Determinant of the covariance matrix near to zero

[Tanja Gabriele Baudson]

Hi all,

I performed a factor analysis across 36 items (item solved correctly
vs incorrectly). When I computed the scale reliability, SPSS showed
the warning above. I know that this may be due to the fact that either
two variables correlate perfectly or that one or more variables can be
predicted from a linear combination of other variables. It was no
problem to rule out the first issue; however, I wonder if there is any
way to find out the "bad apple" if the second reason is correct. I
guess it might be difficult to check for all linear combinations ;)

Is there any remedy for this problem? (As to the reliabilities, which,
afaik, are based on the matrix itself and not on the inverted matrix,
it's maybe no problem; however, I think it might become one if I want
to perform regression analyses and other analyses where the inverted
matrix is involved.)

Your help is greatly appreciated. Thanks in advance!
Tanja
--
Tanja Gabriele Baudson
Universität Trier
FB I Psychologie
Hochbegabtenforschung und -förderung
54286 Trier
Fon 0651/201-4558
Fax [phone]
Email [hidden email]
Web http://www.uni-trier.de/index.php?id=9492

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[Mike]

In the Reliability procedure, you should get the squared multiple
correlation of each iterm with the rest of the items in the "scale"
in the item-total statistics.  If this value is close to 1.00, then you
have the offending item.

-Mike Palij
New York University
[hidden email]

----- Original Message -----
From: "Tanja Gabriele Baudson" <[hidden email]>
To: <[hidden email]>
Sent: Friday, September 17, 2010 6:38 AM
Subject: Determinant of the covariance matrix near to zero

> Hi all,
>
> I performed a factor analysis across 36 items (item solved correctly
> vs incorrectly). When I computed the scale reliability, SPSS showed
> the warning above. I know that this may be due to the fact that either
> two variables correlate perfectly or that one or more variables can be
> predicted from a linear combination of other variables. It was no
> problem to rule out the first issue; however, I wonder if there is any
> way to find out the "bad apple" if the second reason is correct. I
> guess it might be difficult to check for all linear combinations ;)
>
> Is there any remedy for this problem? (As to the reliabilities, which,
> afaik, are based on the matrix itself and not on the inverted matrix,
> it's maybe no problem; however, I think it might become one if I want
> to perform regression analyses and other analyses where the inverted
> matrix is involved.)
>
> Your help is greatly appreciated. Thanks in advance!
> Tanja
> --
> Tanja Gabriele Baudson
> Universität Trier
> FB I Psychologie
> Hochbegabtenforschung und -förderung
> 54286 Trier
> Fon 0651/201-4558
> Fax [phone]
> Email [hidden email]
> Web http://www.uni-trier.de/index.php?id=9492
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD

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[Tanja Gabriele Baudson]

Hi Mike,

is it possible that the squared multiple correlation is based on the
inverse matrix? The SPSS output in this column consists of missing
values only. At least, the warning reads "The determinant of the
covariance matrix is zero or approximately zero. Statistics based on
its inverse matrix cannot be computed and they are displayed as system
missing values." The idea is nice, though :)

Best,
Tanja

On 17 Sep 2010, at 14:18, Mike Palij wrote:

> In the Reliability procedure, you should get the squared multiple
> correlation of each iterm with the rest of the items in the "scale"
> in the item-total statistics.  If this value is close to 1.00, then
> you
> have the offending item.
>
> -Mike Palij
> New York University
> [hidden email]
>
> ----- Original Message -----
> From: "Tanja Gabriele Baudson" <[hidden email]>
> To: <[hidden email]>
> Sent: Friday, September 17, 2010 6:38 AM
> Subject: Determinant of the covariance matrix near to zero
>
>
>> Hi all,
>>
>> I performed a factor analysis across 36 items (item solved correctly
>> vs incorrectly). When I computed the scale reliability, SPSS showed
>> the warning above. I know that this may be due to the fact that
>> either
>> two variables correlate perfectly or that one or more variables can
>> be
>> predicted from a linear combination of other variables. It was no
>> problem to rule out the first issue; however, I wonder if there is
>> any
>> way to find out the "bad apple" if the second reason is correct. I
>> guess it might be difficult to check for all linear combinations ;)
>>
>> Is there any remedy for this problem? (As to the reliabilities,
>> which,
>> afaik, are based on the matrix itself and not on the inverted matrix,
>> it's maybe no problem; however, I think it might become one if I want
>> to perform regression analyses and other analyses where the inverted
>> matrix is involved.)
>>
>> Your help is greatly appreciated. Thanks in advance!
>> Tanja
>> --
>> Tanja Gabriele Baudson
>> Universität Trier
>> FB I Psychologie
>> Hochbegabtenforschung und -förderung
>> 54286 Trier
>> Fon 0651/201-4558
>> Fax [phone]
>> Email [hidden email]
>> Web http://www.uni-trier.de/index.php?id=9492
>>
>> =====================
>> To manage your subscription to SPSSX-L, send a message to
>> [hidden email] (not to SPSSX-L), with no body text
>> except the
>> command. To leave the list, send the command
>> SIGNOFF SPSSX-L
>> For a list of commands to manage subscriptions, send the command
>> INFO REFCARD
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except
> the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD

