Principal Axis Factor and SPSS

[krisscot]

I hope that someone can help clarify some interesting output I came across from a Factor Analysis that I just conducted. I have a 24-item instrument that I used Principal Axis Factoring for. By default, SPSS suggested that there were 5 factors based on the eigenvalue greater than 1 rule. I then tried to run the same procedure but altered the number of factors to be extracted to 3. The eigenvalues for the 3-factor solution were not the same values as the first 3 eigenvalues from the 5-factor solution (all values are based on prerotation). The values are close but shouldn't they be identical given that factors are extracted ortogonally? Thanks!

 

Kris

[Bruce Weaver]

krisscot wrote

I hope that someone can help clarify some interesting output I came across from a Factor Analysis that I just conducted. I have a 24-item instrument that I used Principal Axis Factoring for. By default, SPSS suggested that there were 5 factors based on the eigenvalue greater than 1 rule. I then tried to run the same procedure but altered the number of factors to be extracted to 3. The eigenvalues for the 3-factor solution were not the same values as the first 3 eigenvalues from the 5-factor solution (all values are based on prerotation). The values are close but shouldn't they be identical given that factors are extracted ortogonally? Thanks!

Kris

I am not an expert on factor analysis, but what I have read suggests that the "eigenvalues > 1" rule (aka Kaiser's criterion) is not a particularly good one much of the time.  See the following article for, for example.

   http://www.people.ku.edu/~preacher/pubs/preacher_maccallum_2003.pdf

HTH.

[Ryan]

The OP might find this helpful:

https://people.ok.ubc.ca/brioconn/nfactors/nfactors.html

Ryan

On Thu, Feb 10, 2011 at 8:41 PM, Bruce Weaver <[hidden email]> wrote:

> krisscot wrote:
>>
>> I hope that someone can help clarify some interesting output I came across
>> from a Factor Analysis that I just conducted. I have a 24-item instrument
>> that I used Principal Axis Factoring for. By default, SPSS suggested that
>> there were 5 factors based on the eigenvalue greater than 1 rule. I then
>> tried to run the same procedure but altered the number of factors to be
>> extracted to 3. The eigenvalues for the 3-factor solution were not the
>> same values as the first 3 eigenvalues from the 5-factor solution (all
>> values are based on prerotation). The values are close but shouldn't they
>> be identical given that factors are extracted ortogonally? Thanks!
>>
>> Kris
>>
>
> I am not an expert on factor analysis, but what I have read suggests that
> the "eigenvalues > 1" rule (aka Kaiser's criterion) is not a particularly
> good one much of the time.  See the following article for, for example.
>
>   http://www.people.ku.edu/~preacher/pubs/preacher_maccallum_2003.pdf
>
> HTH.
>
>
> -----
> --
> Bruce Weaver
> [hidden email]
> http://sites.google.com/a/lakeheadu.ca/bweaver/
>
> "When all else fails, RTFM."
>
> NOTE: My Hotmail account is not monitored regularly.
> To send me an e-mail, please use the address shown above.
>
> --
> View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Principal-Axis-Factor-and-SPSS-tp3380434p3380519.html
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
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[Art Kendall]

Parallel analysis is a great way to approximate the number of factors to explore to be retained.

The Kaiser criterion basically says "Why on earth would anybody want to retain a factor that accounts for less than one variable's worth of the total (common) variance?" It does not say "This is about where to look for the number to retain."

There can be as many dimensions as there are variables, but the last extracted usually have very trivial amounts of the total variance one is trying to account for, way beyond "Who cares?". When these methods were started factor analysis took a lot of of time to run.  The number of factors to rotate was a major contributor to that time.  Last week I did a parallel analysis on with 1000 pseudorandom permutations of 40,000 cases and 14 variables in 55 minutes.  I can remember when simply doing a single factor analysis  with 400 cases with none of the permutation would take that long.

Art Kendall
Social Research Consultants

On 2/10/2011 10:17 PM, R B wrote:

The OP might find this helpful:

https://people.ok.ubc.ca/brioconn/nfactors/nfactors.html

Ryan

On Thu, Feb 10, 2011 at 8:41 PM, Bruce Weaver [hidden email] wrote:

krisscot wrote:

I hope that someone can help clarify some interesting output I came across
from a Factor Analysis that I just conducted. I have a 24-item instrument
that I used Principal Axis Factoring for. By default, SPSS suggested that
there were 5 factors based on the eigenvalue greater than 1 rule. I then
tried to run the same procedure but altered the number of factors to be
extracted to 3. The eigenvalues for the 3-factor solution were not the
same values as the first 3 eigenvalues from the 5-factor solution (all
values are based on prerotation). The values are close but shouldn't they
be identical given that factors are extracted ortogonally? Thanks!

Kris

I am not an expert on factor analysis, but what I have read suggests that
the "eigenvalues > 1" rule (aka Kaiser's criterion) is not a particularly
good one much of the time.  See the following article for, for example.

  http://www.people.ku.edu/~preacher/pubs/preacher_maccallum_2003.pdf

HTH.


-----
--
Bruce Weaver
[hidden email]
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

--
View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Principal-Axis-Factor-and-SPSS-tp3380434p3380519.html
Sent from the SPSSX Discussion mailing list archive at Nabble.com.

