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I am performing an LDA with very unequal sample size (ratio 1:10) among 3 groups. The results surprise me, as I was expected from a series of boxplot that some variables that explain much of the between group variance to show up on at least one of the first two axes but they don't. This yield me to the question:

Should unequal sample size be taken into account when performing Linear Discrimant Analysis?

If it matters, I am using the lda function from the MASSpackage in R with all the default parameters.

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    $\begingroup$ some variables that explain much of the between group variance to show up on at least one of the first two axes What do you mean? unwrap please. Are "axes" the discriminants? If yes why "at least first two"? (you have only two with 3 groups) Is "show up" discriminant weights or what? How you estimate how "much a variable explain of the b/w group variance? Etc. I think you ought also to show and even to give your data. $\endgroup$ – ttnphns Jan 25 '17 at 23:40
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"Should unequal sample size be taken into account when performing Linear Discrimant Analysis?"

Yes, definitely. But this would affect the quality of classification, not the axes.

If you have unequal group sizes, set priors based on group sizes and use them instead of equal priors

lda  <- lda(class ~ v1 + v2, data = data)
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    $\begingroup$ I don't think changing the priors would change the "variables that show up on the first two axes" but would change the classification function. $\endgroup$ – David Lane Jan 25 '17 at 20:33
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    $\begingroup$ +1 to what @DavidLane wrote. I don't think this answer answers the question. $\endgroup$ – amoeba Jan 25 '17 at 21:07
  • $\begingroup$ It's not an answer to the question but it speaks to the concern that the variables expected to show up on the discrimination function do not because of unequal sample sizes and @Anna S's suggestion that one should adjust the priors. $\endgroup$ – David Lane Jan 25 '17 at 21:26

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