--
Tanja Gabriele Baudson
Universität Trier
FB I Psychologie
Hochbegabtenforschung und -förderung
54286 Trier
Fon 0651/201-4558
Fax [phone]
Email [hidden email]
Web http://www.uni-trier.de/index.php?id=9492

=====================
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[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
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For a list of commands to manage subscriptions, send the command
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[Mike]

I don't know how SPSS calculates this quantity but someone
with knowledge about the algorithm(s) may supply an answer.
I assume that the inverted matrix is ysed and that SPSS is
warning you that you're attempting to do something equivalent
to division by zero.

It might be possible to obtain the multiple correlation of each
item with others through one of the regression procedures by
running all regressions where each item is the dependent variable
and the remaining variables are predictor/independent variables
though this would probably generate a lot of output.  Perhaps
someone can suggest an alternative method?

-Mike Palij
New


----- Original Message -----
From: "Tanja Gabriele Baudson" <[hidden email]>
To: <[hidden email]>
Sent: Friday, September 17, 2010 8:28 AM
Subject: Re: Determinant of the covariance matrix near to zero

> Hi Mike,
>
> is it possible that the squared multiple correlation is based on the
> inverse matrix? The SPSS output in this column consists of missing
> values only. At least, the warning reads "The determinant of the
> covariance matrix is zero or approximately zero. Statistics based on
> its inverse matrix cannot be computed and they are displayed as system
> missing values." The idea is nice, though :)
>
> Best,
> Tanja
>
> On 17 Sep 2010, at 14:18, Mike Palij wrote:
>
>> In the Reliability procedure, you should get the squared multiple
>> correlation of each iterm with the rest of the items in the "scale"
>> in the item-total statistics.  If this value is close to 1.00, then
>> you
>> have the offending item.
>>
>> -Mike Palij
>> New York University
>> [hidden email]
>>
>> ----- Original Message -----
>> From: "Tanja Gabriele Baudson" <[hidden email]>
>> To: <[hidden email]>
>> Sent: Friday, September 17, 2010 6:38 AM
>> Subject: Determinant of the covariance matrix near to zero
>>
>>
>>> Hi all,
>>>
>>> I performed a factor analysis across 36 items (item solved correctly
>>> vs incorrectly). When I computed the scale reliability, SPSS showed
>>> the warning above. I know that this may be due to the fact that
>>> either
>>> two variables correlate perfectly or that one or more variables can
>>> be
>>> predicted from a linear combination of other variables. It was no
>>> problem to rule out the first issue; however, I wonder if there is
>>> any
>>> way to find out the "bad apple" if the second reason is correct. I
>>> guess it might be difficult to check for all linear combinations ;)
>>>
>>> Is there any remedy for this problem? (As to the reliabilities,
>>> which,
>>> afaik, are based on the matrix itself and not on the inverted matrix,
>>> it's maybe no problem; however, I think it might become one if I want
>>> to perform regression analyses and other analyses where the inverted
>>> matrix is involved.)
>>>
>>> Your help is greatly appreciated. Thanks in advance!
>>> Tanja
>>> --
>>> Tanja Gabriele Baudson
>>> Universität Trier
>>> FB I Psychologie
>>> Hochbegabtenforschung und -förderung
>>> 54286 Trier
>>> Fon 0651/201-4558
>>> Fax [phone]
>>> Email [hidden email]
>>> Web http://www.uni-trier.de/index.php?id=9492
>>>
>>> =====================
>>> To manage your subscription to SPSSX-L, send a message to
>>> [hidden email] (not to SPSSX-L), with no body text
>>> except the
>>> command. To leave the list, send the command
>>> SIGNOFF SPSSX-L
>>> For a list of commands to manage subscriptions, send the command
>>> INFO REFCARD
>>
>> =====================
>> To manage your subscription to SPSSX-L, send a message to
>> [hidden email] (not to SPSSX-L), with no body text except
>> the
>> command. To leave the list, send the command
>> SIGNOFF SPSSX-L
>> For a list of commands to manage subscriptions, send the command
>> INFO REFCARD
>
> --
> Tanja Gabriele Baudson
> Universität Trier
> FB I Psychologie
> Hochbegabtenforschung und -förderung
> 54286 Trier
> Fon 0651/201-4558
> Fax [phone]
> Email [hidden email]
> Web http://www.uni-trier.de/index.php?id=9492
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD

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[Bruce Weaver]

Mike Palij wrote

--- snip ---

It might be possible to obtain the multiple correlation of each
item with others through one of the regression procedures by
running all regressions where each item is the dependent variable
and the remaining variables are predictor/independent variables
though this would probably generate a lot of output.  Perhaps
someone can suggest an alternative method?

-Mike Palij

Run a linear regression with all of the items as explanatory variables, and any variable you wish as the outcome.  Include the collinearity diagnostics.  The R-squared value for each item = 1 - tolerance.