I have a dataset with ordinal variables (Likert scale), I need to find the relation between variables. Only by curiosity, I have performed MCA and PCA. The literature recommends MCA for categorical variables, not PCA, multiple papers mention that PCA is for continuous variables.
The results that I obtained from the two analyses are very similar, the % of inertia (MCA) and variability explained (PCA) are similar for the dimensions (MCA) and PCs (PCA) respectively. The graphic of the dimensions (MCA) has the variables more dispersed and in the PCA plot the variables are more condensed, I mean it is possible to do a more easy interpretation of the variables in the PCA graphic (although the relationship between variables in the two graphics seems similar either). Definitively I would like to use the PCA plot, but in principle, I could not due to the recommendations of the literature. I would like a suggestion or a clarification guide, maybe I am not taking into account a statistical fact (i.e distances). Thanks in advance for your comments.
First, Likert-scored variables are ordinal (i.e., ordered), not nominal. Second, if your variables all measure the same underlying concept and they are thus inter-correlated, you may want to combine them into a single scale.
If you believe that your variables capture one than one underlying concept, then you should examine them with Principal Factors Analysis (which is similar to Principal Components, but uses more realistic assumptions for this case). In addition, you should use an oblique rotation to allow for correlated factors.
Thanks for your guide, David L Morgan, and yes the variables are ordinal, I have corrected that in the question. Please, could you give me examples of the assumptions of PFA that are more realistic in my case? I have read about the non-unique variance assumption of PCA (information that still needs to be digested)... but for sure are others, maybe with more impact on my case...
I said Principal Factors Analysis, but I should have said Principal Axis Factor analysis, which is one of several forms of Exploratory Factor Analysis (EFA). The differences between PCA and EFA are rather technical (they involve assumptions about the communality and uniquenesses of the items).
The easiest way to summarize EFA is that it assumes there are underlying factors that are "causing" the observed variables. This is commonly represented by a diagram with the factors at the top and arrows pointing downward to each of the variables that make up a given factor.
David L Morgan Does not a method applicable for nominal data apply for ordinal data?
Babak Jamshidi Nominal data consists of un-ordered categories (gender or religion). Ordinal data is continuous (e.g., strongly disagree to strongly agree, but it does not meet the assumptions of interval data, where all the items in the ordered set is the same distance apart (such as years of schooling).
You could apply a method for categorical data (such as chi-sq) to an ordinal variable, but that would loose all the information that was in the ordering.
David L Morgan Thank you for your answer. You are right. The main problem is losing the ordering information.
- Badges
- Science topic
- Similar topics
- Biological Science
- Biochemistry
- Enzymology
- Enzymes