Cronbach alpha for PCA

["Abdullah Koçak"]

hi to all,
 
im performing a principical compenent analysis with 76 item.
PCA extracted 12 factor. But the cronbach alpha for the last 3 factor is below ,600.
How can i interperet it. Can i use this factors.
 
best

[Art Kendall]

In my experience, it would be unusual for there to be 12 factors
underlying 76 items.

What are you asking of the data by using a form of factor analysis? Why
did you chose the PCA form of factor analysis?


What is the subject matter area?

How did you select the set of items? Pre-existing scales? Written to
represent specific constructs? For a one time study?

What stopping rule did you use? Why did you retain 12 factors?

How many cases do you have?


see my recent post for some considerations in using factor analysis,

http://listserv.uga.edu/cgi-bin/wa?A2=ind1001&L=spssx-l&P=R42935

Although that post was about dichotomous items, much of it also applies
to interval level items.

Art Kendall
Social Research Consultants


On 1/16/2010 3:24 AM, "Abdullah Koçak" wrote:
> hi to all,
>
> im performing a principical compenent analysis with 76 item.
> PCA extracted 12 factor. But the cronbach alpha for the last 3 factor
> is below ,600.
> How can i interperet it. Can i use this factors.
>
> best

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[statisticsdoc]

Abdullah,
Are you using Kaiser's criterion to decide how many factors to retain (I.e. all factors with eigenvalues greater than one)? This criterion tends to include an excessive number of factors, including some that are neither internally consistent or meaningful. Factors 10 through 12 in your analysis probably fit that description. You might want to consider using a more restrictive rule for retaining factors (e.g. Catell,s scree criterion). You might want to consider "cleaning the battery" - dropping items that do not have a high loading on any of the factors that meet a more stringent criterion for retention). An alpha of .6 is too low - more than half of the variance in scale scores is error or unique v ariance.
Best,
Steve Brand

www.StatisticsDoc.com

---

From: "Abdullah Koçak" [hidden email]

Date: Sat, 16 Jan 2010 10:24:43 +0200

To: <[hidden email]>

Subject: Cronbach alpha for PCA

hi to all,
 
im performing a principical compenent analysis with 76 item.
PCA extracted 12 factor. But the cronbach alpha for the last 3 factor is below ,600.
How can i interperet it. Can i use this factors.
 
best

[SR Millis-3]

Parallel analysis (PA) should be considered as an additional method to determine the number of factors.  The idea behind PA is that the number of factors extracted should have eigenvalues greater than those from a random data matrix of the same dimensions.  To determine this, a set a random data correlation matrices arte created and their eigenvalues are computed.  The eigenvalues from the actual data matrix to be factors are compared to those from the random data – and only factors with eigenvalues greater than those from the random data are retained.

~~~~~~~~~~~
Scott R Millis, PhD, ABPP (CN,CL,RP), CStat, CSci
Professor & Director of Research
Dept of Physical Medicine & Rehabilitation
Dept of Emergency Medicine
Wayne State University School of Medicine
261 Mack Blvd
Detroit, MI 48201
Email:  [hidden email]
Email:  [hidden email]
Tel: [phone]
Fax: [phone]


--- On Sat, 1/16/10, Statisticsdoc Consulting <[hidden email]> wrote:

> From: Statisticsdoc Consulting <[hidden email]>
> Subject: Re: Cronbach alpha for PCA
> To: [hidden email]
> Date: Saturday, January 16, 2010, 9:32 AM
>    Abdullah,Are
> you using Kaiser's criterion to decide how many factors
> to retain (I.e. all factors with eigenvalues greater than
> one)?  This criterion tends to include an excessive number
> of factors, including some that are neither internally
> consistent or meaningful.  Factors 10 through 12 in your
> analysis probably fit that description.  You might want to
> consider using a more restrictive rule for retaining factors
> (e.g. Catell,s scree criterion).  You might want to consider
> "cleaning the battery" - dropping items that do
> not have a high loading on any of the factors that meet a
> more stringent criterion for retention).  An alpha of .6 is
> too low - more than half of the  variance in scale scores is
> error or unique v ariance.Best,Steve
> Brandwww.StatisticsDoc.comFrom:
> "Abdullah Koçak" [hidden email]
> Date: Sat, 16 Jan 2010 10:24:43
> +0200To:
> <[hidden email]>Subject:
> Cronbach alpha for PCAhi to all,
> �
> im performing a principical compenent analysis with 76
> item.
> PCA extracted 12 factor. But the cronbach alpha for the
> last 3 factor is below ,600.
> How can i interperet it. Can i use this factors.
> �
> best
>
>
>

=====================
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[Alexander J. Shackman-2]

code for running parallel analysis available at

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

On Sat, Jan 16, 2010 at 12:51 PM, SR Millis <[hidden email]> wrote:

Parallel analysis (PA) should be considered as an additional method to determine the number of factors.  The idea behind PA is that the number of factors extracted should have eigenvalues greater than those from a random data matrix of the same dimensions.  To determine this, a set a random data correlation matrices arte created and their eigenvalues are computed.  The eigenvalues from the actual data matrix to be factors are compared to those from the random data – and only factors with eigenvalues greater than those from the random data are retained.

