<- file stat 97canon.html -> Here are exchanges about why canonical correlation is the generic label that includes MANOVA and discriminant function and "multivariate multiple regression"; that last one is not necessarily a standard term. *----------------

Canonical corr, etc: naming

=======================Rich Ulrich, 6 May 1997==========ssc,sse,ssm Subject: Re: Canonical correlation with categorical variables Message-ID: <5knju8$dro@usenet.srv.cis.pitt.edu> A few days ago, : >Kerry W Go (kgo@ix.netcom.com) wrote: : >: Is it possible to perform a canonical correlation if some of the : >: variables are continuous and some are categorial? I replied, : > -- That's what MANOVA does. Now, Kerry says, kgo: I was under the impression that MANOVA is used when the dependent : variables are continuous and the independent variables are : categorical. -- Yes, that is the case. I thought it answered your question, in short, since it should remind you what canonical correlation consists of. And what MANOVA consists of. Here is a much longer answer: For MANOVA, the categorical variables are coded into k-1 (scored 0/1, say) dummy variables, and then canonical correlation is obtained on the covariance matrix between the left-side and the right-side variables. So, express your categorical variables the way you want to: treat them as interval, or use 0/1 dummy codes; append them to the list of your continuous variables, on either side of the canonical equation; and carry out your canonical correlation. The only problem then is figuring out what that messy solution can tell you.... kgo: What if, for example, one of the dependent variables is : categorical and one is continuous, and one of the independent : variables is catagorical and one is continuous? Would MANOVA still : work? No, not until you have a handier computer program than I have seen. Discriminant function is the subset of MANOVA which may be used to display can-corr results when you have just one categorical variable on the left side vs continuous variables. The testing is fairly straightforward, and data-displays include groups centroids, and the 'classification table'. MANOVA displays can-corr tests when there are multiple-category-variables on the left, vs continuous variables; there may be numerous tests provided, both multivariate and univariate, to try to cover the problems that may be intended. A simple Correspondence analysis shows some can-corr results when you have one categorical variable on each side; the testing is often only incidental to getting the graphical data display, and the ordering obtained for categories. (And it is possible to use more than one variable per side, in some fashion.) In sum - You can carry out a canonical correlation of whatever variables you have on hand, and you can include dummy variables to encode each categorical variable, to add to continuous variables. But, presenting your results becomes increasing difficult. I can imagine that someone might set up a "multivariate-multiple regression" with just a couple of dummy variables. But I don't think I would be very happy with any such analysis, unless I could read good sense into the dummy variables themselves. I hope this helps with your question....

Canonical correlation (what)

=======================Rich Ulrich, 07 May 1997==========ssc,sse,ssm Subject: Re: Canonical correlation with categorical variables Message-ID: <5kqm46$sc2@usenet.srv.cis.pitt.edu> << ...in answer to a Q. about canonical correlation and categorical variables, I wrote ... >> : > -- That's what MANOVA does. Paige Miller (paigem@kodak.com) wrote: : Let me chime in with a comment/question. I don't quite think that : canonical correlation and MANOVA are equivalent when some of the : independent variables are categorical. At least, that's my : understanding. -- sorry, you are wrong. Discriminant function is the *simple* case of MANOVA, where you just do *one* eigen-problem/ canonical correlation. A MANOVA may perform several analyses (one for each main-effect variable, for instance), but each one is a canonical correlation. : The reason I say that is: if all of your independent and dependent : variables are continuous, you could perform multiple regression or you : could perform canonical correlation, and the two procedures do not give : the same results. They do not optimize the same objective function. Now, << ... stuff deleted >> ??? "multiple regression" usually is used to label an analysis with many predictors and just one outcome. "Multivariate multiple-regression" is a name sometimes used for many-to-many prediction, with continuous variables, and so far as I know, it is precisely a canonical correlation - maximizing the correlation of the left side variables with the right side. So I am curious as to what analyses you are describing, above, where you think there are different results... *--------FAQ edit: one week later: Frank Ivis (FIVIS@ARF.ORG) wrote: : Rich, : The SPSS Reference Guide (1990) (p. 801) has an example of : 'multivariate multiple regression', including syntax and output using the : MANOVA procedure. : Hope this helps, -- THANKS - that is probably where I saw it, years ago. But if we don't find it other places, I guess we should not assume that people know what we mean by it. *--------

Canonical//multiv. multiple regr

=======================Rich Ulrich, 08 May 1997==========ssc,sse,ssm Subject: Re: Canonical correlation with categorical variables Message-ID: <5ktg4s$a67@usenet.srv.cis.pitt.edu> Paige Miller (paigem@kodak.com) wrote: : Richard F Ulrich wrote: << ... snip>> : > ??? "multiple regression" usually is used to label an analysis with : > many predictors and just one outcome. "Multivariate : > multiple-regression" is a name sometimes used for many-to-many prediction, : > with continuous variables, and so far as I know, it is precisely a : > canonical correlation - maximizing the correlation of the left side : > variables with the right side. : > : > So I am curious as to what analyses you are describing, above, where : > you think there are different results... : Multivariate multiple regression optimizes a least squares criterion. It : actually performs a multiple regression for each dependent variable. Okay, Paige, I admit I am surprised a bit: I have just checked 7 MV-text books and two stat manuals, and I STILL cannot find anything labeled, precisely, "multivariate multiple regression". Tabachnick and Fidell's text discusses the canonical analysis that I had in mind, under the name, "multivariate analysis of covariance". The BMDP manual offers (it looks like) just what you are describing, as "multivariate regression." Well, Multivariate ANOVA has multiple criteria and uses canonical roots; so it seems to me that prefacing Multiple regression with "multivariate" ought to be the same generalization. But most of my texts are not new, and don't discuss either model. * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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