Calcite | Level 5

Eigenvalue

Assume you have 26 variables and have performed a principal component analysis. Your first 3 eigenvalues are 14, 7.8, and 1.015. Is that good? Is that bad? Does the answer depend on other issues in your research?

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Accepted Solutions
Barite | Level 11

Re: Eigenvalue

It's difficult to answer your question without seeing more detailed output. I assume you are running a correlation PCA (i.e. PROC PRINCOMP without the COV option), in which case the eigenvalues will sum to 26. So roughly 84% of the variance is summarised by 2 dimensions and it is possible to give an excellent graphical summary of the data with just one plot of PC 1 vs PC 2. That might be good or bad. Were you expecting a high degree of correlation among the 26 variables? Or did you believe you had measured 26 different things? The number of observations makes a difference too, the results would be more remarkable if you had 80 observations rather than 8.

2 REPLIES 2
Barite | Level 11

Re: Eigenvalue

It's difficult to answer your question without seeing more detailed output. I assume you are running a correlation PCA (i.e. PROC PRINCOMP without the COV option), in which case the eigenvalues will sum to 26. So roughly 84% of the variance is summarised by 2 dimensions and it is possible to give an excellent graphical summary of the data with just one plot of PC 1 vs PC 2. That might be good or bad. Were you expecting a high degree of correlation among the 26 variables? Or did you believe you had measured 26 different things? The number of observations makes a difference too, the results would be more remarkable if you had 80 observations rather than 8.

Diamond | Level 26

Re: Eigenvalue

@zahidhasandipu wrote:

Assume you have 26 variables and have performed a principal component analysis. Your first 3 eigenvalues are 14, 7.8, and 1.015. Is that good? Is that bad? Does the answer depend on other issues in your research?

"Good" is not a mathematical or statistical term. "Bad" is not a mathematical or statistical term. There's no way for us to answer this.

Now that you have these eigenvalues, what are you going to do with them?

--
Paige Miller
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