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From |
David Airey <david.airey@vanderbilt.edu> |

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:

Judith Abrams <abramsj@karmanos.org> asks:

> 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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