Determinant of correlation matrix (R matrix) - factor analysis

[espglp]

Hi,

I have a question regarding the determinant of correlation matrix in the factor analysis. There are two samples. One is 2.34E-004, and another 7.63E-004. Does that mean is 0.000234 and 0.000763?


Actually, the threshold of identification of multicollearity is the determinant of correlation matrix is over 0.00001. If the correlation matrix shows the one single tailed (all significant for all variable correlations), does this threshold has to be 0.001? Alternatively, the threshold of 0.00001 would sufficiently to measure the issue of multicollearity no matter it is two-tailed or one-tailed? Thanks

Michael

[Maguin, Eugene]

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of espglp
Sent: Wednesday, July 31, 2013 4:27 PM
To: [hidden email]
Subject: Determinant of correlation matrix (R matrix) - factor analysis

Hi,

I have a question regarding the determinant of correlation matrix in the factor analysis. There are two samples. One is 2.34E-004, and another 7.63E-004. Does that mean is 0.000234 and 0.000763?

>>Yes.

Actually, the threshold of identification of multicollearity is the determinant of correlation matrix is over 0.00001. If the correlation matrix shows the one single tailed (all significant for all variable correlations), does this threshold has to be 0.001? Alternatively, the threshold of 0.00001 would sufficiently to measure the issue of multicollearity no matter it is two-tailed or one-tailed? Thanks

>>Are you sure this is stated correctly? Maybe I'm misreading your statement but wouldn't evidence of multicollinearity be that the determinant is less than 0.00001?   I can't comment on the other two sentences; I don't have enough experience.  Gene Maguin



Michael



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[espglp]

Possibly, it could ask for the determinant of the R matrix to test for multicollinearity or singularity. The determinant of R-matrix should be greater than 0.00001. If the value is greater than 0.00001, thus, multicollinearity is not a problem for these data. However, I am not sure whether this threshold can also be applied to the one tailed test (since the correlation matrix (R-matrix) are significant in the one tailed test)? If so, the threshold of greater than 0.00001 would be still valid in one tailed test? If not, the determinant of value has to be over 0.001 based on the one tailed test (all variables are significant in the correlation matrix).

Probably, this threshold (0.00001) would be sufficiently to measure multicollinearity or sigularity, no matter where is one-tailed or two-tailed. Please help me clarify this concern. Thanks

 

[Mark Miller]

The [calculated] determinant of a matrix is a lousy measure of multicollinearity.

The real issue is whether the correlation matrix is FULL RANK, which means

in other words that it has a full set of positive eigenvalues (i.e. is Positive Definite)

Examining the eigenvalues is more informative and less subject to precision issues.

If any eigenvalue is zero or less than some epsilon, then you have multicollinearity-- full stop.

... mark miller

On Wed, Jul 31, 2013 at 3:03 PM, espglp <[hidden email]> wrote:

Possibly, it could ask for the determinant of the R matrix to test for
multicollinearity or singularity. The determinant of R-matrix should be
greater than 0.00001. If the value is greater than 0.00001, thus,
multicollinearity is not a problem for these data. However, I am not sure
whether this threshold can also be applied to the one tailed test (since the
correlation matrix (R-matrix) are significant in the one tailed test)? If
so, the threshold of greater than 0.00001 would be still valid in one tailed
test? If not, the determinant of value has to be over 0.001 based on the one
tailed test (all variables are significant in the correlation matrix).

Probably, this threshold (0.00001) would be sufficiently to measure
multicollinearity or sigularity, no matter where is one-tailed or
two-tailed. Please help me clarify this concern. Thanks





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[Rich Ulrich]

Even if you have "true multicollinearity" -- indicated by a
determinant of zero or within machine roundoff-error of zero --
it is possible to define a factor analysis, though the number of
factors will be reduced by one (or more).   However, the lack
of full rank says that the computer program cannot use the
simple inverse as a step in the solution, but would have to use
some other, more tedious method.  IIRC, SPSS simply drops some
variable when it finds itself with a pivot element *too*, too close
to zero (if nothing else, later computations become increasingly
imprecise), and you can specify a different limit.

