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I have found some references to "Descriptive Discriminant Analysis" or DDA. In particular, this paper recommends it as a follow-up to a significant MANOVA result. Briefly, it is described as "a statistical procedure which creates a set of perfectly uncorrelated linear equations that together model the differences among groups in the MANOVA".

However, I have found surprisingly little mention of DDA elsewhere, which made me wonder if it has a more common name, or if it has been superceded by other methods, or if it is in fact the same as Linear Discriminant Analysis (LDA). I have tried following up references within the above source, but other articles do not seem to make a distinction, and simply refer to discriminant analysis, or LDA. Here it is mentioned briefly in contrast to "predictive" discriminant analysis. I can see that there is a difference in motivation between simply wanting to describe differences among groups and wanting to predict group membership, but it is not clear to me why these different aims cannot both be met by an LDA.

DDA is implemented separately to Linear Discriminant Analysis (LDA) in the R package DiscriMiner. There the main reference is in French, which made me wonder if this is simply an issue of mis-translating the name of another test.

Does "Descriptive Discriminant Analysis" exist in its own right, and if so, how does it differ from Linear DA?

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    $\begingroup$ +1. I suspect it's the same thing. See here stats.stackexchange.com/questions/82959 (and links from there) on the relationship between LDA and MANOVA. $\endgroup$
    – amoeba
    Commented Aug 2, 2016 at 16:59
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    $\begingroup$ And my answer here stats.stackexchange.com/questions/111044 about LDA as a "post hoc" (rather follow up) after MANOVA. $\endgroup$
    – amoeba
    Commented Aug 2, 2016 at 17:02
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    $\begingroup$ I checked Huberty & Olejnik textbook on LDA/MANOVA and they actually use terms "descriptive discriminant analysis" and "predictive discriminant analysis" (both refer to LDA, but to different aspects of it). I will post an answer, probably tomorrow. $\endgroup$
    – amoeba
    Commented Aug 3, 2016 at 0:28

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There exists a real difference between Descriptive Discriminant Analysis(DDA) and Predictive Discriminant Analysis (PDA). which is depicted in the diagram given below. I found it here: http://as.wiley.com/WileyCDA/WileyTitle/productCd-0471468150.htmlenter image description here

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