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This is a follow-up to to my previous question: How can MANOVA report a significant difference when none of the univariate ANOVAs reaches significance?

I have two IVs with each having three levels and two DVs. MANOVA reported significant main and interaction effects.

I am now facing a new issue which is concerning the possible post-hoc test. What I have done, is to follow up my MANOVA with univariate ANOVAs. However, my univariate analyses (2 of my DVs) did not indicate significance.

I tried reading on Discriminant Function Analysis and want to apply it as another follow-up. However, given that I have two IVs for my [two-way] MANOVA, I would need a Factorial Discriminant Analysis, but am unable to conduct it in SPSS. Does it exist?

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    $\begingroup$ Here is the original post: stats.stackexchange.com/questions/129123. Why do you copy-paste it here? Are you satisfied with the answer there? Can you "accept" it? If you don't have access to your old "kea" account, you can ask StackExchange administrators to merge your accounts. $\endgroup$ – amoeba Jan 5 '15 at 10:44
  • $\begingroup$ Hi there @amoeba thank you for your help in the previous post. However, it seems that as it is insignificant, I am unsure of how I will be reporting this in my thesis. Hence I am trying to find out other means of post-hoc rather than running two univariate tests (one for each of my DV). $\endgroup$ – kea Jan 5 '15 at 10:51
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    $\begingroup$ Please edit your post to remove a copy-pasted original post, put a link to the old post to provide the context, and make this one be a separate NEW question. $\endgroup$ – amoeba Jan 5 '15 at 11:02
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    $\begingroup$ Hi in regards to the discriminant analysis, I would just like to ask if it would be fine for me to create an interaction variable to serve as the grouping variable (DV) for the discriminant analysis that correspond to the combination of the 2 IVS used in the MANOVA. Doing so would then just create the new interaction variable with 9 conditions (3x3 of my IVS as mentioned earlier for the MANOVA). Hope that someone can help me with this as I have been unable to find any support in regards to this. $\endgroup$ – kea Jan 6 '15 at 4:09
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    $\begingroup$ kea, I am afraid you forgot to merge your other unregistered account with this one. $\endgroup$ – chl Jan 8 '15 at 14:33
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This is a tricky question.

First, here I explained How can MANOVA report a significant difference when none of the univariate ANOVAs reaches significance?

Second, make sure that you understand the difference between using univariate ANOVAs and discriminant analysis as follow-ups for MANOVA; see my answer here: Post-hoc tests for MANOVA: univariate ANOVAs or discriminant analysis? The summary is that you use discriminant analysis if you want to find out which linear combination of your DVs leads to maximum group separability (usually in order to try to interpret this linear combination). This linear combination is called "[first] discriminant axis".

Third, as you say, there is no such thing as "factorial LDA"; I don't know about SPSS specifically, but I've never seen "factorial LDA" mentioned in the literature (I use "LDA" to refer to linear discriminant analysis). However, MANOVA is very intimately related to LDA, as I explain here in much detail: How is MANOVA related to LDA? So if you understand the math behind MANOVA/LDA, you can manually obtain discriminant axis for each of your factors -- i.e. three discriminant axes in total (for factor A, factor B, and for interaction AB). See in particular the Update to my answer in the linked post, regarding factorial MANOVA. I cross-post here my figure from that thread as an appetizer:

factorial MANOVA and LDA

Note that these will be three different axes, i.e. three different linear combinations. What you suggested in the comments (to create a new "composite" interaction variable with 9 conditions and use it for LDA) is smart and not entirely meaningless, but would only result in one single [most discriminative] axis, and that is not what you probably want here. Instead, you want to see which linear combination of your DVs best separates levels of factor A, which one -- levels of factor B, which one -- levels of AB.

I have no idea whether this is implemented in SPSS (or in any other package); in the worst case, you might need to go through the computations yourself.

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  • $\begingroup$ I believe that "factorial DA" is used in place of Canonical Discriminant Analysis, and in this case this is usually applied for descriptive, not predictive, purpose. $\endgroup$ – chl Jan 8 '15 at 14:40
  • $\begingroup$ @chl: Thanks, I am glad to see you here. I am not an expert on MANOVA and only know about it because I am working with dimensionality reduction and am well familiar with PCA/LDA/CCA etc. But mostly I find that questions on MANOVA attract almost no interest at all on CV and often seem to remain unanswered unless I try to answer them... I have just edited my answer to restructure it a bit and provide a figure. ... $\endgroup$ – amoeba Jan 8 '15 at 14:46
  • $\begingroup$ ... Re your comment: what is Canonical Discriminant Analysis? If you mean this, then I prefer to call it simply LDA (it would be weird to restrict the name "LDA" to only two groups). And yes, here I am only talking about dimensionality reduction part of LDA, not the classification part. In any case, Wikipedia says it's LDA with more than 2 groups (levels of one factor), whereas here we need more than 1 factor... $\endgroup$ – amoeba Jan 8 '15 at 14:47
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    $\begingroup$ In R, function candiscList() from "candisc" package "performs a generalized canonical discriminant analysis for all terms in a multivariate linear model" (ref: candiscList help page). See also a worked example of two-way canonical discriminant analysis in section 4.2 of the first reference in the help page of the heplot() function from "heplots" package. Hope this helps ! $\endgroup$ – Rodolphe Jul 31 '15 at 16:14
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    $\begingroup$ @Rodolphe: Wow, thanks for this pointer. I guess you refer to the papers by Michael Friendly, such as HE Plots for Multivariate Linear Models (2007) and Data Ellipses, HE Plots and Reduced-Rank Displays for Multivariate Linear Models: SAS Software and Examples (2006). Very interesting! $\endgroup$ – amoeba Jul 31 '15 at 16:37

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