Interpret Linear Discriminant Analysis and visualization

#1
Hello,

I performed a LDA in R but I'm a bit concerned about how I could present my results.

I didn't do any scaling before the data analysis, is it recommended to do so?

When I do the LDA, I got the following coefficients:

Coefficients of linear discriminants:
LD1
CHP -8.7908674
CD 6.6956730
CH 9.5463453
ESL 22.3475689
SDBottom -392.2736953
SDMiddle 52.2500963
SDTop 40.8531601
SL -0.4170077
TCDiameter -25.2242270
TCHeight 27.4153806
THeight 74.9738324
VFD 22.6521590
VTD -74.1032630

As I didn't scale, these coefficients are hardly interpretable. How could get the variables that are the most influential in the separation of my classes?

Secondly, how could I plot the individuals and the variables (such as biplot in PCA) so it could be simple to interpret for a posterior presentation?

Thanks in advance
 

hlsmith

Not a robit
#2
I will initially apologize for my lack of knowledge about LDA. Two things, why can you scale your variables? Second, I thought there were great similarities between logistic reg. If you can resolve your issues, perhaps explore similar models. Though there isn't a clean way to rank coefficients in logistic reg either, but you could look to see how much more of the AUC adding a term helps or something of that nature (perhaps wald stat value).
 
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#3
You do not have to scale. However, the variability of the features and their correlations must be the same in each class. If that assumption fails, LDA may misfire. There are other situations in which LDA misfires and is suboptimal to other classification methods... I'm afraid there are limitations to discussing such topics on forums, because one would need to show you graphs of the boundaries, etc. The best thing I can do is delegate you to a relatively concise exposition of LDA in chapter 4 of this wonderful book:

https://web.stanford.edu/~hastie/Papers/ESLII.pdf
 
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hlsmith

Not a robit
#4
However, the variability of the features and their correlations must be the same in each class.
Can you add on this. I had initially thought you were referring to the use of both continuous, binary, and multi-categorical. But when rereading the sentence I realized I was unsure.
 
#5
LDA requires that all the features be scale variables, not categorical or ordinal. Moreover, it requires that all of the features had joint normal distribution.... I know. Moreover, LDA requires that the covariance matrix of features in class A be the same as that in class B. That is what I meant by "the variability of the features and their correlations must be the same in each class".
 
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