Dear Rene,

Factor analysis is of 2 type. Exploratory factor analysis and Confirmatory factor analysis.

In CFA, the test is to check, if some set of observed data can be predicted from the known factor model, establish the validity of the factor model,compare 2 models, test significance of and relationship between factor models.

EFA, is used to reduce data to summary variables and explore the underlying theoretical structure of the phenomena. It is used to identify the relationship between the variables and respondent. It is commonly used by researchers when developing a Scale and serves to identify a set of latent constructs.

PCA is a method of factor extraction, which is an integrated part/ a sub step of EFA.

So, EFA and PCA can not be separated.

In your case,since the items has already been identified by you and now you are trying only to identify the principal factors from those items, PCA is your next step.

Hi Rene,

I have my personal opinion of the use of PCA and, in companion with EFA, I see a value if you have no clue about the meaning/structure of the data. PCA simply reduces the set of items to a smaller number of composites based on their correlation. The idea is simply to regard "correlation" as implying "information overlap". Accordingly, the rationale is to substitute two correlating items with one composite and keep most of the relevant amount of information (the communality) and decreasing the complexity. It is simply a data reduction strategy. With socalled formative constructs (I prefer indexes or aggregate constructs, you instead have some theoretical rationale of grouping the items. This rationale would not necessarily be wrong even if the correlation among the measured variables is zero.

Think for instance, you want to investigate the role of sporting activities (SA) on wellbeing. The SA composites could be represented as the sum of specific activites such as

- fitness training with heavy weights

- jogging

- cycling

Although there may be persons who do several of these things, I would assume rather low correlations. Nevertheless, the total sum is a content valid composite of SA. Hence, I would define inclusion criteria and base my procedure on this rationale. With regard to the practical ways to implement the composites, there are two ways. The first is the most straightforward: you simply add the variables together. A more sophisticated way would be (if the variable is a IV), to set up a regression structure with a phantom latent variable which has a fixed-to-zero error term and fixed-to-one effects from the variables. Although this will lead to exactly the same composite (the latent is nothing more as the sum of the predictors), the model tests whether all effects on your DV emerge from the composite or not better from one or more of the predictors. This can inform you about the adequateness of the overall composite.

The disadvantage of course is that you possibly pump up the model too much, especially, when the composite is only one of several IVs.

Best,

Holger

Hello Rene,

PCA and common factor analysis (which I presume is what you mean by EFA) are different animals. As Holger Steinmetz correctly notes, PCA might rightly be characterized as a data/dimension reduction strategy.

PCA assumes: (a) all variance in a data set is common variance; and, as a result, (b) there is no presence of specific or error (as in measurement error) variance. These assumptions are unrealistic for measurement of perceptions, sentiment, attitude, opinion, and the like. Further, unless the number of variables under consideration is moderate to large, a PCA solution will tend to yield estimated loadings that are biased higher than those of common factor analysis (see Richard Gorsuch, 1983, Factor analysis (2nd ed.). Lawrence Erlbaum), which could easily lead to differing interpretations of salience (sufficient variable-factor loadings to consider as non-zero) and therefore factor solutions. For these reasons, common factor analysis (e.g., principal axis, maximum likelihood extraction) is likely to work better in your situation.

Good luck with your work.