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Per Wiki, generalized variance is the determinant of a covariance matrix: https://en.wikipedia.org/wiki/Generalized_variance

I have heard that if the determinant is small, there is strong correlation among the variables. If the determinant is large, there is weak correlation among the variables.

Are there good guidelines as to how to interpret generalized variance? Is generalized variance even useful in practice?

confused
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    What you heard is only a faint shadow of the truth, because "small" and "large" depend very strongly on how many variables are involved. – whuber Jul 15 '20 at 12:42
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    Usefull in which context? [here](https://www.jstor.org/stable/2528931?seq=1#metadata_info_tab_contents) is a paper using it ... See also https://stats.stackexchange.com/questions/273236/generalized-variance-in-high-dimension-setting-pn and https://stats.stackexchange.com/questions/421674/minimum-generalized-variance-for-outlier-detection – kjetil b halvorsen Jul 15 '20 at 16:00
  • @whuber is there a way to normalize it? – confused Jul 16 '20 at 12:36
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    It's better to examine all the eigenvalues. (The determinant is merely their product.) – whuber Jul 16 '20 at 13:21
  • @kjetilbhalvorsen as a single metric to measure overall variance/covariance for your variables. – confused Jul 17 '20 at 11:24
  • I found some more useful info. So the squareroot of the generalized variance is the area of the prediction ellipsis around your distribution, and so smaller means more correlated, and larger means less correlated. And then I guess you can get a sense of which way it is correlated by using some formulas with eigenvalues. So now using the eigenvalues and what not, I might be able to have a single metric that tracks changes in the behavior of my data over time. I guess looking at the weights within PCA would give you similar metrics, but just interesting to think about. – confused Jul 20 '20 at 09:51
  • So PCA may be more useful than I thought. I was just taught it was a way to condense your data and either plot it or run a regression (couldn't care about either since plotting is for the bobs and there are probably better models for prediction purposes (since you lose interpretation with PCA) - but the weights (or other related metrics) may be a nice way to see how my data changes over time. – confused Jul 20 '20 at 09:59

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