Multiple Regression Model: Univariate or Multivariate GLM?

by Karen

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I would love to promise that the reason there is so much confusing terminology in statistics is NOT because statisticians like to laugh at hapless users of statistics as they try to figure out already confusing concepts.  See my post on the different meanings of the term “level” in statistics.  (There are other examples–how many different meanings does “beta” have in statistics?  I can think of three off the top of my head.  That will have to be another post).

But today I talk about the difference between multivariate and multiple, as they relate to regression.

A regression analysis with one dependent variable and 8 independent variables is NOT a multivariate regression.  It’s a multiple regression.  Multivariate analysis ALWAYS refers to the dependent variable.

So when you’re in SPSS, choose univariate GLM for this model, not multivariate.

I know what you’re thinking–but what about multivariate analyses like cluster analysis and factor analysis, where there is no dependent variable, per se?

Well, I respond, it’s not really about dependency.  It’s about which variable’s variance is being analyzed.  A regression model is really about the dependent variable.  We’re just using the predictors to model the mean and the variation in the dependent variable.

Note: this is actually a situation where the subtle differences in what we call that Y variable can help.  Calling it the outcome or response variable, rather than dependent, is more applicable to something like factor analysis.

So when to choose multivariate GLM?  When you’re jointly modeling the variation in multiple response variables.

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{ 7 comments… read them below or add one }

Ram April 8, 2015 at 12:40 am

Hello Karen,
“A regression analysis with one dependent variable and 8 independent variables is NOT a multivariate regression. It’s a multiple regression. Multivariate analysis ALWAYS refers to the dependent variable”…
………………..Can you please give some reference for this quote??

Reply

Bonnie March 8, 2015 at 8:40 pm

Hi Karen,

Just wondered what your take is on using the terms Univariate or Bivariate analysis when you are talking about testing an association between two variables (such as exposure and an outcome variable)? I have seen both terms used in the situation and I was wondering if they can be used interchangeably? Kind Regards Bonnie

Reply

Karen March 23, 2015 at 12:32 pm

Good question.

When you’re talking about descriptive statistics, univariate means a single variable, so an association would be bivariate.

But once you’re talking about modeling, the term univariate or multivariate refers to the number of dependent variables. You don’t ever tend to use bivariate in that context. But for example, a univariate anova has one dependent variable whereas a multivariate anova (MANOVA) has two or more.

This is why a regression with one outcome and more than one predictor is called multiple regression, not multivariate regression.

Reply

sylvia October 31, 2014 at 2:22 pm

Hi Karen,
I have a question about multiple regression, when we choose predictors to include in the regression model based on univariate analysis, do we set the P-value at 0.1 or 0.2? Or it should be at the level of 0.05?

Thanks

Reply

Karen November 3, 2014 at 4:41 pm

Hi Sylvia,

There’s no rule about where to set a p-value in that context. It depends on how inclusive you want to be.

Reply

Suresh Kumar February 13, 2012 at 8:16 am

Hello there,
My name is Suresh Kumar. Currently, I’m learning multivariate analysis, since i am only familiar with multiple regression. I want to ask you about my doubt in Factor Analysis (FA)in searching the dominant FACTOR not Factors. in Multiple Regression (MR)we can use t-test best on the residual of each independent variable.
My doubt is whether FA is only to find factors not the dominant factor or we can also use it to find the dominant factor as what we can in MR. Instead of data reduction, what else can we do with FA?
Once we have done getting the factors through FA, is it possible to use MR to find the influence or impact on something? or from FA we continue to Confirmatory FA and next using SEM?
If FA to deal with dependent variables, then how to check the factors influencing the dependent variables?
Are we dealing with multiple dependent variables and multiple independent variables if we want to find out the influencing factors?
Thanking you in advance.
Regards
Suresh Kumar

Reply

Karen February 24, 2012 at 8:06 pm

Hi Suresh,

Factor Analysis is doing something totally different than multiple regression. You’re right, it’s for data reduction, but specifically in a situation where theoretically there is a latent variable.

You can then use the factor scores, in a MR, and that is equivalent to running an SEM.

A really great book with all the details on this is Larry Hatcher’s book on Factor Analysis and SEM using SAS. I forget the exact title, but you can easily search for it. Even if you don’t use SAS, he explains the concepts and the steps so well, it’s worth getting.

Best,
Karen

Reply

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