Although many textbooks on multivariate statistics discuss the common factor analysis model, few of these books mention the problem of factor score indeterminacy (FSI). Thus, many students and contemporary researchers are unaware of an important fact. Namely, for any common factor model with known (or estimated) model parameters, infinite sets of…

When comparing relations and means of latent variables, it is important to establish measurement invariance (MI). Most methods to assess MI are based on confirmatory factor analysis (CFA). Recently, new methods have been developed based on exploratory factor analysis (EFA); most notably, as extensions of multi-group EFA, researchers introduced…

The procedures of carrying out factorial invariance to validate a construct were well developed to ensure the reliability of the construct that can be used across groups for comparison and analysis, yet mainly restricted to the frequentist approach. This motivates an update to incorporate the growing Bayesian approach for carrying out the Bayesian…

There has been increasing interest in applying integrative data analysis (IDA) to analyze data across multiple studies to increase sample size and statistical power. Measures of a construct are frequently not consistent across studies. This article provides a tutorial on the complex decisions that occur when conducting harmonization of measures…

Factor loadings and item discrimination parameters play a key role in scale construction. A multitude of heuristics regarding their interpretation are hardwired into practice--for example, neglecting low loadings and assigning items to exactly one scale. We challenge the common sense interpretation of these parameters by providing counterexamples…

Exploratory factor analysis (EFA) is a data reduction technique used to condense data into smaller sets of summary variables by identifying underlying factors potentially accounting for patterns of collinearity among said variables. Using an illustrative example, the 5 general steps of EFA are described with best practices for decision making…

Socioscientific issues, issues that center on the intersection between scientific and social problems in real-world contexts, are valuable tools to use in science instruction due to their association with gains in scientific literacy, argumentation skills, and content knowledge. However, due to their complex nature, crafting instruction using…

Since Cronbach's (1951) elaboration of a from its introduction by Guttman (1945), this coefficient has become ubiquitous in characterizing assessment instruments in education, psychology, and other social sciences. Also ubiquitous are caveats on the calculation and interpretation of this coefficient. This article summarizes a recent contribution…

This paper presents heuristic explanations of factor scores, structure coefficients, and communality coefficients. Common misconceptions regarding these topics are clarified. In addition, (a) the regression (b) Bartlett, (c) Anderson-Rubin, and (d) Thompson methods for calculating factor scores are reviewed. Syntax necessary to execute all four…

Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger and Swineford ("Psychometrika" 47:41-54, 1937). The bi-factor model has a general factor, a number of group factors, and an explicit bi-factor structure. Jennrich and Bentler ("Psychometrika" 76:537-549, 2011) introduced an exploratory form of bi-factor…

In exploratory or unrestricted factor analysis, all factor loadings are free to be estimated. In oblique solutions, the correlations between common factors are free to be estimated as well. The purpose of this article is to show how likelihood-based confidence intervals can be obtained for rotated factor loadings and factor correlations, by…

Bifactor latent structures were introduced over 70 years ago, but only recently has bifactor modeling been rediscovered as an effective approach to modeling "construct-relevant" multidimensionality in a set of ordered categorical item responses. I begin by describing the Schmid-Leiman bifactor procedure (Schmid & Leiman, 1957) and highlight its…

Few instruments have been designed specifically to address the needs of college counseling centers. This article reviews existing instruments and presents 4 studies that describe the development and psychometric properties of a new instrument, the Counseling Center Assessment of Psychological Symptoms-62 (CCAPS-62). Study 1 describes the initial…

Multiracial Americans represent a rapidly growing population (Shih & Sanchez, 2009); however, very little is known about the types of challenges and resilience experienced by these individuals. To date, few psychological measures have been created specifically to investigate the experiences of multiracial people. This article describes 2…

Psychometric evaluation of presenting problem checklists is vital, given increasing clinical severity among college students. However, checklist research has focused on students at public universities and utilized inappropriate methodologies when doing so. It is unclear whether checklists used at academically selective universities reliably and…