Dear Philip,

It is impossible for someone else to say what you have done without seeing your output. However, I can advise you as to what you should have done: I would recommend a different technique to PCA at the initial stage, such as principle axis factoring or maximum likelihood. This is because PCA focuses on total variance rather than shared variance. Using an orthogonal rotation such as varimax is standard practice, so is losing half your items and ending up with 5 factors of about 5 items each.

Please refer to my study guide for more information.

Perhaps your confusion is around definitions: PCA is an EFA technique but there are several others, which are collectively called factor analysis techniques. However, PCA produces components rather than factors.

EFA

Dear Peter

Thank you for your reply. My SPSS output (and indeed the menu within SPSS) states I have done 'factor analysis, and I'm not sure how to tell SPSS which you want'. I have been told that the 2 techniques provide almost identical output but the difference is conceptual, in terms of which I wanted to do. I also don't understand the difference between factors and components - I have heard them used synonymously.

However, I have found and downloaded your study guide which I will carefully read through and hopefully I will then know 1) what I wanted to do, 2) what I should have done and 3) what I did do!

Incidentally, how do you tell SPSS that you want to use the Principal Axis Factoring Method (or is this what it does anyway? I did check commonalities, rotate the factors and check correlations and multicollinearity. So perhaps I have indeed done EFA.

Best

Philip

Dear Philip,

PCA overestimates component loadings and the amount of variance explained by its components, and underestimates the correlations between components. Because of it, PCA yields the index value for ranking, while EFA yields the true scores.

If you look at the results once again, you will notice the differences.

Namely, if you want to investigate only the relation between indicator and latent (measurement model), you must used the PCA. If you want to get true scores for experimentally studies, then you must used the EFA.

Dear Philip,

i think you can get to choose a different method under one of the buttons on the right hand side of the dialogue box. Principl axis factoring is not the recommended technique when you are developing your own instrument. The sources I base my advice on are Andy Field, and Tabachnick and Fidell.

Dear Peter

Thank you. I have now found the drop down menu where Principal components is the default option, but Principal Axis Factoring is also there. I hadn't realised there were several methods of factor extraction. None of the options is, however, called EFA, and according to Hahs-Vaughn, all those methods are applicable for EFA anyway. I'll check Field and Tabachnik & Fidell.

Incidentally, can you explain to me the difference between factors and components, as you mention above? Many thanks.

Best

Philip

EFA is Exploratory Factor Analysis while PCA is Principal Component Analysis. PCA is one of the extraction method under EFA. So there is no such thing as PCA vs EFA!

First of all, you run EFA. Then you need to state the extraction method for your EFA, and PCA is one of them. If you dont select the extraction method, your EFA procedure will use PCA by default.

Among the choice for extraction method are PCA, Unweighted Least Square, Generalized Least Square, Maximum Likelihood, Principal Axis Factoring, Alpha Factoring and Image Factoring. So, forget about EFA vs PCA!

Yes thanks Zainudin. I have been doing some more reading on the subject, and playing around with SPSS, and realise that PCA is but one of a number of possible extraction methods for factor analysis on SPSS. So although some do draw a distinction between EFA and PCA, they ought really to draw a distinction between PCA and other methods of extraction.

I'm now very clear that I have done PCA, so the important thing now is to justify why I did so.

You should explore when to use which extraction method when doing EFA. Why, by default Spss gives you the PCA if you dont choose any other method.

Dear Philip

As you have discovered, some of the confusion here is related to terminology, and in particular "EFA", which is used by different researchers in a more restrictive or less restrictive sense. The more restrictive sense assumes a reference to the 'common factor model', and it is in this sense that a distinction of some sort can be drawn between PCA, which is not explicitly based on the common factor model, and other extraction methods which are. As you have no doubt discovered in your reading, PCA operates by redistributing the total variance in the observed variables, whereas extraction methods based on the common factor model redistribute the 'shared' variance in the observed variables. In practice, it is quite likely that PCA will give very similar results to other extraction methods in terms of factor loadings, etc, but there is this distinction in the methodology and assumptions behind the methodology. To make a decision about which extraction method is appropriate in any given circumstances, one of the criteria (of course) is what your objectives are in doing the analysis. However, if your objectives are only vaguely expressed, they may be of limited help in the decision.

Dear Eddie thanks for this. I've now realised that PCA is a particular method of extracting factors, so I have still done an exploratory factor analysis (as opposed to confirmatory).

I'm quite surprised that there is so much confusion given that devising a questionnaire with a small number of factors from a larger set of items must be a fairly common procedure in psychometric psychology. I have gone with PCA (with varimax orthogonal rotation) as I have found other articles which appear to have done the same.

But in terms of my objectives, and the consequence of the extraction method on what I am trying to do, I cannot grasp the distinction between redistributing the total variance or the 'shared' variance among the observed variables. If I understood that, and could therefore clarify in my mind which type of extraction I wanted (PCA or perhaps Prinicipal Axis Factoring, which was also suggested by someone previously in this thread), then I would be much clearer.