# [R] Multivariate multiple linear regression question

Michael Friendly friendly at yorku.ca
Mon Feb 22 14:38:35 CET 2016

```Hi Vivendra

A few suggestions:

* You will get more interpretable tests by using Type II (partial) tests
of terms in your model via
library(car)
Manova(MRI_model)
as opposed to the Type I (sequential) tests available from manova()

* You will be able to understand the results better by making heplots via
library(helplots)
heplot(MRI_model)
but you will have to read the associated vignettes to learn how to
interpret them.

* You can test for equality of covariance matrices in the various
groups using heplots::boxM(), new in the development version on
R-Forge
install.packages("heplots", repos="http://R-Forge.R-project.org")
library(helplots)
res <- boxM(MRI_model, group=group)
res
plot(res)

* You can visually assess the correlations in the groups using
car::scatterplot(..., ellipse=TRUE, groups=)

-Michael

On 2/20/2016 12:53 PM, Virendra Mishra wrote:
> Hi R-users,
>
> I have a fairly simple question to ask but I havent yet got an answer to
> the question. I will describe my experiment, analysis and what have I done
> and what is the question in the following paragraphs and I would appreciate
> if anyone could point me to use right statistical tools to answer my
> question.
>
> Experiment:
> I have 2 groups and both groups undergo 2 set of evaluations, one with MRI
> scanner and the other in the lab to test for their behavior. Both these
> evaluations are known to have statistically significant relationship with
> age and gender.
>
> Statistical question of interest:
> Whether there is:
> 1) statistically significant difference between the 2 groups on each
> evaluation ?
> 2) Whether there is any relationship between and within the 2 groups
> between each evaluation
>
> Model:
>
> I model the problem as following:
> MRI_measure = Intercept + Slope1 * Age + Slope 2 * Gender + Slope3 * Group
> [Age is continuous and gender , Group are factors/categorical]
>
> Lab_measure = Intercept + Slope1 * Age + Slope 2 * Gender + Slope3 * Group
> [Age is continuous and gender , Group are factors/categorical]
>
> In order to obtain the solution in R:
> MRI_model<-lm(cbind(MRI_measure, Lab_measure) ~ age+gender+group,
> data=data)
>
> Result of R:
> manova(MRI_model) suggests that yes indeed all the slopes are significantly
> different than 0 suggesting a relationship between my measures.
>
> Question:
> 1) In order to test whether the difference in the MRI_measure is
> statistically significant different between the 2 groups, I use
> MRI_model\$fitted.values for each dependent measure and do a statistical
> test (either t-test or Wilcox) and claim that the difference is
> significant.
> In the paper I write, multivariate multiple linear regression was performed
> for the groups while controlling for age and gender. The regressed out
> MRI_measure was statistically compared to see if the difference is
> different.
>
> I am assuming that the predicted/fitted.values in model are the regressed
> out variables. Can I show this and use this result? Is this right
>
> If no, what is the correct way to statistically compare whether my 2 groups
> differ in their MRI measure and lab measure when controlled for age and
> gender. Any R library, literature, possibly a script will be greatly
> appreciated.
>
> 2) I also want to see if there is any relationship between MRI_measure and
> Lab_measure within the group after they are controlled for age and gender.
> What is the correct way to do this in R?
>
> Further, I also want to see if there is any significantly different
> association between the 2 groups for my set of dependent variables. I am
> thinking this can be done: I first find the correlation between 2 dependent
> variable in each group and test if this correlation is statistically
> different between the 2 groups? Is this logic right? And if it is, how do I
> compare the correlation? If not, what is the right way to do this? Any R
> library, literature, possibly a script will be greatly appreciated.
>
> I do appreciate any reply.
>
> Thanks
>
> Regards
>
> Virendra
>
> 	[[alternative HTML version deleted]]
>

```