A simple question

[Hector Maletta]

I think they are different things. The Likert scale is a simple sum of
Likert scores, unweighted. The loadings of variables on the first factor in
factor analysis are correlations between the observed variables and the
unobserved factor's scores (which can be estimated as a function of observed
variables, and generated by SPSS). Factor scores, unlike Likert scales, are
WEIGHTED sums of items values. The fact that all factor loadings are
"statistically significant" means that, given the size of your sample" you
can discard (with say 95% confidence) the null hypothesis that each factor
loading is zero at population level, but this is not the same as proving
that the true value of the loading is the one you got. On the other hand, if
you rotate the factor solution you get a different structure: which one is
the "true" one?



And what about the other factors, beyond the first? Are they "statistically
significant" too? May your variables be measuring more than one underlying
trait?



If your seven items have such a high correlation with the total Likert
scale, I wonder whether you need going into the trouble of performing a
factor analysis at all.



Just some random thoughts.



Hector



  _____

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Juanito Talili
Sent: 08 May 2008 03:06
To: [hidden email]
Subject: factor loadings vs item-total correlation




One domain in a self-administered questionnaire has seven items which were
quantified using 5-point Likert scale.  This domain was subjected to
one-factor CFA and found that the factor loadings of the seven items are
statistically significant.

Using the same data (data used in the CFA), the item-total correlation was
computed for each item and found that the coefficients are close to 1.0
(ranging from 0.7 to 0.9).

Do the item-total correlations validate the factor loadings? Or, are they
two different things with different uses? Please comment.

Thank you.



  _____

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[Muir Houston]

But surely a consideration must be what theory is driving your variable selection? - Perhaps you should build models by entering variables considered most influential by past research then estimate subsequent models by adding variables guided by theory - this should be a basic consideration when constructing models - otherwise you are on a fishing expedition
 
if existing research suggest that certain variables are not important or do not lead to a a better 'fit' -- then do not include them in the model
 
 
Muir Houston
Research Fellow
CRLL
Institute of Education
University of Stirling
FK9 4LA
01786-46-7615

________________________________

From: SPSSX(r) Discussion on behalf of Ornelas, Fermin
Sent: Thu 08/05/2008 18:10
To: [hidden email]
Subject: Re: collinearity and stepwise regression



I think the original question mentioned that collinearity was not severe. Having said that, if the number of variables was not very large, I suggest to proceed first to reduce it to a satisfactory level, i.e. variance proportion coefficients le .5, condition index LT 30 and VIF < 10. After satisfying this criteria then proceed to final model selection. There is another point to consider that if collinearity is not degrading and if the purpose of the model is prediction then the model should be fine. We know that if collinearity is severe then hypotheses testing are seriously questionable.

Fermin Ornelas, Ph.D.
Management Analyst III, AZ DES
1789 W. Jefferson Street
Phoenix, AZ 85007
Tel: [phone]
E-mail: [hidden email]


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Alexander J. Shackman
Sent: Thursday, May 08, 2008 9:36 AM
To: [hidden email]
Subject: Re: collinearity and stepwise regression

how severe is the collinearity, exactly? if extreme, collinear variables
could be collapsed using either pca/factor-analysis, or by taking the mean
of z-transformed vars

hth, alex

On Thu, May 8, 2008 at 10:42 AM, SR Millis <[hidden email]> wrote:

