Exploratory factor analysis (EFA) is one of the most commonly-reported quantitative methodology in the social sciences, yet much of the detail regarding what happens during an EFA remains unclear. The goal of this brief technical note is to explore what "rotation" is, what exactly is rotating, and why we use rotation when performing…

The full-information maximum likelihood (FIML) method makes it possible to estimate and analyze structural equation models (SEM) even when data are partially missing, enabling incomplete data to contribute to model estimation. The cornerstone of FIML is the missing-at-random (MAR) assumption. In (unidimensional) computerized adaptive testing…

Exploratory factor analysis (EFA) methods are used extensively in the field of assessment and evaluation. Due to EFA's widespread use, common methods and practices have come under close scrutiny. A substantial body of literature has been compiled highlighting problems with many of the methods and practices used in EFA, and, in response, many…

Multiple-group confirmatory factor analysis (MG-CFA) is among the most productive extensions of structural equation modeling. Many researchers conducting cross-cultural or longitudinal studies are interested in testing for measurement and structural invariance. The aim of the present paper is to provide a tutorial in MG-CFA using the freely…

In several studies unit-weighted sum scales based on the unweighted sum of items are derived from the pattern of salient loadings in confirmatory factor analysis. The problem of this procedure is that the unit-weighted sum scales imply a model other than the initially tested confirmatory factor model. In consequence, it remains generally unknown…

"R" (R Development Core Team, 2011) is a very powerful tool to analyze data, that is gaining in popularity due to its costs (its free) and flexibility (its open-source). This article gives a general introduction to using "R" (i.e., loading the program, using functions, importing data). Then, using data from Canivez, Konold, Collins, and Wilson…

The uses and methodology of factor analysis are widely debated and discussed, especially the issues of rotational use, methods of confirmatory factor analysis, and adequate sample size. The variety of perspectives and often conflicting opinions can lead to confusion among researchers about best practices for using factor analysis. The focus of the…

Exploratory factor analysis (EFA) is a common technique utilized in the development of assessment instruments. The key question when performing this procedure is how to best estimate the number of factors to retain. This is especially important as under- or over-extraction may lead to erroneous conclusions. Although recent advancements have been…

Student learning and program effectiveness is often assessed using rubrics. While much time and effort may go into their creation, it is equally important to assess how effective and efficient the rubrics actually are in terms of measuring competencies over a number of criteria. This study demonstrates the use of common factor analysis to identify…

The present study was designed to test for item order effects by measuring four distinct constructs that contribute substantively to anxiety-related psychopathology (i.e., anxiety sensitivity, fear of negative evaluation, injury/illness sensitivity, and intolerance of uncertainty). Participants (n = 999; 71% women) were randomly assigned to…

Establishing model parsimony is an important component of structural equation modeling (SEM). Unfortunately, little attention has been given to developing systematic procedures to accomplish this goal. To this end, the current study introduces an innovative application of the jackknife approach first presented in Rensvold and Cheung (1999). Unlike…

Exploratory Factor Analysis (EFA) is a powerful and commonly-used tool for investigating the underlying variable structure of a psychometric instrument. However, there is much controversy in the social sciences with regard to the techniques used in EFA (Ford, MacCallum, & Tait, 1986; Henson & Roberts, 2006) and the reliability of the outcome.…

This paper discusses how a seldom-used statistical procedure, recursive regression (RR), can numerically and graphically illustrate data-driven nonlinear relationships and interaction of variables. This routine falls into the family of exploratory techniques, yet a few interesting features make it a valuable compliment to factor analysis and…

Following an exploratory factor analysis, factor scores may be computed and used in subsequent analyses. Factor scores are composite variables which provide information about an individual's placement on the factor(s). This article discusses popular methods to create factor scores under two different classes: refined and non-refined. Strengths and…