# re: st: collinearity in hotelling

 From David Airey To statalist@hsphsun2.harvard.edu Subject re: st: collinearity in hotelling Date Fri, 28 May 2004 13:07:55 -0500

I used hotelling to compare some before and after data from patients who
underwent a surgical procedure. First I made a difference score for each
measure, and then tested whether the vector of mean difference scores was
equal to a vector of zeros.

The Hotelling T-squared procedure dropped 18 of the 28 variables "due to
collininearity." I don't know how to interpret collininearity in this
context.

Any information is appreciated.

There was a bug related to hotelling and collinearity that was brought up previously. Don't know if same or different issue:

Below is that message:

> Using the following dataset I compared the 2 groups with respect
> to x1 and x2 using Hotelling's T squared statistic.
>
> group animal x1 x2 x3
> |--------------------------------------
> 1. | 0 1 52.2 35.4 12.4
> 2. | 0 2 32.6 42.3 25.1
> 3. | 0 3 48.5 37.0 14.5
> 4. | 0 4 32.1 46.5 21.4
> 5. | 0 5 38.4 46.0 15.6
> |--------------------------------------
> 6. | 1 6 19.2 50.1 30.7
> 7. | 1 7 11.7 55.0 33.3
> 8. | 1 8 7.0 64.5 28.5
> 9. | 1 9 6.4 50.2 43.4
> 10. | 1 10 6.2 50.0 43.8
> +--------------------------------------
>
> I got the following results:
>
> 2-group Hotelling's T-squared = 40.80087
> F test statistic: ((10-2-1)/(10-2)(2)) x 40.80087 = 17.850381
>
> H0: Vectors of means are equal for the two groups
> F(2,7) = 17.8504
> Prob > F(2,7) = 0.0018
>
> I didn't include all 3 x variables because x1+x2+x3=100. Since
> I had given the investigator a long sermon about why I couldn't
> include x1 and x2 and x3, I decided to run Hotelling's T square
> with all 3 variables just to demonstrate that it would fail b
> ecause of a singular matrix. Instead of failing, I got these
> results:
>
> 2-group Hotelling's T-squared = 40.80087
> F test statistic: ((10-3-1)/(10-2)(3)) x 40.80087 = 10.200218
>
> H0: Vectors of means are equal for the two groups
> F(3,6) = 10.2002
> Prob > F(3,6) = 0.0090
>
> Shouldn't I have received an error message?
>
> The regression command operated as expected. When I executed
> regress x1 x2 x3, x1 was dropped. The results of Manova were
> consistent with Hotelling's T-square.

Notice that the T-squared value is the same and the difference in
the F test and p-value are due to the number of degrees of
freedom.

It is as if -hotelling- drops one of the collinear variables, but
forgets to adjust the degrees of freedom downward accordingly.

I will look into fixing -hotelling- so that it displays a message
saying that a particular variable (or variables) are dropped due
to collinearity and then have it adjust the d.f.s.

This fix will probably be available in time for an ado-file
udpate we are planning for next week.

Ken Higbee khigbee@stata.com
StataCorp 1-800-STATAPC

-Dave

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