Hi all,
I have two 'basic' questions when I'm doing data analysis of a scale validation. Hope to hear different opinions.
1. It's a simple tool using 5-Likert scale. I plan to use data of median, SD, skewness and kurtosis as descriptive data of each item. I've read some papers defining normality as skewness and kurtosis values between 2 and -2. Do you think it's a good idea to do so on a 5-Likert scale?
2. When conducting an exploratory factor analysis, a previous study selected 'Principle components' and reported one component. Another paper reported three components (small sample) using the same extraction method. In this case, should I choose 'Principle axis factoring' instead? Or the same type as previous studies selected would be better? These two methods showed quite different results of the factor loading of one item. It would affect CFA and interpretation significantly.
Thanks for your help! Looking forward to hear from you!
Hello Xiaoyi,
Common factor analysis (CFA) and principal component analysis (PCA) both presume that your observed variables are continuous and interval (or ratio) strength. Folks using Likert-type response scale scores would be best served by:
1. Having multiple, similar items (relating to the same target perception / opinion / sentiment / attribute / concept). Then, either: (a) create a summated score and treat it as a continuous variable; (b) apply polytomous IRT model to develop a more accurate scale value for any given case; or (c) factor the set of scores and use estimated factor scores in lieu of observed scores.
If you are unable to do this, and must instead treat an individual item as a variate, then you can: (a) presume that the ordered steps represent an underlying, continuous variable, and start the process with polychoric rather than Pearson correlations; or (b) opt for an ordinal factoring approach.
2. In my view, CFA is far more appropriate for variables of human perception than PCA. The principal reason is that PCA presumes all observed variance to be common variance (e.g., no such thing as specific variance or error variance). This is an unrealistic expectation in this context. CFA presumes to account for only that variance which is common (and dependable, given the data).
Therefore, I would opt for factor analysis over PCA, despite what other authors had chosen to use.
Good luck with your work.
I agree with David Morse entirely on your second point.
On your first point you are IMO entirely off base. Basically this is because normal distributions have nothing to do with ordinal variables. Normal distributions are about continuos variables which are completely different. There are some that argue scales made from likert items can be treated as continuous variables. Looking at scale construction against the definition of continuous variables which can be found in any introductory calculus text. The +2 and -2 you are referring to come from the normal distributions symmetry. If you want something similar to that for an ordinal variable I would refer you to the the attached bounds from that theorem. In anticipation of someone commenting that such distinctions make no difference in the "real-world" simply remember that "A difference that makes no difference is no difference"- 🖖 Spock. And yes doing things in the best way does indeed sometimes pays
off. You might wish to look at the first section of the second attachment for another example. Best wishes David Booth
In addition to what David Morse and David Booth have said, I suggest consulting this excellent paper from Costello & Osborne (2005), who provided an excellent guideline for EFA. PCA is not the right tool for your purpose, though PCA and EFA are available in the same menu in SPSS. You may find more information in this discussion: https://www.researchgate.net/post/How-can-I-decide-between-using-principal-components-analysis-versus-factor-analysis
Lastly, consider using parallel analysis to identify the number of factors.
Costello, A. B., & Osborne, J. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical assessment, research, and evaluation, 10(1), 7.
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