> Rather than solving problems caused by collinearity, when using a stepwise
> method, variable selection is made arbitrarily by collinearity.  See Frank
> Harrell's book, "Regression modeling strategies."
>
>
> Scott R Millis, PhD, MEd, ABPP (CN,CL,RP), CStat
> Professor & Director of Research
> Dept of Physical Medicine & Rehabilitation
> Wayne State University School of Medicine
> 261 Mack Blvd
> Detroit, MI 48201
> Email:  [hidden email]
> Tel: [phone]
> Fax: [phone]
>
>
> --- On Wed, 5/7/08, Zdaniuk, Bozena <[hidden email]> wrote:
>
> > From: Zdaniuk, Bozena <[hidden email]>
> > Subject: collinearity and stepwise regression
> > To: [hidden email]
> > Date: Wednesday, May 7, 2008, 4:33 PM
> > Hello, everybody. Would collinearity (not a severe one) be
> > less of a problem in a stepwise regression, since the
> > variables are entered one at a time?
> > Thanks in advance for any thoughts on that.
> > Bozena
> >
> > Bozena Zdaniuk, Ph.D.
> > University of Pittsburgh
> > UCSUR, 6th Fl.
> > 121 University Place
> > Pittsburgh, PA 15260
> > Ph.: 412-624-5736
> > Fax: [phone]
> > Email: [hidden email]
> >
> >
> > RD
> >
> > =====================
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> > [hidden email] (not to SPSSX-L), with no body
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> > command
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>

--
Alexander J. Shackman
Laboratory for Affective Neuroscience
Waisman Laboratory for Brain Imaging & Behavior
University of Wisconsin-Madison
1202 West Johnson Street
Madison, Wisconsin 53706

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

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--
The University of Stirling (a charity registered in Scotland, number
SC 011159) is a university established in Scotland by charter at Stirling,
FK9 4LA.  Privileged/Confidential Information may be contained in this
message.  If you are not the addressee indicated in this message (or
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[Henrik Lolle]

On the other hand, with a forced one factor solution the two methods
substantially give the same information; especially if you, by clicking
on either "correlations" or "covariances" in the reliability analysis,
also get the standardized version of Cronbach's alpha. But, of course,
the two methods will be different things, if you do not force the
factor analysis to be a one factor solution.

Isn't this right?

Best,
Henrik

Quoting Hector Maletta <[hidden email]>:

> I think they are different things. The Likert scale is a simple sum of
> Likert scores, unweighted. The loadings of variables on the first factor in
> factor analysis are correlations between the observed variables and the
> unobserved factor's scores (which can be estimated as a function of observed
> variables, and generated by SPSS). Factor scores, unlike Likert scales, are
> WEIGHTED sums of items values. The fact that all factor loadings are
> "statistically significant" means that, given the size of your sample" you
> can discard (with say 95% confidence) the null hypothesis that each factor
> loading is zero at population level, but this is not the same as proving
> that the true value of the loading is the one you got. On the other hand, if
> you rotate the factor solution you get a different structure: which one is
> the "true" one?
>
>
>
> And what about the other factors, beyond the first? Are they "statistically
> significant" too? May your variables be measuring more than one underlying
> trait?
>
>
>
> If your seven items have such a high correlation with the total Likert
> scale, I wonder whether you need going into the trouble of performing a
> factor analysis at all.
>
>
>
> Just some random thoughts.
>
>
>
> Hector
>
>
>
>  _____
>
> From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
> Juanito Talili
> Sent: 08 May 2008 03:06
> To: [hidden email]
> Subject: factor loadings vs item-total correlation
>
>
>
>
> One domain in a self-administered questionnaire has seven items which were
> quantified using 5-point Likert scale.  This domain was subjected to
> one-factor CFA and found that the factor loadings of the seven items are
> statistically significant.
>
> Using the same data (data used in the CFA), the item-total correlation was
> computed for each item and found that the coefficients are close to 1.0
> (ranging from 0.7 to 0.9).
>
> Do the item-total correlations validate the factor loadings? Or, are they
> two different things with different uses? Please comment.
>
> Thank you.
>
>
>
>  _____
>
> Be a better friend, newshound, and know-it-all with Yahoo! Mobile. Try
> <http://us.rd.yahoo.com/evt=51733/*http:/mobile.yahoo.com/;_ylt=Ahu06i62sR8H
> DtDypao8Wcj9tAcJ%20>  it now. ===================== 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
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************************************************************
Henrik Lolle
Department of Economics, Politics and Public Administration
Aalborg University
Fibigerstraede 1
9200 Aalborg
Phone: [phone]
************************************************************

=====================
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[Ornelas, Fermin-2]

Of course when undertaking research one should not ignore past investigations and empirical findings, especially if one is trying to present results or publish them. Sometimes even if variables are collinear but if the variables are crucial to a particular model a researcher may have not option to keep them in the model. Consideration also must be given to the scope and purpose of the model.

