Stats quest re Factor Loadings

[KEVIN MANNING]

Hello all,

    A statistical question:  I have run a prinicapl components analysis of tests of executive functioning resulting in four factors.  I am trying to determine a cut-off for the loading to determine which measures to include in each factor.  I have received varying advice, with either a .4 or .5 as the cut-off.  Not sure which to use (if either).

    I realize the definition of factors is guided by theory, but this is an exploratory procedure, and I want to include the the loadings for each factor that explain the most variance.  Thank you.

  Kevin Manning

[Art Kendall]

This is where the art (no pun intended) of factor analysis comes in.



Try using |.5| with no second loading gt |.35| and relax the criteria if
you don't end up with at least 5 or 4  variables on each factor.

At this stage interpretability carries a lot of weight, so subject
matter matters.

If you keep items that are not as clean, you could use the "alpha if
item deleted" as a decision aid for final item selection.

Eliminating splitters sometimes carries more weight in deciding about an
item than the absolute size of the loading.




Art Kendall
Social Research Consultants.

KEVIN MANNING wrote:

>Hello all,
>
>    A statistical question:  I have run a prinicapl components analysis of tests of executive functioning resulting in four factors.  I am trying to determine a cut-off for the loading to determine which measures to include in each factor.  I have received varying advice, with either a .4 or .5 as the cut-off.  Not sure which to use (if either).
>
>    I realize the definition of factors is guided by theory, but this is an exploratory procedure, and I want to include the the loadings for each factor that explain the most variance.  Thank you.
>
>  Kevin Manning
>
>
>
>

[statisticsdoc]

Stephen Brand
www.statisticsdoc.com

Kevin,

Art's post has good advice to follow, so I just would offer a couple of
other suggestions.

(1) You might want to consider looking at your factor loadings after
rotation.  A varimax rotation of the factors will usually result in a
smaller number of items having a higher and cleaner loading on a factor
(i.e., "simple structure").  You are more likely to see items with
relatively large and unique loadings.

(2) You might also consider varying the number of factors slightly.  Having
too many factors runs the risk of adding junk factors with low loadings.
Having too few factors runs the risk that certain items that load on the
excluded factor will not have high loadings on the factors that you have
retained.

Did you get four factors from the analysis because it retained all of the
factors with eigenvalues above one?  You may want to consider using other
criteria, such as the scree criterion of the eigenvalues, to set the number
of factors.  The scree criterion is based on the plot of the eigenvalues.
If the eigenvalue for the fourth factor is smaller than the third factor,
but not much different from the fifth and sixth, then your four-factor
solution might fit the criterion.  Look for the point at which the size of
the eigenvalues of successive factors does not change a great deal.

(3) If you drop some items that have split loadings, or have low loadings on
all factors (because they do not share a lot of variance with the other
items), refactor the remaining items - you might get a cleaner structure.

Remember, as Art said, keep your focus on the interpretability and meaning
of the factors.  IMHO, that is the key criterion for judging the adequacy of
a factor analysis - did it uncover a structure that makes sense.

HTH,

Stephen Brand


For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
KEVIN MANNING
Sent: Friday, November 17, 2006 11:03 AM
To: [hidden email]
Subject: Stats quest re Factor Loadings


Hello all,

    A statistical question:  I have run a prinicapl components analysis of
tests of executive functioning resulting in four factors.  I am trying to
determine a cut-off for the loading to determine which measures to include
in each factor.  I have received varying advice, with either a .4 or .5 as
the cut-off.  Not sure which to use (if either).

    I realize the definition of factors is guided by theory, but this is an
exploratory procedure, and I want to include the the loadings for each
factor that explain the most variance.  Thank you.

  Kevin Manning

[Salbod]

I would like to read a discussion of the ideas underlying Stephen Brand's
suggestion #3. Does anyone have references regarding refactoring after
removing low loadings and split loadings?

Thank you,

Stephen Salbod
Pace University, NYC

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Statisticsdoc
Sent: Friday, November 17, 2006 9:54 PM
To: [hidden email]
Subject: Re: Stats quest re Factor Loadings

Stephen Brand
www.statisticsdoc.com

Kevin,

Art's post has good advice to follow, so I just would offer a couple of
other suggestions.

