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I have a data set of some 40+ individuals and 10 variables. Each individual is asked to rank these 10 variables from least preferred (1) to most preferred (10). Is it sensible to apply principle component analysis on this type of data? I know it is applicable when it would have been on something like a Likert scale, but here every individual / row / tuple would exactly contain every 1-10 value once.

gung - Reinstate Monica
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StudentJ
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  • Not an answer, but a related question worth reading http://stats.stackexchange.com/q/141646/3277. – ttnphns Oct 15 '16 at 21:56
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    The fact that data row sums are constant and hence the data are singular does not preclude doing PCA on it because PCA can cope with singular data. The problem is however that you (perhaps) see the values as _ordinal_ rather numeric, scale. I.e. rank=1 - rank=2 distance is not claimed to be equal to rank=4 - rank=5 distance; actually the distance isn't specifically defined. Is that what you will agree with? In yes then [CatPCA](http://stats.stackexchange.com/q/215404/3277) might be a method to go for. – ttnphns Oct 15 '16 at 22:08

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