3 disorders were female gender, older age, and earthquake disaster exposure. In addition, the interaction effects of residence (urban/rural) and number of siblings of study subjects on symptoms of the 3 disorders were examined. Implications of findings on intervention and prevention of mental health problems among adolescents after experiencing earthquake disasters are discussed.

In the lead article, Davenport, Davison, Liou, & Love demonstrate the relationship among homogeneity, internal consistency, and coefficient alpha, and also distinguish among them. These distinctions are important because too often coefficient alpha—a reliability coefficient—is interpreted as an index of homogeneity or internal consistency. We argue that factor analysis should be conducted before calculating internal consistency estimates of reliability. If factor analysis indicates the assumptions underlying coefficient alpha are met, then it can be reported as a reliability coefficient. However, to the extent that items are multidimensional, alternative internal consistency reliability coefficients should be computed based on the parameter estimates of the factor model. Assuming a bifactor model evidenced good fit, and the measure was designed to assess a single construct, omega hierarchical—the proportion of variance of the total scores due to the general factor—should be presented. Omega—the proportion of variance of the total scores due to all factors—also should be reported in that it represents a more traditional view of reliability, although it is computed within a factor analytic framework. By presenting both these coefficients and potentially other omega coefficients, the reliability results are less likely to be misinterpreted.