MANOVA and Extra Sums-of-Squares Tests

[chris33]

I would like to conduct an extra sum-of -squares test that compares a full MANOVA model (with all 1st order interactions) to a reduced model (no interactions) to determine if I can drop all interactions at the same time.  This is analagous to an extra sum-of-squares F-test in ANOVA, but instead using MANOVA.  Is there a command in R that does this?  If not, is there a command that calculates residual sum-of-squares and cross-product matrices?  Thanks.

[John Fox]

Dear chris33,

You can use the anova() function to compare the two multivariate linear models. Alternatively, the Anova() function in the car package will compute "type II" or "type III" MANOVA tests, which aren't quite what you're asking about.

I hope this helps,
 John

------------------------------------------------
John Fox
Sen. William McMaster Prof. of Social Statistics
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
http://socserv.mcmaster.ca/jfox/

On Tue, 13 Mar 2012 12:31:25 -0700 (PDT)
 chris33 <[hidden email]> wrote:

> I would like to conduct an extra sum-of -squares test that compares a full
> MANOVA model (with all 1st order interactions) to a reduced model (no
> interactions) to determine if I can drop all interactions at the same time.
> This is analagous to an extra sum-of-squares F-test in ANOVA, but instead
> using MANOVA.  Is there a command in R that does this?  If not, is there a
> command that calculates residual sum-of-squares and cross-product matrices?
> Thanks.
>
> --
> View this message in context: http://r.789695.n4.nabble.com/MANOVA-and-Extra-Sums-of-Squares-Tests-tp4470077p4470077.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

______________________________________________
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[chris33]

Hi John,

Thanks for your response.  The anova funtion will not work in my case, because I have multiple response variables.  In other words, I would like to conduct an extra sums-of-squares and cross-products test between the following models:

FULL.MODEL:   (Y1, Y2, Y3, Y4, Y5) as a function of  X1 + X2 + X3 + X4 + X1*X2 +X1*X3 + X1*X4
REDUCED.MODEL:   (Y1, Y2, Y3, Y4, Y5) as a function of X1 + X2 + X3 + X4

So, I suppose that I would need to calculate the residual sum-of-squares and cross-product matrices for each of these models as a start.  Any ideas how I would go about this in R?  Thanks again,

Chris  

[John Fox]

Dear chris33,

Well, actually as I said, the anova() function *will* do what you want. You can fit multivariate linear models with lm(),

mod.1 <- lm(cbind(Y1, Y2, Y3, Y4, Y5) ~ X1*X2 +X1*X3 + X1*X4)
mod.2 <- lm(cbind(Y1, Y2, Y3, Y4, Y5) ~ X1 + X2 + X3 + X4)

and then use anova() to get multivariate tests,

anova(mod.1, mod.2)

See ?anova.mlm for more information.

Best,
 John

On Tue, 13 Mar 2012 14:49:01 -0700 (PDT)
 chris33 <[hidden email]> wrote:

> Hi John,
>
> Thanks for your response.  The anova funtion will not work in my case,
> because I have multiple response variables.  In other words, I would like to
> conduct an extra sums-of-squares and cross-products test between the
> following models:
>
> FULL.MODEL:   (Y1, Y2, Y3, Y4, Y5) as a function of  X1 + X2 + X3 + X4 +
> X1*X2 +X1*X3 + X1*X4
> REDUCED.MODEL:   (Y1, Y2, Y3, Y4, Y5) as a function of X1 + X2 + X3 + X4
>
> So, I suppose that I would need to calculate the residual sum-of-squares and
> cross-product matrices for each of these models as a start.  Any ideas how I
> would go about this in R?  Thanks again,
>
> Chris  
>
> --
> View this message in context: http://r.789695.n4.nabble.com/MANOVA-and-Extra-Sums-of-Squares-Tests-tp4470077p4470459.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[chris33]

Hi John,

Thanks again.  That looks like an easy and convenient approach.  Regards,

Chris