~~~~~~~~~~~
Scott R Millis, PhD, ABPP (CN,CL,RP), CStat, CSci
Professor & Director of Research
Dept of Physical Medicine & Rehabilitation
Dept of Emergency Medicine
Wayne State University School of Medicine
261 Mack Blvd
Detroit, MI 48201
Email:  [hidden email]
Email:  [hidden email]
Tel: [phone]
Fax: [phone]


--- On Sat, 1/16/10, Statisticsdoc Consulting <[hidden email]> wrote:

> From: Statisticsdoc Consulting <[hidden email]>
> Subject: Re: Cronbach alpha for PCA
> To: [hidden email]
> Date: Saturday, January 16, 2010, 9:32 AM
>    Abdullah,Are
> you using Kaiser's criterion to decide how many factors
> to retain (I.e. all factors with eigenvalues greater than
> one)?  This criterion tends to include an excessive number
> of factors, including some that are neither internally
> consistent or meaningful.  Factors 10 through 12 in your
> analysis probably fit that description.  You might want to
> consider using a more restrictive rule for retaining factors
> (e.g. Catell,s scree criterion).  You might want to consider
> "cleaning the battery" - dropping items that do
> not have a high loading on any of the factors that meet a
> more stringent criterion for retention).  An alpha of .6 is
> too low - more than half of the  variance in scale scores is
> error or unique v ariance.Best,Steve
> Brandwww.StatisticsDoc.comFrom:
> "Abdullah Koçak" [hidden email]
> Date: Sat, 16 Jan 2010 10:24:43
> +0200To:
> <[hidden email]>Subject:
> Cronbach alpha for PCAhi to all,
> Â
> im performing a principical compenent analysis with 76
> item.
> PCA extracted 12 factor. But the cronbach alpha for the
> last 3 factor is below ,600.
> How can i interperet it. Can i use this factors.
> Â
> best
>
>
>

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
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--
Alexander J. Shackman, Ph.D.
Wisconsin Psychiatry Institute & Clinics and
Department of Psychology
University of Wisconsin-Madison
1202 West Johnson Street
Madison, Wisconsin 53706

Telephone: [phone]
Fax: [phone]
Email: [hidden email]
http://psyphz.psych.wisc.edu/~shackman

[E. Bernardo]

I wonder why SPSS does not include the parallel analysis in their point-click procedure considering that it is very much demand by researchers.

