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Problem: Which method should I use to observe whether there is one common factor/component explaining six different measures (i.e., face and objects)?

Study: In this study, we have four measures of faces and two measures of objects. Of the 6 measures, half were measuring memory, and half were measuring perception. We want to determine if the underlying mechanism of these six measures is related to (1) faces or objects, and (2) memory or perception.

It would be great if anyone could provide some insights into which is a better method (PCA or EFA, maybe even CFA).

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As @Adrian Keister mentions in the comments, there are many posts on this site that cover the differences between principal component analysis (PCA) and exploratory factor analysis (EFA), e.g., What are the differences between Factor Analysis and Principal Component Analysis? & Is there any good reason to use PCA instead of efa. See these posts for more detail, though, because you have specific factor structures in mind that you want to test (e.g., a single-factor model, a two-factor model where Factor 1 = faces & Factor 2 = objects, a two-factor model where Factor 1 = memory & Factor 2 = perception) I would suggest using EFA over PCA if you decide to explore the factor structure. Though because you already have specific factor structures in mind, you could skip the EFA/PCA step and compare competing models using confirmatory factor analysis (CFA). For more information on why one may use CFA instead of EFA, see my answer to a previous question here. Finally, for an accessible discussion of factor analysis and its relationship to similar methods, such as PCA, I recommend reading Thompson, 2004.

References

Thompson, B. (2004). Exploratory and confirmatory factor analysis. American Psychological Association.

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