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There was a post once upon time dealing with the differences of multivariable and multivariate regression. I have seen the relevant post here. However I am having this debate with a colleague and while I agree with the information of this post, my colleague insist that multivariable regression is actually just multivariate regression. The definitions of this individual are :

  1. multivariate regression: one end point, multiple linear predictors
  2. multivariate multiple regression: multiple endpoints and multiple linear predictors.

Whereas I think the definitions are:

  1. multivariable multiple regression: one endpoint, multiple linear predictors
  2. multivariate multiple regression : several endpoints, several linear predictors.

So, is this all a matter of semantics? Are they the same thing? Why does there need to be a distinction for multivariable and multivariate if one kind of is a subset of the other?

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"Multiple" within regression context stands for multiple predictors (IVs) and "Multivariate" stands for multiple predictands (DVs). "Multivariable" is quite uncommon. –  ttnphns Dec 9 '11 at 18:23
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@ttnphns That's a nice clean distinction; I like it. But some authorities disagree about this characterization of "multiple" vs "multivariate." Web searches turn up uses of "multivariate" in both senses. Arguing seems pointless: as with many other statistical terms, we just need to be aware there can be various meanings and to be clear about how we use them. –  whuber Dec 9 '11 at 18:32
    
@whuber I have also read that multivariate is used in both senses (as you described), however I have also read in some texts that this ambiguous use is incorrect and that the distinction between multivariable and multivariate is important. –  user4673 Dec 9 '11 at 18:47
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Yes, maintaining a distinction is useful--some techniques are unique to regression with multiple (correlated) dependent variables--but it appears that different people make their distinctions in different ways and no one way appears to be sufficiently standard to cry out for universal adoption. This is no surprise given the similarity of the terms "multiple regression" and "multivariate regression." A similar problem with potential confusion plagues "general linear model" and "generalized linear model," even though those terms do appear to have standard meanings. –  whuber Dec 9 '11 at 19:49
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The distinction is important, but we have no way of imposing a terminology on "the world" (except, perhaps, by writing seminal papers). Just make sure that when you read a paper, you know which interpretation of the terms the author means, and make sure to explain to your own readers which one you mean. That will be the best you can hope for (as you don't even manage to agree with a colleague :-) ). I'm going with @whuber here. –  Nick Sabbe Dec 9 '11 at 19:50

1 Answer 1

up vote 4 down vote accepted

I found this to be the most useful response:

The distinction is important, but we have no way of imposing a terminology on "the world" (except, perhaps, by writing seminal papers). Just make sure that when you read a paper, you know which interpretation of the terms the author means, and make sure to explain to your own readers which one you mean.

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Thanks for making an official summing-up of the comments (+1). –  whuber Jan 17 '12 at 0:04

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