 

Eins

--- On Sat, 1/16/10, Alexander J. Shackman <[hidden email]> wrote:

From: Alexander J. Shackman <[hidden email]>
Subject: Re: Cronbach alpha for PCA
To: [hidden email]
Date: Saturday, 16 January, 2010, 7:01 PM

code for running parallel analysis available at

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

On Sat, Jan 16, 2010 at 12:51 PM, SR Millis <srmillis@...> wrote:

Parallel analysis (PA) should be considered as an additional method to determine the number of factors.  The idea behind PA is that the number of factors extracted should have eigenvalues greater than those from a random data matrix of the same dimensions.  To determine this, a set a random data correlation matrices arte created and their eigenvalues are computed.  The eigenvalues from the actual data matrix to be factors are compared to those from the random data – and only factors with eigenvalues greater than those from the random data are retained.

~~~~~~~~~~~
Scott R Millis, PhD, ABPP (CN,CL,RP), CStat, CSci
Professor & Director of Research
Dept of Physical Medicine & Rehabilitation
Dept of Emergency Medicine
Wayne State University School of Medicine
261 Mack Blvd
Detroit, MI 48201
Email:  aa3379@...
Email:  srmillis@...
Tel: [phone]
Fax: [phone]


--- On Sat, 1/16/10, Statisticsdoc Consulting <statisticsdoc@...> wrote:

> From: Statisticsdoc Consulting <statisticsdoc@...>
> Subject: Re: Cronbach alpha for PCA
> To: SPSSX-L@...
> Date: Saturday, January 16, 2010, 9:32 AM
>    Abdullah,Are
> you using Kaiser's criterion to decide how many factors
> to retain (I.e. all factors with eigenvalues greater than
> one)?  This criterion tends to include an excessive number
> of factors, including some that are neither internally
> consistent or meaningful.  Factors 10 through 12 in your
> analysis probably fit that description.  You might want to
> consider using a more restrictive rule for retaining factors
> (e.g. Catell,s scree criterion).  You might want to consider
> "cleaning the battery" - dropping items that do
> not have a high loading on any of the factors that meet a
> more stringent criterion for retention).  An alpha of .6 is
> too low - more than half of the  variance in scale scores is
> error or unique v ariance.Best,Steve
> Brandwww.StatisticsDoc.comFrom:
> "Abdullah Koçak" kocaka@...
> Date: Sat, 16 Jan 2010 10:24:43
> +0200To:
> <SPSSX-L@...>Subject:
> Cronbach alpha for PCAhi to all,
> Â
> im performing a principical compenent analysis with 76
> item.
> PCA extracted 12 factor. But the cronbach alpha for the
> last 3 factor is below ,600.
> How can i interperet it. Can i use this factors.
> Â
> best
>
>
>

=====================
To manage your subscription to SPSSX-L, send a message to
LISTSERV@... (not to SPSSX-L), with no body text except the
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--
Alexander J. Shackman, Ph.D.
Wisconsin Psychiatry Institute & Clinics and
Department of Psychology
University of Wisconsin-Madison
1202 West Johnson Street
Madison, Wisconsin 53706

Telephone: [phone]
Fax: [phone]
Email: shackman@...
http://psyphz.psych.wisc.edu/~shackman

---

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[Humphrey Paulie]

Dear colleagues,

In an ANOVA study, I found out that Levenes test is significant, that is the assumption of equal variances for the groups is violated. In such cases I suppose one should use Welsh and Brown-Forsythe tests, right?

The table called Robust Tests of Equality of Means showed that  Welsh and Brown-Forsythe tests are not significant. Sig. for both was around 0.60.

Does this mean that the differences among the means is not significant?

This table has Statistic(a), df1, df2 and Sig. How should I report it? There is no F. what is df2?

Usually when the assumption is not violated its reported like F(2, 85)=0.42, p=0.65.

Could you please tell how should I report ANOVA results in text when the assumption of equal variances is violated?

Cheers

Humphrey

 

[Allan Lundy, PhD]

Dear Listers,
I have a doctoral student client who was to construct a number of scales from a large set of items.  However, his intuitive grouping of items into scales was a bust.  His advisor "suggested" he do factor analysis to derive better scales, so he enlisted my help.  I ran PCA and got a reasonable set of 9 components.  Then he noted that he was expected to report Cronbach's alpha for each new "scale."  However, it seems to me that if a scale is constructed as a weighted sum of items, an alpha using the same set of items would be misleading and/or irrelevant, because in effect alpha would weight the items equally.  I looked into previous discussions of this and found one apparently by Abdullah around mid-January:

