I find difficult to implement Principal Component Analysis (PCA )in categorical data. Is it good to apply PCA in categorical data? Are there any alternatives to PCA in my case?
You indeed can apply it. The thing is that PCA ignores the categories when computing its decomposition, and the usefulness of the method depends on what your problem or goal is. I attach three papers where we use PCA to model specific categories for classification purposes. In addition, there are some other data decomposition methods that consider the categories, such as Linear Discriminant Analysis, Biased Discriminant Analysis, etc. I also attach another paper where we study some of these methods for email filtering.
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Article PCA document reconstruction for email classification
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Dual scaling of multiple-choice data in the response-pattern format (Nishisato, 1980) and multiple-correspondence analysis are essentially principal component analysis of categorical data. For the exact similarity and differences between the two can be found in the book by Nishisato (1980)" Analysis of Categorical Data: Dual Scaling and Its Applications. University of Toronto Press."
PCA is oriented to explain variance of many variables by means of some linear combinations of them (principal components). With categorical data, multiple correspondence analysis is fine. I prefer to use R because the results are clear and easy to interpret. See FactoMineR package.
I agree w/ JO Pinilla, you can use MCA (as implemented in R, by the Factominer package) used on categorical data or quantified qualitative data. See also Le, S., Josse, J. & Husson, F. (2008). FactoMineR: An R Package for Multivariate Analysis. Journal of Statistical Software, 25(1), 1–18.