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Exploratory Factor Analysis and Theory Generation in Psychology

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Abstract

Exploratory factor analysis is a statistical method widely used in quantitative psychology for the construction of scales and measurement instruments. It aims to reduce the complexity of a data set and explain the common and unique variance using latent variables. In introductory textbooks, exploratory factor analysis is generally presented in contrast to confirmatory factor analysis as a theory- or a hypothesis-generating process that does not require prior background, theory or hypothesis to be performed. The aim of the present paper is to analyze this claim and clarify in which sense exploratory factor analysis is theory-laden. We provide a careful examination of the concepts it involves and thereby establish a clear limitation of the epistemic scope of exploratory factor analysis.

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Notes

  1. See Comrey (1988) for methodological considerations regarding scale development.

  2. Currently, CFA is used to refer to confirmatory factor analysis. It should be noted, however, that CFA has also been used previously in the psychology literature as an acronym for common factor analysis, which is, basically, factor analysis.

  3. See Borsboom (2008) on the distinction between observed and latent variables.

  4. See Stevens (1946) for the different types of scales and their relationship with categorical and continuous data, as well as Mellenbergh (1994) for different types of items.

  5. EFA should not be confused with another different (although comparable) statistical technique known as principal component analysis (cf. Borgatta and Stull 1986). In comparison with EFA, principal component analysis rather models the principal components as linear combinations of the observed variables (see Jolliffe and Morgan 1992). Principal component analysis, which is a descriptive statistical tool, is also used in psychological research, mainly in psychometrics (see for example Jolliffe 2002, ten Berge et al. 1992, Kiers and Berge 1994, ten Berge and Kiers 1997 and Kiers and Mechelen 2001). The main difference between principal component analysis and EFA is that the latter accounts for potential error in measurement.

  6. Many factor extraction techniques assume that the variables are continuous and normally distributed (Byrne 2012, p.128-9). However, these assumptions are not necessary conditions to perform an EFA. First, different estimators have been developed to deal with categorical data and, further, if the data approximates a normal distribution, then not addressing the fact that the data is categorical is likely negligible (see Byrne 2012, pp.128-32). Second, there are extraction techniques that address the violation of the assumption of normality (see Flora et al. 2012, pp.10-1). See Michell (1997, 2003, 2004) for a criticism of the violation of the assumption of continuity as well as Borsboom and Mellenbergh (2004) for an answer to Michell.

  7. See Velicer and Jackson (1990a, 1990b) and Finch and West (1997).

  8. An eigenvalue represents the proportion of the variance explained by the factor (cf. Tabachnick and Fidell 2013).

  9. When the variances of observed and latent variables are equal to one and factors are orthogonal, the loading of a variable on a factor is the correlation between the two (Tabachnick and Fidell 2013, p.614).

  10. In contrast, principal component analysis provides a formative measurement model.

  11. Formally, CFA generates an estimated population covariation matrix using the hypothesized model and determines whether it fits the covariation matrix of the sample.

  12. A formal definition will be provided below.

  13. During CFA, one can add covariation relations between items as well as covariation relations between factors. Hence, formally, measurement models for CFA are defined on the grounds of \(\mathcal {R}_{M}\subseteq \mathcal {V}\times \mathcal {V}_{j}, \text { with } \mathcal {V}_{j} \in \mathcal {V}_{\times } \). The measurement model provided by EFA, however, only yields relationships between items and factors.

  14. As a caveat, the reader should keep in mind that we are not arguing in favor of a specific terminology that we think should be used in psychology. The aim of this paper is to examine the extent of EFA’s theory-ladenness as it is used in psychological research during scale development. Accordingly, we adopt the aforementioned definitions only to make our analysis as explicit and non-ambiguous as possible. Though some readers might disagree with the terminology we use, the emphasis should rather be on the conclusions we reach and the notions we analyze.

  15. Given that a conceptual background is understood as a set, its size corresponds to its cardinality.

  16. This would not be the case for principal component analysis, which is a tool that aims to describe samples (cf. Kiers and Mechelen 2001).

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Acknowledgments

I am indebted to the comments, suggestions, and criticisms made by anonymous referees on previous drafts of this paper, as well as those made by the editor. Thanks also to Stephan Hartmann and Gregory Gandenberger for valuable comments and suggestions. This research was financially supported by the Social Sciences and Humanities Research Council of Canada.

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  1. Munich Center for Mathematical Philosophy, Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, D-80539, München, Germany

    Clayton Peterson

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Peterson, C. Exploratory Factor Analysis and Theory Generation in Psychology. Rev.Phil.Psych. 8, 519–540 (2017). https://doi.org/10.1007/s13164-016-0325-0

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