Box's test warning

[The Burl]

Hello,

I'm neck-deep in dissertation data analysis and can't get Box's to run for my MANCOVA. I get this warning in the output:
Warnings
Box's Test of Equality of Covariance Matrices is not computed because there are fewer than two nonsingular cell covariance matrices.

Here's how I set up my data:
looking at 2 groups
6 DVs
1 fixed factor (IV) at 2 levels. (this may be my problem...) Isn't this fixed factor essentially just set up as a grouping variable?? So I have 1's for one group and 2's denoting the second group...
My fixed factor is set up as "nominal" and my DVs are "Scale"

Please help!
Thanks in advance!
-Jon

[David Marso]

Maybe a more detailed data description?
Actual SYNTAX!
Sample sizes? Covariance matrices for each group.
etc etc...
Since this is a DATA DEPENDENT issue, you must be more forthcoming about the specifics.
Do you have an adviser overseeing the project?  
Maybe that person should sit down with you and help nail the issue?
This could be as simple as the one or more of the dependent variables being linearly related within one or both of the groups.  This would certainly be the case if one of the groups has fewer than 6 observations.

The Burl wrote

Hello,

I'm neck-deep in dissertation data analysis and can't get Box's to run for my MANCOVA. I get this warning in the output:
Warnings
Box's Test of Equality of Covariance Matrices is not computed because there are fewer than two nonsingular cell covariance matrices.

Here's how I set up my data:
looking at 2 groups
6 DVs
1 fixed factor (IV) at 2 levels. (this may be my problem...) Isn't this fixed factor essentially just set up as a grouping variable?? So I have 1's for one group and 2's denoting the second group...
My fixed factor is set up as "nominal" and my DVs are "Scale"

Please help!
Thanks in advance!
-Jon

[The Burl]

Yep. Sure do have an adviser. Most people working on dissertations do...

Here's the covariance matrix between my two groups after I split the file by my two groups. Hope this helps.

covariances.pdf

[David Marso]

Hammering away with the following indicates that both are npd!
Also several HUGE correlations!
You did not answer the critical question!!!
SAMPLE SIZE for each group???
data list list / v1 to v6.
begin data
44.389 22.886 21.503 25.124 15.228 16.916
22.886 19.302 3.584 11.095 7.594 8.462
21.503 3.584 17.919 14.029 7.635 8.454
25.124 11.095 14.029 19.374 9.533 9.521
15.228 7.594 7.635 9.533 9.892 5.853
16.916 8.462 8.454 9.521 5.853 13.457
55.915 26.646 29.269 38.409 13.996 26.429
26.646 21.635 5.011 16.137 9.195 11.583
29.269 5.011 24.258 22.271 4.801 14.846
38.409 16.137 22.271 34.081 8.639 19.834
13.996 9.195 4.801 8.639 9.501 5.089
26.429 11.583 14.846 19.834 5.089 20.452
end data.
compute gp=$CASENUM GT 6.
LIST.
MATRIX.
GET COV01 / FILE * / VAR v1 to v6.
COMPUTE C1=COV01(1:6,:).
PRINT C1.
COMPUTE C2=COV01(7:12,:).
PRINT C2.
COMPUTE Inv1=GINV(C1).
COMPUTE Inv2=GINV(C2).
PRINT Inv1.
PRINT Inv2.
CALL EIGEN(C1,EVec1,EValue1).
PRINT EVec1.
PRINT EValue1.
CALL EIGEN(C2,EVec2,EValue2).
PRINT EVec2.
PRINT EValue2.

COMPUTE D1I=INV( SQRT( MDIAG(DIAG(C1)))).
PRINT D1I.
COMPUTE R1=D1I * C1 * D1I.
PRINT R1.
COMPUTE D2I=INV( SQRT( MDIAG(DIAG(C2)))).
PRINT D2I.
COMPUTE R2=D2I * C2 * D2I.
PRINT R2.

END MATRIX.

The Burl wrote

Yep. Sure do have an adviser. Most people working on dissertations do...

Here's the covariance matrix between my two groups after I split the file by my two groups. Hope this helps.

covariances.pdf

[The Burl]

about 150 for each sub-group. You're getting me fired up about statistics! :)

[The Burl]

What does NPD stand for! Tell me this is good! Get my Box's to run of I just won't report the damn thing!!

[SR Millis-3]

NPD = Not Positive Definite

Not so good...

