A study with 4 non conceptually overlapping variables, with different data collection methodologies for each one (knowledge questionnaire, likert scale, practical skills and a checklist of yes and no for daily practices) yielded through a PCA only 2 main components. How can this discrimination be theoretically explained?
If variables are not overlapping, maybe need 4 PCA separately. 4 principal components you may get.
Provide all your eigenvalues (not just the first 9) and the cor matrix.
The PCA also allows to group in the smaller amount of factors, in addition you are evaluating variables that differ in amount of options between likert and dichotomous, you should only perform in analysis according to the same criteria of options as mentioned above PCA separately, this should be confirmed by confirmatory factor analysis without correlation factors
pca is not about interpretation. It is a data reduction technique, nothing more. modern factor analysis with correlated factors and an explicit unexplained variance offers much more,see
Just to add an example to Kelvyn Jones' answer.
Imagine you measure response times when participants fill out two sets if theoretically unrelated online questionnaires. "Accidentally" one questionnaire is comprised of short questions (not more than 5 words per question), and one of long questions (more than 5 words).So,since these two questionnaires have nothing to do with each other the response times of survey 1 will not correlate with those in survey 2. However, if you still run a PCA on these response times, it will assign a huge amount of variance to a component that explains the response times only related to the length of the questions. This means nothing ...
Now, it follows, another suggestion here would be, that you check the correlations between the variables of interest before you do factor analyses. If there are none, and if you would run a principal factor analysis (PFA) you would not obtain mysterious (survey length) as factor, because (long story short) theoretically unrelated response times do not correlate individually (which is the mathematical starting point of the PFA, but not of the PCA; which is their only difference).
Hope this helps
Best, René
For me PCA is data reduction pure and simple and not really there for interpretation. Recent developments in factor analysis as part of Exploratory Structural Equation Modelling (ESEM) which include factors tat can be correlated would seem to offer more:
Article Understanding the population structure of the GHQ-12: Method...
I agree with Kelvyn Jones about PCA. Unfortunately, the default settings for the "factor analysis" command in some of the major stats packages give the so-called "little jiffy" approach (i.e., PCA + eigenvalues < 1 + Varimax rotation). Here is a nice "teaching" article that explains why that is usually a bad approach that ought to be avoided.
- http://quantpsy.org/pubs/preacher_maccallum_2003.pdf
By the way, here are a couple of interesting articles for anyone who is contemplating "principal components regression" (PCR).
- https://www.jstor.org/stable/2685559?seq=1#metadata_info_tab_contents
Article The principal problem with principal components regression
HTH.
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