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I would like to perform PCA on my data set (n=179). My result currently ends up with only one factor. I do not really know how to proceed further since I wanted to do Cluster analysis afterwards but I think with only one factor it is not possible.

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    $\begingroup$ Can you show the results of PCA? What do you mean that you get only one factor? And in any case it is possible to do cluster analysis on one variable/component. $\endgroup$ – DataD'oh Sep 16 '17 at 11:33
  • $\begingroup$ I dont know how to show it but: only one component s value is over 1 in the Total variance explained field. This one component explains 72 % or all variables. Like this, no rotated component matrix is available $\endgroup$ – Barbara Bodnár Sep 16 '17 at 11:49
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    $\begingroup$ Sounds like the variables are heavily correlated. You might need to look into those relationships and possibly exclude some of them. If you're only getting one factor which describes almost three quarters of the data, its probably quite telling in itself. $\endgroup$ – Andrew Tice Sep 16 '17 at 11:59
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First, if you have only 9 variables, you can do cluster analysis on the original variables and not do PCA at all. Why are you doing PCA?

Second, it is possible to do cluster analysis on one variable. See, for instance, this thread

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  • $\begingroup$ I did PCA because of my supervisor suggestion, I do not have a better answer for that unfortunately. So with 9 variables (n=193) you would suggest to do directly cluster analysis ? The scope of my research is market segmentation. $\endgroup$ – Barbara Bodnár Sep 17 '17 at 14:54
  • $\begingroup$ Yes, I think that if your goal is cluster analysis, leaving the variables as is makes sense. $\endgroup$ – Peter Flom - Reinstate Monica Sep 17 '17 at 22:55
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PCA works best if you have a lot of data. In particular if some variables aren't continuous or you have many duplicate samples. As a rule of thumb, I have seen the recommendation of at least 3p² samples. So for p=9, that rule would suggest you need many more samples to get a reliable estimate from PCA. Unfortunately, I can't find any source for that rule of thumb.

Because of this, I would suggest to not use PCA here for analysis. Because I don't see why you need it, and it just adds to your problems. You can definitely cluster multiple variables. But you can still try PCA for visualization only.

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