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I am using XLStat for a PCA of time-series water chemistry data. I have 23 analytes and 29 samples. I am using a correlation matrix for PCA as I find it more interpretable in the context of hydrochemistry. The data is also standardized to a variance of 1 and a mean of 0 to avoid the effect of differing units.

The results of the PCA look great. Very easy to interpret and everything makes a lot of sense. There are numerous significant correlations present in the correlation matrix(alpha=0.5). A KMO sampling adequacy test yields a value of 0.64. The problem is that I keep having an observed chi-squared of "-Inf" for Bartlett's Sphericity Test. Essentially, this means that the chi-squared could not be computed.

  1. What is going on here? This value makes no sense given the strong correlations in the matrix.

  2. Can I continue with PCA despite the failed test?

  3. Could the problem be that by normalizing the data I am imposing normality upon it falsely?

Data:

http://www.filedropper.com/wcrb_1

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    $\begingroup$ KMO isn't needed for PCA, actually, it is for factor analysis (see and a link therein). Bartlett's test - hard to say what was wrong without having data (you could show your data, btw). This test is for large sample from normal population (e.g. see). This test is mainly for factor analysis. What might be a reason to use it in the context of PCA as long as PCA is seen as just a data reduction transformation? $\endgroup$
    – ttnphns
    Sep 26, 2014 at 15:10
  • $\begingroup$ Thanks for the response. I didn't realize KMO was more aimed at factor analysis. The real problem is the failure of Bartlett's Sphericity Test. How do I include my data? $\endgroup$
    – Matt
    Sep 29, 2014 at 14:58
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    $\begingroup$ Thanks for sharing it. Exemplarily done work! I ran PCA in SPSS and confirm every figure except Bartlett's (and contributions / cosines which I didn't check. BTW, how did you compute them?) Now, "my" Bartlett's was: Approx. Chi-square 997.054; df 253; Sig. .00000. SPSS computes the test as written here. Could it be that your program simply considered the determinant of the matrix so close to 0 that it skipped computing the chi-sq value? $\endgroup$
    – ttnphns
    Sep 29, 2014 at 19:00
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    $\begingroup$ Wow. Thanks for checking this out and the praise. I appreciate it a lot. That is interesting that SPSS had no problem computing a chi-squared. I wonder if I have uncovered a bug in XLStat? It is nice to have external confirmation of results. I have to claim ignorance in the computation of the contributions and cosines. I checked the box in XLstat and that is what I got. I suppose that is the risk of powerful stats programs in the hands of inexperienced users: too much information and not enough knowledge to handle it properly. $\endgroup$
    – Matt
    Sep 30, 2014 at 21:24
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    $\begingroup$ It may have been a bug of XLStat as well as its intended behaviour. As I said, your correlation matrix is virtually singular, but the program might be designed to skip such cases. XLStat may be computing the chi-sq value a bit different way than SPSS does. $\endgroup$
    – ttnphns
    Oct 1, 2014 at 3:19

1 Answer 1

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Turning my 1st comment into an answer, per advice by @StephanKolassa...

KMO isn't needed for PCA, actually, it is for factor analysis (see and a link therein). Bartlett's test - hard to say what was wrong without having data (you could show your data, btw). This test is for large sample from normal population (e.g. see). This test is mainly for factor analysis. What might be a reason to use it in the context of PCA as long as PCA is seen as just a data reduction transformation?

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