At 04:24 AM 1/16/2010, you wrote:

hi to all,
 
im performing a principical compenent analysis with 76 item.
PCA extracted 12 factor. But the cronbach alpha for the last 3 factor is below ,600.
How can i interperet it. Can i use this factors.
 
best

This seems to have elicited 5 comments, but they were on methods of extracting a reasonable number of factors, not the applicability of alpha to a weighted-item scale.  So:  Do you agree with me that alpha is inappropriate?  Does anyone know of a statistic that could be regarded as the equivalent of alpha in this situation: a measure of how well the (weighted) items intercorrelate?

Thanks!  And keep these interesting discussions coming!
Allan

Allan Lundy, PhD
Research Consulting
[hidden email]

Business & Cell (any time): 215-820-8100
Home (8am-10pm, 7 days/week): 215-885-5313
Address:  108 Cliff Terrace, Wyncote, PA 19095
Visit my Web site at www.dissertationconsulting.net ===================== 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

[Maurice Vergeer]

Hi Allan,

first, I'd recommend PAF instead of PCA, because the former one allows
for errors in the measurements of the items.
Second, factors saved with the procedure factor analysis (i.e.
weighted scales) correlate very strongly (r>.90) with summated
(unweighted) scales. So, Cronbach alpha is a good measure for the
reliability check.
Third, in psychology they state that .85 is a good scale based on 15
items. If you have less items a lower Cronbach Alpha is acceptable..
To check what the alpha would have been if you had 15 items you can
use the Spearman-Brown formula to artificially increase the scale's
length.

I hope this helps.

Maurice

On Sun, Oct 17, 2010 at 02:03, Allan Lundy, PhD <[hidden email]> wrote:

>
> Dear Listers,
> I have a doctoral student client who was to construct a number of scales
> from a large set of items.�  However, his intuitive grouping of items into
> scales was a bust.�  His advisor "suggested" he do factor analysis to derive
> better scales, so he enlisted my help.�  I ran PCA and got a reasonable set
> of 9 components.�  Then he noted that he was expected to report Cronbach's
> alpha for each new "scale."�  However, it seems to me that if a scale is
> constructed as a weighted sum of items, an alpha using the same set of items
> would be misleading and/or irrelevant, because in effect alpha would weight
> the items equally.�  I looked into previous discussions of this and found one
> apparently by Abdullah around mid-January:
>
> At 04:24 AM 1/16/2010, you wrote:
>
> hi to all,
>
> im performing a principical compenent analysis with 76 item.
> PCA extracted 12 factor. But the cronbach alpha for the last 3 factor is
> below ,600.
> How can i interperet it. Can i use this factors.
>
> best
>
> This seems to have elicited 5 comments, but they were on methods of
> extracting a reasonable number of factors, not the applicability of alpha to
> a weighted-item scale.�  So:�  Do you agree with me that alpha is
> inappropriate?�  Does anyone know of a statistic that could be regarded as
> the equivalent of alpha in this situation: a measure of how well the
> (weighted) items intercorrelate?
>
> Thanks!�  And keep these interesting discussions coming!
> Allan
>
> Allan Lundy, PhD
> Research Consulting
> [hidden email]
>
> Business & Cell (any time): 215-820-8100
> Home (8am-10pm, 7 days/week): 215-885-5313
> Address:�  108 Cliff Terrace, Wyncote, PA 19095
> Visit my Web site at www.dissertationconsulting.net
>
> ===================== 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

--
___________________________________________________________________
Maurice Vergeer
Department of communication
Radboud University�  (www.ru.nl)
PO Box 9104
NL-6500 HE Nijmegen
The Netherlands

Visiting Professor Yeungnam University, Gyeongsan, South Korea

contact:
E: [hidden email]
T: [phone] (direct)/ 3612372 (secretary) / maurice.vergeer (skype)
personal webpage: www.mauricevergeer.nl
blog:�  http://blog.mauricevergeer.nl/
Journalism: www.journalisteninhetdigitaletijdperk.nl
