Sample size recommendations in confirmatory factor analysis (CFA) have recently shifted away from observations per variable or per parameter toward consideration of model quality. Extending research by Marsh, Hau, Balla, and Grayson (1998), simulations were conducted to determine the extent to which CFA model convergence and parameter estimation are affected by n as well as by construct reliability, which is a measure of measurement model quality derived from the number of indicators per factor (p/f) and factor loading magnitude. Results indicated that model convergence and accuracy of parameter estimation were affected by n and by construct reliability within levels of n. Sample size recommendations for applied researchers using CFA are presented herein as a function of relevant design characteristics.

The accuracy of AIC and BIC is evaluated under simulated multiple regression conditions, varying number of total and valid predictors, R², and n. AIC and BIC were increasingly accurate as n increased and as total predictors decreased. Interactions of the ratio of valid/total predictors affected accuracy.

The purpose of this article is to demonstrate how hierarchical linear modeling (HLM) can be used to enhance visual analysis of single-case research (SCR) designs. First, the authors demonstrated the use of growth modeling via HLM to augment visual analysis of a sophisticated single-case study. Data were used from a delayed multiple baseline design, across groups of participants, with an embedded changing criterion design in a single-case literacy project for students with moderate intellectual disabilities (MoID). Visual analysis revealed a functional relation between instruction and sight-word acquisition for all students. Growth HLM quantified relations at the group level and revealed additional information that included statistically significant variability among students at initial-baseline probe and also among growth trajectories within treatment subphases. Growth HLM showed that receptive vocabulary was a significant predictor of initial knowledge of sight words, and print knowledge significantly predicted growth rates in both treatment subphases. Next, to show the benefits of combining these methodologies to examine a different behavioral topography within a more commonly used SCR design, the authors used repeated-measures HLM and visual analysis to examine simulated data within an ABAB design. Visual analysis revealed a functional relation between a hypothetical intervention (e.g., token reinforcement) and a hypothetical dependent variable (e.g., performance of a target response). HLM supported the existence of a functional relation through tests of statistical significance and detected significant variance among participants' response to the intervention that would be impossible to identify visually. This study highlights the relevance of these procedures to the identification of evidence-based interventions.

The purpose of our study was to examine the role that child sexual abuse may play in body surveillance and sexual risk behaviors among undergraduate women. First, a measured variable path analysis was conducted, which assessed the relations among a history of child sexual abuse, body surveillance, and sexual risk behaviors. Furthermore, body shame, sexual selfefficacy, and alexithymia were examined as intervening variables. Second, a multigroup path analysis was conducted comparing the hypothesized models applied to data from 556 ethnically diverse women. Within the overall model, results revealed that a history of child sexual abuse and body surveillance were not related to one another, but both variables were directly related to sexual risk behaviors. Moreover, body shame mediated the relationship between body surveillance and alexithymia, and alexithymia mediated the relationship between body shame and sexual self-efficacy. Child sexual abuse history was related directly with body shame and alexithymia. Results from the multigroup path analysis revealed that the model was invariant between African American and White women, although one difference emerged: body surveillance significantly predicted alexithymia in White, but not African American, women. Furthermore, White, Asian/Pacific Islander, and Hispanic/Latina women demonstrated more body shame than African American women, and White women endorsed higher levels of sexual self-efficacy than African American and Asian/Pacific Islander women. Counseling interventions that seek to decrease alexithymic symptoms, body surveillance, and body shame, while also increasing sexual self-efficacy, seem especially warranted.

Douglas, Roussos, and Stout introduced the concept of differential bundle functioning (DBF) for identifying the underlying causes of differential item functioning (DIF). In this study, reference group was simulated to have higher mean ability than the focal group on a nuisance dimension, resulting in DIF for each of the multidimensional items that, when examined together, produced DBF. The empirical power and the Type I error of the Simultaneous Item Bias Test for DBF analysis were examined under various sample sizes, ratios of reference to focal group sizes, correlations between target and nuisance dimensions, magnitudes of DIF/ DBF, test lengths, percentages of test items in the bundle, and item discriminations. Power was generally high in cells with larger DIF magnitudes, higher percentages of items in the bundle, larger sample sizes, and with the nuisance dimension having a higher discrimination than the target dimension. Type I error rates approximated the nominal alpha rate for all conditions.