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[Maguin, Eugene]

Bruce, Art, RB,

 

I understand (and agree) with your comments on the how to number of factors but I don't think that was Kris' question. Look at the last sentence.

 

Gene

---

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of krisscot
Sent: Thursday, February 10, 2011 6:57 PM
To: [hidden email]
Subject: Principal Axis Factor and SPSS

I hope that someone can help clarify some interesting output I came across from a Factor Analysis that I just conducted. I have a 24-item instrument that I used Principal Axis Factoring for. By default, SPSS suggested that there were 5 factors based on the eigenvalue greater than 1 rule. I then tried to run the same procedure but altered the number of factors to be extracted to 3. The eigenvalues for the 3-factor solution were not the same values as the first 3 eigenvalues from the 5-factor solution (all values are based on prerotation). The values are close but shouldn't they be identical given that factors are extracted ortogonally? Thanks!

 

Kris

[Art Kendall]

How close is close?

Art Kendall


On 2/11/2011 9:08 AM, Gene Maguin wrote:

Bruce, Art, RB,

 

I understand (and agree) with your comments on the how to number of factors but I don't think that was Kris' question. Look at the last sentence.

 

Gene

---

From: SPSSX(r) Discussion [[hidden email]] On Behalf Of krisscot
Sent: Thursday, February 10, 2011 6:57 PM
To: [hidden email]
Subject: Principal Axis Factor and SPSS

I hope that someone can help clarify some interesting output I came across from a Factor Analysis that I just conducted. I have a 24-item instrument that I used Principal Axis Factoring for. By default, SPSS suggested that there were 5 factors based on the eigenvalue greater than 1 rule. I then tried to run the same procedure but altered the number of factors to be extracted to 3. The eigenvalues for the 3-factor solution were not the same values as the first 3 eigenvalues from the 5-factor solution (all values are based on prerotation). The values are close but shouldn't they be identical given that factors are extracted ortogonally? Thanks!

 

Kris

===================== 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

[Art Kendall]

I find no difference in the initial eigenvalues, as I would expect. In the simulation I did they describe a 50 dimensional space.

I do find that the eigenvalues describing the 23 dimensional space are different from those describing a 3 dimensional space.

Copy the syntax below into the syntax window of a new instance of SPSS.
Run it.
Look at the output file.

Is this a different kind of pattern than you were describing?

Art Kendall
Social Research Consultants

new file.
input program.
vector x (50,f3).
loop id = 1 to 250.
loop #p = 1 to 50.
compute x(#p) = rnd(rv.normal(50,10)).
end loop.
end case.
end loop.
end file.
end input program.
dataset name input.
dataset declare free.
dataset declare three.
dataset activate input.
OMS
 /SELECT TABLES
 /IF COMMANDS = ["Factor Analysis"]
     SUBTYPES = ["Total Variance Explained"]
 /DESTINATION FORMAT = SAV NUMBERED = test viewer = no
  OUTFILE = free.
factor variables= x1 to x50/print=initial /criteria= mineigen(1) iterate (50) rconverge(.04).
omsend.
dataset activate input.
OMS
 /SELECT TABLES
 /IF COMMANDS = ["Factor Analysis"]
     SUBTYPES = ["Total Variance Explained"]
 /DESTINATION FORMAT = SAV NUMBERED = test viewer = no
  OUTFILE = three.
factor variables= x1 to x50/print=initial /criteria=factors(3).
omsend.
match files /file = free
 /rename (InitialEigenvalues_Total RotationSumsofSquaredLoadings_Total = Initial Rotation)
 /file= three
 /rename =
(InitialEigenvalues_Total RotationSumsofSquaredLoadings_Total = Initial3 Rotation3)
 /by var1
 /keep = var1 Initial Rotation Initial3 Rotation3.
dataset name combined. 
compute diffinitial = Initial  - Initial3.
compute diffrotated = Rotation - Rotation3.
formats Var1 (f2) Initial Rotation Initial3 Rotation3 (f6.3)
  diffInitial diffRotated (f20.16).

list variables = var1 Initial initial3 diffinitial rotation rotation3 diffrotated.




On 2/11/2011 9:58 AM, Art Kendall wrote:

How close is close?

Art Kendall


On 2/11/2011 9:08 AM, Gene Maguin wrote:

Bruce, Art, RB,

 

I understand (and agree) with your comments on the how to number of factors but I don't think that was Kris' question. Look at the last sentence.

 

Gene

---

From: SPSSX(r) Discussion [[hidden email]] On Behalf Of krisscot
Sent: Thursday, February 10, 2011 6:57 PM
To: [hidden email]
Subject: Principal Axis Factor and SPSS

I hope that someone can help clarify some interesting output I came across from a Factor Analysis that I just conducted. I have a 24-item instrument that I used Principal Axis Factoring for. By default, SPSS suggested that there were 5 factors based on the eigenvalue greater than 1 rule. I then tried to run the same procedure but altered the number of factors to be extracted to 3. The eigenvalues for the 3-factor solution were not the same values as the first 3 eigenvalues from the 5-factor solution (all values are based on prerotation). The values are close but shouldn't they be identical given that factors are extracted ortogonally? Thanks!

 

Kris

===================== 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