For my undergrad dissertation I'm assessing the unidimensionality of a 75-item questionnaire using PCA and CFA (because a secondary analysis requires this). The total sample is 1040 participants, which I have split into two groups to do the analyses separately.

After looking at the scree plot it's not looking very unidimensional, as it suggested extracting 18 factors, and the first factor accounts for just 18% of the variance. I want to run a CFA on this first factor anyway, so that I can report the fit statistics, even though I suspect they'll be poor. After running a different extraction method to the scree plot (Very Simple Structure), a two-factor model was proposed, and a PCA with oblique rotation reveals two factors which makes sense conceptually, and account for 24% of the variance, so I will run this as a comparison.

The one-factor model consists of 34 items and the two-factor model consists of 52 items (if I take loadings above 0.4)

My question is:

  1. In my CFA sample, do I include ALL 75 questions, even if many of them didn't load onto either factor? Or would I include only the 34 items for the one-factor CFA, and the 52 items for the two factor CFA?

My understanding is that because I am not trying to produce a unidimensional model (e.g. by removing items), but rather am trying to test if the existing 75-item questionnaire (which is already in use in clinical samples) is unidimensional, I would keep all 75 factors in both the one-factor and two-factor CFA. Is that correct?

I realise that (a) EFA is probably better than PCA for this task and (b) I will get poor fitting models in each, but I've already written all the codes for this and I am prepared for discussing this outcome in my project.

Below is the code for my CFA

    one.factor.model <-   'Factor1 =~ Q14 + Q27 + Q11 + Q29 + Q65 + Q72 + Q62 + Q28 + Q30 + Q38 + Q6 (etc)
 Factor1 ~~ 1*Factor1'
    one.factor.fit <- cfa(one.factor.model, data= data)
    summary(one.factor.fit, fit.measures=TRUE)


  • $\begingroup$ Hello @Mohanasundaram, thanks for your answer! Can I get a bit of clarification please? As I said, the one-factor model consists of 34 items at above 0.4, so all these questions will be saved in the 'one factor model' in the code. But I'm trying to ask about the data set I test it on. Should this sample consisting of all 75 of my original items, or should it be cut down and reduced to 34? I thought that if I cut it down, I'm not really learning anything about the unidimensionality of the original scale (as I want to do) but instead creating a new scale entirely $\endgroup$ – T August Apr 18 at 19:08
  • $\begingroup$ There is no universal cut-off for factor loading. As per Awang (2014), if you are developing a new model, loadings should be mroe than 0.5 and if you studuying and established model, loadings should be above 0.6. However, Salkind (2010) suggests that the items loadings above 0.4 can be included. I suggest you to refer the answers by Holger Steinmetz here, researchgate.net/post/… $\endgroup$ – Mohanasundaram Apr 19 at 0:26

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