My major objective is to find if one data set is closer to another. With ten data sets I want to know which one are making clusters or can say have less distance with each other. I have already tried correspondence analysis, however it is not useful for factors having degree of freedom less than three. Any lead would be highly appreciated
Hello Bahadur,
With nominal variables, any quantification method is arbitrary and the chosen values (or their differences) won't correspond to any tangible characteristic in the same way that a measurement scale would operate. So, distance measures created from nominal variables can only be interpreted in a relative way.
That said, of course you can create Mahalanobis (or any other distance metric for subsequent clustering) once you've quantified the variables. Two-category variables are the easiest (e.g., 0 & 1 values, or 1 & 2 values, for example). Three or more category variables must be recast into k - 1 dummy variates (where k is the number of categories for the given nominal variable) in order to capture all of the information.
Do note that the variance of a score (technically, the SD) is proportional to its influence in cluster solutions. This has implications for the relative proportions of cases in each level of the nominal variable (for example, if one sample has a split by sex of 90:10, whereas another sample has a split of 50:50, the variable of sex will be more influential in the second sample than in the first, unless you standardize the "scores").
Good luck with your work.
Dear Bahadur;
A distance for mixed nominal, ordinal and continuous data is developed by applying the Kullback–Leibler divergence to the general mixed-data model, an extension of the general location model that allows for ordinal variables to be incorporated in the model. The distance obtained can be considered as a generalization of the Mahalanobis distance to data with a mixture of nominal, ordinal and continuous variables. Moreover, it includes as special cases previous Mahalanobis-type distances developed by Bedrick et al. (Biometrics 56 (2000) 394), for more details see;
Article A generalized Mahalanobis distance for mixed data
No, because what is the mean of a nominal variable? And what is the distance from one category of your nominal variable to another category?
As data preparation for clustering, I would try Jaccard distance. That's technically a binary distance for dummified data as David Morse mentioned.
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