(1) You might want to consider looking at your factor loadings after
rotation.  A varimax rotation of the factors will usually result in a
smaller number of items having a higher and cleaner loading on a factor
(i.e., "simple structure").  You are more likely to see items with
relatively large and unique loadings.

(2) You might also consider varying the number of factors slightly.  Having
too many factors runs the risk of adding junk factors with low loadings.
Having too few factors runs the risk that certain items that load on the
excluded factor will not have high loadings on the factors that you have
retained.

Did you get four factors from the analysis because it retained all of the
factors with eigenvalues above one?  You may want to consider using other
criteria, such as the scree criterion of the eigenvalues, to set the number
of factors.  The scree criterion is based on the plot of the eigenvalues.
If the eigenvalue for the fourth factor is smaller than the third factor,
but not much different from the fifth and sixth, then your four-factor
solution might fit the criterion.  Look for the point at which the size of
the eigenvalues of successive factors does not change a great deal.

(3) If you drop some items that have split loadings, or have low loadings on
all factors (because they do not share a lot of variance with the other
items), refactor the remaining items - you might get a cleaner structure.

Remember, as Art said, keep your focus on the interpretability and meaning
of the factors.  IMHO, that is the key criterion for judging the adequacy of
a factor analysis - did it uncover a structure that makes sense.

HTH,

Stephen Brand


For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
KEVIN MANNING
Sent: Friday, November 17, 2006 11:03 AM
To: [hidden email]
Subject: Stats quest re Factor Loadings


Hello all,

    A statistical question:  I have run a prinicapl components analysis of
tests of executive functioning resulting in four factors.  I am trying to
determine a cut-off for the loading to determine which measures to include
in each factor.  I have received varying advice, with either a .4 or .5 as
the cut-off.  Not sure which to use (if either).

    I realize the definition of factors is guided by theory, but this is an
exploratory procedure, and I want to include the the loadings for each
factor that explain the most variance.  Thank you.

  Kevin Manning

[statisticsdoc]

Stephen,

Anecdotally, Ledyard Tucker used to call it this process "cleaning the
battery."  It is most appropriate for exploratory work undertaken for scale
development purposes.

HTH,

Stephen Brand

For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
Stephen Salbod
Sent: Saturday, November 18, 2006 2:07 PM
To: [hidden email]
Subject: Re: Stats quest re Factor Loadings


I would like to read a discussion of the ideas underlying Stephen Brand's
suggestion #3. Does anyone have references regarding refactoring after
removing low loadings and split loadings?

Thank you,

Stephen Salbod
Pace University, NYC

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Statisticsdoc
Sent: Friday, November 17, 2006 9:54 PM
To: [hidden email]
Subject: Re: Stats quest re Factor Loadings

Stephen Brand
www.statisticsdoc.com

Kevin,

Art's post has good advice to follow, so I just would offer a couple of
other suggestions.

(1) You might want to consider looking at your factor loadings after
rotation.  A varimax rotation of the factors will usually result in a
smaller number of items having a higher and cleaner loading on a factor
(i.e., "simple structure").  You are more likely to see items with
relatively large and unique loadings.

(2) You might also consider varying the number of factors slightly.  Having
too many factors runs the risk of adding junk factors with low loadings.
Having too few factors runs the risk that certain items that load on the
excluded factor will not have high loadings on the factors that you have
retained.

Did you get four factors from the analysis because it retained all of the
factors with eigenvalues above one?  You may want to consider using other
criteria, such as the scree criterion of the eigenvalues, to set the number
of factors.  The scree criterion is based on the plot of the eigenvalues.
If the eigenvalue for the fourth factor is smaller than the third factor,
but not much different from the fifth and sixth, then your four-factor
solution might fit the criterion.  Look for the point at which the size of
the eigenvalues of successive factors does not change a great deal.

(3) If you drop some items that have split loadings, or have low loadings on
all factors (because they do not share a lot of variance with the other
items), refactor the remaining items - you might get a cleaner structure.

