The present study describes an R function that implements six corrective procedures developed by Bartlett, Swain, and Yuan in the correction of 21 statistics associated with the omnibus Chi-square test, the residuals, or fit indices in confirmatory factor analysis (CFA) and structural equation modeling (SEM).

To evaluate the fit of a confirmatory factor analysis model, researchers often rely on fit indices such as SRMR, RMSEA, and CFI. These indices are frequently compared to benchmark values of 0.08, 0.06, and 0.96, respectively, established by Hu and Bentler (1999). However, these indices are affected by model characteristics and their sensitivity to…

Measures initially designed to be single-trait often yield data that are compatible with both an essentially unidimensional factor-analysis (FA) solution and a correlated-factors solution. For these cases, this article proposes an approach aimed at providing information for deciding which of the two solutions is the most appropriate and useful.…

American Educational Research Association (AERA) standards stipulate that researchers show evidence of the internal structure of instruments. Confirmatory factor analysis (CFA) is one structural equation modeling procedure designed to assess construct validity of assessments that has broad applicability for counselors interested in instrument…

A latent variable modeling procedure is discussed that can be used to test if two or more homogeneous multicomponent instruments with distinct components are measuring the same underlying construct. The method is widely applicable in scale construction and development research and can also be of special interest in construct validation studies.…

A promising "underlying bivariate normal" approach was proposed by Jöreskog and Moustaki for use in the factor analysis of ordinal data. This was a limited information approach that involved the maximization of a composite likelihood function. Its advantage over full-information maximum likelihood was that very much less computation was…

Item response theory (IRT) is a psychometric technique used in the development, evaluation, improvement, and scoring of multi-item scales. This pedagogical article provides the necessary information needed to understand how to conduct, interpret, and report results from two commonly used ordered polytomous IRT models (Samejima's graded…

Item-level information, such as difficulty and discrimination are invaluable to the test assembly, equating, and scoring practices. Estimating these parameters within the context of large-scale performance assessments is often hindered by the use of unbalanced designs for assigning examinees to tasks and raters because such designs result in very…

This article describes the logic and procedures behind testing for factorial invariance across groups in the context of construct validation. The procedures include testing for configural, measurement, and structural invariance in the framework of multiple-group confirmatory factor analysis (CFA). The "forward" (sequential constraint imposition)…

Linear factor analysis (FA) models can be reliably tested using test statistics based on residual covariances. We show that the same statistics can be used to reliably test the fit of item response theory (IRT) models for ordinal data (under some conditions). Hence, the fit of an FA model and of an IRT model to the same data set can now be…

This paper developed a Democratic Classroom Survey to measure students' perceived democratic environment of the classroom. Perceived democratic environment is one of the most important variables for understanding classroom activity and indeed any type of group activity, but actually measuring perceptions in an objective manner has been…

Most personality tests are made up of Likert-type items and analyzed by means of factor analysis (FA). In this type of application, the fit of the model at the level of individual respondents is almost never assessed. This article proposes procedures for assessing individual fit (scalability). The procedures are intended for the analysis of…

Recently, within the field of special education, attention has been accorded to the conceptualization and measurement of family outcomes. The Family Quality of Life (FQOL) Scale is an instrument that can be used to measure family outcomes for families who have children with disabilities, and it has been demonstrated to have psychometric validity.…

This article describes the development and validation of the Internalized Racial Oppression Scale (IROS) for Black individuals in 2 studies using a total sample of 468 Black college students. The IROS is intended to measure the degree to which racial oppression is internalized and replicated by Black individuals in the United States. An…

In a recent article, A. Maydeu-Olivares and D. L. Coffman (2006, see EJ751121) presented a random intercept factor approach for modeling idiosyncratic response styles in questionnaire data and compared this approach with competing confirmatory factor analysis models. Among the competing models was the CT-C(M-1) model (M. Eid, 2000). In an…