CENMEP New Media and European Parliament Elections 2009
http://mauricevergeer.ruhosting.nl/cenmep

Recent publications:
- Eisinga, R., Franses, Ph.H. & Vergeer, M. (accepted for
publication). Weather conditions and daily television use in the
Netherlands, 1996-2005. International Journal of Biometeorology.
- Vergeer, M. & Pelzer, B. (2009). Consequences of media and Internet
use for offline and online network capital and well-being. A causal
model approach. Journal of Computer-Mediated Communication, 15,
189-210.
- Vergeer, M., Coenders, M. & Scheepers, P. (2009). Time spent on
television in European countries. In R.P. Konig, P.W.M. Nelissen, &
F.J.M. Huysmans (Eds.), Meaningful media: Communication Research on
the Social Construction of Reality (54-73). Nijmegen, The Netherlands:
Tandem Felix.
- Hermans, L., Vergeer, M., &�  d’Haenens, L. (2009). Internet in the
daily life of journalists. Explaining the use of the Internet through
work-related characteristics and professional opinions. Journal of
Computer-Mediated Communication, 15, 138-157.
___________________________________________________________________

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[Art Kendall]

PAF is conventionally used in scale construction rather than PCA because only the common variance of items is a measure of the underlying (latent) construct).  Unique item variance is pooled with the random error variance.

What stopping rule did you use to determine the number of factors to retain?

Did you try parallel mapping?  See the archives for syntax for this.  In my experience, YMMV, the number of factors (scales) retained is in the vicinity of the number where the obtained eigenvalue is at least 1.00 more than the eigenvalue for factoring many pseudo-randomly generated data sets with the same number of cases and items.

It is also conventional to use unit weights is getting a total (mean) score.  In scale construction factor scores produced by the software are not used. Also retain only items that load cleanly on one factor.  This helps divergent validity.   In these  post hoc exploratory situations it is usual to have many items fail to load cleanly on a factor.

Of course interpretability of the set of items that are used on a factor is critical in deciding whether to use that factor to create a scale.  Sets of items that do not reach .75 or so are not useful for further analysis in this study. The constructs that are suggested by the set of items can still be useful as clues to developing new items in further research.


Art Kendall
Social Research Consultants



On 10/16/2010 8:03 PM, Allan Lundy, PhD wrote:

Dear Listers,
I have a doctoral student client who was to construct a number of scales from a large set of items.  However, his intuitive grouping of items into scales was a bust.  His advisor "suggested" he do factor analysis to derive better scales, so he enlisted my help.  I ran PCA and got a reasonable set of 9 components.  Then he noted that he was expected to report Cronbach's alpha for each new "scale."  However, it seems to me that if a scale is constructed as a weighted sum of items, an alpha using the same set of items would be misleading and/or irrelevant, because in effect alpha would weight the items equally.  I looked into previous discussions of this and found one apparently by Abdullah around mid-January:

At 04:24 AM 1/16/2010, you wrote:

hi to all,
 
im performing a principical compenent analysis with 76 item.
PCA extracted 12 factor. But the cronbach alpha for the last 3 factor is below ,600.
How can i interperet it. Can i use this factors.
 
best

This seems to have elicited 5 comments, but they were on methods of extracting a reasonable number of factors, not the applicability of alpha to a weighted-item scale.  So:  Do you agree with me that alpha is inappropriate?  Does anyone know of a statistic that could be regarded as the equivalent of alpha in this situation: a measure of how well the (weighted) items intercorrelate?

Thanks!  And keep these interesting discussions coming!
Allan

Allan Lundy, PhD
Research Consulting
[hidden email]

Business & Cell (any time): 215-820-8100
Home (8am-10pm, 7 days/week): 215-885-5313
Address:  108 Cliff Terrace, Wyncote, PA 19095
Visit my Web site at www.dissertationconsulting.net ===================== 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