Remember, as Art said, keep your focus on the interpretability and meaning
of the factors.  IMHO, that is the key criterion for judging the adequacy of
a factor analysis - did it uncover a structure that makes sense.

HTH,

Stephen Brand


For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
KEVIN MANNING
Sent: Friday, November 17, 2006 11:03 AM
To: [hidden email]
Subject: Stats quest re Factor Loadings


Hello all,

    A statistical question:  I have run a prinicapl components analysis of
tests of executive functioning resulting in four factors.  I am trying to
determine a cut-off for the loading to determine which measures to include
in each factor.  I have received varying advice, with either a .4 or .5 as
the cut-off.  Not sure which to use (if either).

    I realize the definition of factors is guided by theory, but this is an
exploratory procedure, and I want to include the the loadings for each
factor that explain the most variance.  Thank you.

  Kevin Manning

[Art Kendall]

I have seen it done as a follow-up.  I don't  recall seeing it make a
difference wrt which items group together to form scales.
Although, I have seldom seen "factor scores" used instead of unit
weighted (one, zero) items in a summed scale.

P.S.  I just assumed the OP was using rotated loadings.
 I should have mentioned doing a parallel analysis on, say, 10K
simulated data sets with the same number of cases and variables and the
same response categories.

Art Kendall
Social Research Consultants

Stephen Salbod wrote:

>I would like to read a discussion of the ideas underlying Stephen Brand's
>suggestion #3. Does anyone have references regarding refactoring after
>removing low loadings and split loadings?
>
>Thank you,
>
>Stephen Salbod
>Pace University, NYC
>
>-----Original Message-----
>From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
>Statisticsdoc
>Sent: Friday, November 17, 2006 9:54 PM
>To: [hidden email]
>Subject: Re: Stats quest re Factor Loadings
>
>Stephen Brand
>www.statisticsdoc.com
>
>Kevin,
>
>Art's post has good advice to follow, so I just would offer a couple of
>other suggestions.
>
>(1) You might want to consider looking at your factor loadings after
>rotation.  A varimax rotation of the factors will usually result in a
>smaller number of items having a higher and cleaner loading on a factor
>(i.e., "simple structure").  You are more likely to see items with
>relatively large and unique loadings.
>
>(2) You might also consider varying the number of factors slightly.  Having
>too many factors runs the risk of adding junk factors with low loadings.
>Having too few factors runs the risk that certain items that load on the
>excluded factor will not have high loadings on the factors that you have
>retained.
>
>Did you get four factors from the analysis because it retained all of the
>factors with eigenvalues above one?  You may want to consider using other
>criteria, such as the scree criterion of the eigenvalues, to set the number
>of factors.  The scree criterion is based on the plot of the eigenvalues.
>If the eigenvalue for the fourth factor is smaller than the third factor,
>but not much different from the fifth and sixth, then your four-factor
>solution might fit the criterion.  Look for the point at which the size of
>the eigenvalues of successive factors does not change a great deal.
>
>(3) If you drop some items that have split loadings, or have low loadings on
>all factors (because they do not share a lot of variance with the other
>items), refactor the remaining items - you might get a cleaner structure.
>
>Remember, as Art said, keep your focus on the interpretability and meaning
>of the factors.  IMHO, that is the key criterion for judging the adequacy of
>a factor analysis - did it uncover a structure that makes sense.
>
>HTH,
>
>Stephen Brand
>
>
>For personalized and professional consultation in statistics and research
>design, visit
>www.statisticsdoc.com
>
>
>-----Original Message-----
>From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
>KEVIN MANNING
>Sent: Friday, November 17, 2006 11:03 AM
>To: [hidden email]
>Subject: Stats quest re Factor Loadings
>
>
>Hello all,
>
>    A statistical question:  I have run a prinicapl components analysis of
>tests of executive functioning resulting in four factors.  I am trying to
>determine a cut-off for the loading to determine which measures to include
>in each factor.  I have received varying advice, with either a .4 or .5 as
>the cut-off.  Not sure which to use (if either).
>
>    I realize the definition of factors is guided by theory, but this is an
>exploratory procedure, and I want to include the the loadings for each
>factor that explain the most variance.  Thank you.
>
>  Kevin Manning
>
>
>
>