Any limit that you see which is not zero or "computer-zero"  is
someone's arbitrary choice and rule-of-thumb.  The numeric value
of a determinant does get smaller as the count of correlated
variables increases.

--
Rich Ulrich

> Date: Wed, 31 Jul 2013 15:03:02 -0700

> From: [hidden email]
> Subject: Re: Determinant of correlation matrix (R matrix) - factor analysis
> To: [hidden email]
>
> Possibly, it could ask for the determinant of the R matrix to test for
> multicollinearity or singularity. The determinant of R-matrix should be
> greater than 0.00001. If the value is greater than 0.00001, thus,
> multicollinearity is not a problem for these data. However, I am not sure
> whether this threshold can also be applied to the one tailed test (since the
> correlation matrix (R-matrix) are significant in the one tailed test)? If
> so, the threshold of greater than 0.00001 would be still valid in one tailed
> test? If not, the determinant of value has to be over 0.001 based on the one
> tailed test (all variables are significant in the correlation matrix).
>
> Probably, this threshold (0.00001) would be sufficiently to measure
> multicollinearity or sigularity, no matter where is one-tailed or
> two-tailed. Please help me clarify this concern. Thanks
> [snip ...]

[espglp]

HI Mark,

Thanks for your reply.

Could you provide any literature in order to support your idea? Thanks

[Jon K Peck]

The determinant is the product of the eigenvalues, so a zero determinant and any zero eigenvalue is the same thing mathematically.

But bear in mind that other than an exact linear dependency, multicollinearity is a matter of degree not a yes/no decision.


Jon Peck (no "h") aka Kim
Senior Software Engineer, IBM
[hidden email]
phone: [phone]




From:        Mark Miller <[hidden email]>
To:        [hidden email],
Date:        07/31/2013 04:30 PM
Subject:        Re: [SPSSX-L] Determinant of correlation matrix (R matrix) -              factor analysis
Sent by:        "SPSSX(r) Discussion" <[hidden email]>

---

The [calculated] determinant of a matrix is a lousy measure of multicollinearity.
The real issue is whether the correlation matrix is FULL RANK, which means
in other words that it has a full set of positive eigenvalues (i.e. is Positive Definite)
Examining the eigenvalues is more informative and less subject to precision issues.
If any eigenvalue is zero or less than some epsilon, then you have multicollinearity-- full stop.

... mark miller


On Wed, Jul 31, 2013 at 3:03 PM, espglp <yundian1234@...> wrote:
Possibly, it could ask for the determinant of the R matrix to test for
multicollinearity or singularity. The determinant of R-matrix should be
greater than 0.00001. If the value is greater than 0.00001, thus,
multicollinearity is not a problem for these data. However, I am not sure
whether this threshold can also be applied to the one tailed test (since the
correlation matrix (R-matrix) are significant in the one tailed test)? If
so, the threshold of greater than 0.00001 would be still valid in one tailed
test? If not, the determinant of value has to be over 0.001 based on the one
tailed test (all variables are significant in the correlation matrix).

Probably, this threshold (0.00001) would be sufficiently to measure
multicollinearity or sigularity, no matter where is one-tailed or
two-tailed. Please help me clarify this concern. Thanks





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[espglp]

Please, who could help me double confirm this expression is correct? Many thanks

"I have a question regarding the determinant of correlation matrix in the factor analysis. There are two samples. One is determinant = 2.34E-004, and another is determinant =  7.63E-004. Does that mean is 0.000234 and 0.000763"?

[David Marso]

I believe Gene answered this in the affirmative.
Please consult a reference concerning conversion of scientific notation to decimal notation!
Move to the left!

espglp wrote

Please, who could help me double confirm this expression is correct? Many thanks

"I have a question regarding the determinant of correlation matrix in the factor analysis. There are two samples. One is determinant = 2.34E-004, and another is determinant =  7.63E-004. Does that mean is 0.000234 and 0.000763"?