Dear all,
I performed a PCA analysis on a Likert scale with 5 questions which ordinal responses can be 1,2,3,4,5 and 6 (from strongly disagree to strongly agree). I did it in two independent samples. I obtained only one principal component in each group. Now I want to compare the principal component in each group. If my data were continuous, I know that the Principal components are continuous. However, as my Likert scale does not have continuous data (It can't), I would like to know if the resulting principal components should be considered continuous data or something else.
Of course, this is important to determine which test(s) should I use to determine if there is association between the two groups that I want to compare.
Very much thank you,
Nicole
I am at a loss as to way you have gone down the principal component route. And why you extracted the component from the groups separately. Can you explain more about why you are doing this? And why you haven't used methods that have been developed to handle ordinal scale items like IRT and Mokken scaling?
Hello Nicole,
If your goal is to compare groups on their scores on some common factor or component, then your options are:
1. Re-estimate the component/factor with both groups' data sets combined. Save the component/factor scores, then compare. As they stand, if you wish to be conservative and consider the scores as ordinal, then a test such as Mann-Whitney-Wilcoxon will work.
2. Adopt a scaling (IRT) method, as suggested by Ronán Michael Conroy . These have the ability to take graded/ordered response scale items and yield an overall score that is defensibly interval strength.
3. Consider revising the component/factor analysis by starting with polychoric correlations instead of Pearson correlations. That should result in defensibly interval scores on the component/factor.
For all three approaches, a number of comparison tests could be chosen. Let me suggest these non-parametric options: (a) Cliff's dominance statistic (proportion of times a randomly selected case from set "A" has a score exceeding that of a randomly selected case from set "B", after subtracting the proportion of times that a case "B" score > a case "A" score); (b) an exact/permutation test (for which sample means or medians would be a sufficient statistic; (c) Mann-Whitney-Wilcoxon test.
Finally, though you didn't ask, it's probably wiser to use common factor analysis, with either principal axis factor or maximum likelihood extraction than to use principal components analysis. Measures of human judgment / perception / opinion / sentiment simply do not live up to the assumptions made for PCA regarding the scores on the variables (e.g., no measurement error; no specific or unique variance).
Good luck with your work.
Dear professor Ronán Michael Conroy I certainly followed your advice of using the IRT and Mokken scaling, and that is my main approach of analysis so far. However, a colleague advised me that principal components was another option. However, I mistakenly did with both groups separately. As I understand form professor David Morse , I should have obtained the principal components (or the factors) with both groups together.
Dear professors David Morse and Ronán Michael Conroy . Everything is far clearer to me thanks to your really amazing advice.
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