Abstract
Keywords
FACTOR 9.2 was developed for three reasons. First, exploratory factor analysis (FA) is still an active field of research although most recent developments have not been incorporated into available programs. Second, there is now renewed interest in semiconfirmatory (SC) solutions as suitable approaches to the complex structures are commonly found in item analysis (e.g., McDonald, 2000). Finally, some popular item response theory (IRT) models can be fitted as FA models by using an underlying-variables approach. A program incorporating developments along these lines was thought to be highly useful for practitioners.
Program Description
FACTOR 9.2 provides comprehensive modeling capacities, procedures, indices, and statistics. It can fit unidimensional and multidimensional versions of the standard linear FA model and of the two-parameter and graded-response normal-ogive IRT models. In this latter case, it provides both the factor-analytical parameterization (thresholds and loadings) and the IRT parameterization (difficulties and discriminations). For all the models, the multidimensional versions can be exploratory or SC. In the exploratory versions, 30 rotation procedures are available. In the SC versions, orthogonal and oblique rotations against a semispecified target can be performed (Browne, 1972). This second approach leads to independent-cluster-basis and bifactor solutions (among others) to be obtained. The estimation procedures available are unweighted least squares, maximum likelihood, and minimum rank factor analysis (principal components analysis can also be performed). FACTOR requires the number of factors to be specified. However, it also includes three procedures to help determine the most appropriate number: the minimum average partial test, parallel analysis (the classical approach, but also as proposed in Timmerman & Lorenzo-Seva, 2011), and the Hull method (Lorenzo-Seva, Timmerman, & Kiers, 2011).
At the individual level, FACTOR computes Anderson–Rubin factor scores for the linear model, and Bayes Expected a Posteriori (EAP) scores for the IRT models. In addition to the point estimates, FACTOR also reports standard errors (or PSD’s) and reliability estimates. In the linear model, it also provides a person-fit statistic (Ferrando, 2009).
A wide array of statistics are available in FACTOR for assessing the adequacy of the data and model-data fit. As far as the adequacy of the data is concerned, the program computes (a) univariate and multivariate descriptive statistics, (b) bar charts, and (c) measures of adequacy including Bartlett’s test and the Kaiser–Meyer–Olkin (KMO) index. As for model-data fit assessment, it provides a detailed analysis of the residuals as well as the goodness-of-fit chi-square statistic and a series of goodness-of-fit indices such as the goodness-of-fit index (GFI), comparative fit index (CFI), non-normed fit index (NNFI), and root mean square error of approximation (RMSEA).
FACTOR has been developed in Visual C++ to be run in Microsoft Windows operating systems. It has been tested in several computers with different processor chips and versions of Windows (XP/Vista/Windows 7/Windows 8). The number of variables and respondents the program can handle is not limited by software.
Availability and Accompanying Documentation
The program and accompanying material are available at no charge from the website http://psico.fcep.urv.cat/utilitats/factor. The documentation consists of (a) a brief guide to program usage, (b) various methodological technical reports produced by the authors, and (c) some program manuals produced by factor users.
Footnotes
Declaration of Conflicting Interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The development of Factor 9.2 was supported by a grant from the Spanish Ministry of Economy and Competitivity (PSI2011-22683), and from the Research and Information Society of the Catalan Ministry of Universities (2009SGR1549).