http://www2.gsu.edu/~mkteer/npdmatri.html

 

~~~~~~~~~~~
Scott R Millis, PhD, ABPP, CStat, PStat®
Board Certified in Clinical Neuropsychology, Clinical Psychology, & Rehabilitation Psychology 
Professor
Wayne State University School of Medicine
Email: [hidden email]
Email: [hidden email]
Tel: [phone]

---

From: The Burl <[hidden email]>
To: [hidden email]
Sent: Thursday, June 13, 2013 4:40 PM
Subject: Re: Box's test warning

What does NPD stand for! Tell me this is good! Get my Box's to run of I just
won't report the damn thing!!



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[Bruce Weaver]

Re NPD:

http://www-01.ibm.com/support/docview.wss?uid=swg21477275
http://www2.gsu.edu/~mkteer/npdmatri.html

The Burl wrote

What does NPD stand for! Tell me this is good! Get my Box's to run of I just won't report the damn thing!!

[David Marso]

NPD = Non Positive Definite = VERY VERY BAD!
OTOH:  You have been naughty, so the MVA faeries are b-slapping you ;-)!
Hint:
data list list / v1 to v6.
begin data
44.389 22.886 21.503 25.124 15.228 16.916
22.886 19.302 3.584 11.095 7.594 8.462
21.503 3.584 17.919 14.029 7.635 8.454
25.124 11.095 14.029 19.374 9.533 9.521
15.228 7.594 7.635 9.533 9.892 5.853
16.916 8.462 8.454 9.521 5.853 13.457
55.915 26.646 29.269 38.409 13.996 26.429
26.646 21.635 5.011 16.137 9.195 11.583
29.269 5.011 24.258 22.271 4.801 14.846
38.409 16.137 22.271 34.081 8.639 19.834
13.996 9.195 4.801 8.639 9.501 5.089
26.429 11.583 14.846 19.834 5.089 20.452
end data.
COMPUTE test=v2 + v3.
COMPUTE brnfart=v1-test.
FORMATS ALL (F8.5).
LIST.




      V1       V2       V3       V4       V5       V6     TEST  BRNFART

44.38900 22.88600 21.50300 25.12400 15.22800 16.91600 44.38900   .00000
22.88600 19.30200  3.58400 11.09500  7.59400  8.46200 22.88600   .00000
21.50300  3.58400 17.91900 14.02900  7.63500  8.45400 21.50300   .00000
25.12400 11.09500 14.02900 19.37400  9.53300  9.52100 25.12400   .00000
15.22800  7.59400  7.63500  9.53300  9.89200  5.85300 15.22900  -.00100
16.91600  8.46200  8.45400  9.52100  5.85300 13.45700 16.91600   .00000
55.91500 26.64600 29.26900 38.40900 13.99600 26.42900 55.91500   .00000
26.64600 21.63500  5.01100 16.13700  9.19500 11.58300 26.64600   .00000
29.26900  5.01100 24.25800 22.27100  4.80100 14.84600 29.26900   .00000
38.40900 16.13700 22.27100 34.08100  8.63900 19.83400 38.40800   .00100
13.99600  9.19500  4.80100  8.63900  9.50100  5.08900 13.99600   .00000
26.42900 11.58300 14.84600 19.83400  5.08900 20.45200 26.42900   .00000


Number of cases read:  12    Number of cases listed:  12

[The Burl]

Dang it!

So... based on the hint, throwing out variable 5 (the negative result) would right the ship? Variable 5 being "higher levels"

So my data are generating a negative eigenvalue?? How is that possible!!?? Ahh!

[The Burl]

Can someone explain the consequences of this NPD problem if I move forward anyway and report my Pillai's Trace, F-values, Partial Eta's etc.? Any possible solutions? Is it OK to look at the one-way results individually?  

The links were very helpful BTW, thank you.

[David Marso]

Actually the culprit appears to be the first variable (I suspect it is an exact sum of the 2nd and 3rd).
Note that the test=v2+v3, brnfart=v1-test .
Clobbering v1 results in PD matrices for the remaining vars.
The negative eigenvalue(s) from my MATRIX code might be simply a side effect of running the code against a matrix which is reported to only 3 sig digits.  Same with the brnfart values not being exactly 0.
Another notable source of NPD matrices is the use of pairwise deletion of missing data.

The Burl wrote

Dang it!

So... based on the hint, throwing out variable 5 (the negative result) would right the ship? Variable 5 being "higher levels"

So my data are generating a negative eigenvalue?? How is that possible!!?? Ahh!

[Mark Miller]

NPD can also mean that you have a ZERO (within tolerance) eigenvalue.

That is probably quite likely when you have two vars which are essentially collinear.

Negative eigenvalues often means you hit a saddle-point.

... Mark Miller

On Thu, Jun 13, 2013 at 2:35 PM, David Marso <[hidden email]> wrote:

Actually the culprit appears to be the first variable (I suspect it is an
exact sum of the 2nd and 3rd).
Note that the test=v2+v3, brnfart=v1-test .
Clobbering v1 results in PD matrices for the remaining vars.
The negative eigenvalue(s) from my MATRIX code might be simply a side effect
of running the code against a matrix which is reported to only 3 sig digits.
Same with the brnfart values not being exactly 0.
Another notable source of NPD matrices is the use of pairwise deletion of
missing data.


The Burl wrote

> Dang it!
>
> So... based on the hint, throwing out variable 5 (the negative result)
> would right the ship? Variable 5 being "higher levels"
>
> So my data are generating a negative eigenvalue?? How is that possible!!??
> Ahh!

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[The Burl]

Two thumbs pointing at this guy who just got his Box's test to run! I can theoretically throw that variable out, so I'm all good. Of course Box's is significant which is an entire other can of worms!

Thanks for the help David. Maybe I will get that degree finished after all...

-Jon

[David Marso]

"Any possible solutions?"
Yes:  get rid of the first variable.
This is a situation where 'size' doesn't matter!

The Burl wrote

Can someone explain the consequences of this NPD problem if I move forward anyway and report my Pillai's Trace, F-values, Partial Eta's etc.? Any possible solutions? Is it OK to look at the one-way results individually?  

The links were very helpful BTW, thank you.

The Burl wrote

Can someone explain the consequences of this NPD problem if I move forward anyway and report my Pillai's Trace, F-values, Partial Eta's etc.? Any possible solutions? Is it OK to look at the one-way results individually?  

The links were very helpful BTW, thank you.

[Ryan]

Hi all,

I recently saw a message on the SPSS newsgroups asking about fitting Generalized Additives Models (GADs) in SPSS. The IBM website states:

http://www-01.ibm.com/support/docview.wss?uid=swg21479641

Has anyone ever employed a GAD in SPSS? If yes, would you mind posting the model and code to the list?

Thanks,

Ryan