Fermin Ornelas, Ph.D.
Management Analyst III, AZ DES
1789 W. Jefferson Street
Phoenix, AZ 85007
Tel: [phone]
E-mail: [hidden email]

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Muir Houston
Sent: Thursday, May 08, 2008 3:41 PM
To: [hidden email]
Subject: Re: collinearity and stepwise regression

But surely a consideration must be what theory is driving your variable selection? - Perhaps you should build models by entering variables considered most influential by past research then estimate subsequent models by adding variables guided by theory - this should be a basic consideration when constructing models - otherwise you are on a fishing expedition

if existing research suggest that certain variables are not important or do not lead to a a better 'fit' -- then do not include them in the model


Muir Houston
Research Fellow
CRLL
Institute of Education
University of Stirling
FK9 4LA
01786-46-7615

________________________________

From: SPSSX(r) Discussion on behalf of Ornelas, Fermin
Sent: Thu 08/05/2008 18:10
To: [hidden email]
Subject: Re: collinearity and stepwise regression



I think the original question mentioned that collinearity was not severe. Having said that, if the number of variables was not very large, I suggest to proceed first to reduce it to a satisfactory level, i.e. variance proportion coefficients le .5, condition index LT 30 and VIF < 10. After satisfying this criteria then proceed to final model selection. There is another point to consider that if collinearity is not degrading and if the purpose of the model is prediction then the model should be fine. We know that if collinearity is severe then hypotheses testing are seriously questionable.

Fermin Ornelas, Ph.D.
Management Analyst III, AZ DES
1789 W. Jefferson Street
Phoenix, AZ 85007
Tel: [phone]
E-mail: [hidden email]


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Alexander J. Shackman
Sent: Thursday, May 08, 2008 9:36 AM
To: [hidden email]
Subject: Re: collinearity and stepwise regression

how severe is the collinearity, exactly? if extreme, collinear variables
could be collapsed using either pca/factor-analysis, or by taking the mean
of z-transformed vars

hth, alex

On Thu, May 8, 2008 at 10:42 AM, SR Millis <[hidden email]> wrote:

> Rather than solving problems caused by collinearity, when using a stepwise
> method, variable selection is made arbitrarily by collinearity.  See Frank
> Harrell's book, "Regression modeling strategies."
>
>
> Scott R Millis, PhD, MEd, ABPP (CN,CL,RP), CStat
> Professor & Director of Research
> Dept of Physical Medicine & Rehabilitation
> Wayne State University School of Medicine
> 261 Mack Blvd
> Detroit, MI 48201
> Email:  [hidden email]
> Tel: [phone]
> Fax: [phone]
>
>
> --- On Wed, 5/7/08, Zdaniuk, Bozena <[hidden email]> wrote:
>
> > From: Zdaniuk, Bozena <[hidden email]>
> > Subject: collinearity and stepwise regression
> > To: [hidden email]
> > Date: Wednesday, May 7, 2008, 4:33 PM
> > Hello, everybody. Would collinearity (not a severe one) be
> > less of a problem in a stepwise regression, since the
> > variables are entered one at a time?
> > Thanks in advance for any thoughts on that.
> > Bozena
> >
> > Bozena Zdaniuk, Ph.D.
> > University of Pittsburgh
> > UCSUR, 6th Fl.
> > 121 University Place
> > Pittsburgh, PA 15260
> > Ph.: 412-624-5736
> > Fax: [phone]
> > Email: [hidden email]
> >
> >
> > RD
> >
> > =====================
> > 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
>

--
Alexander J. Shackman
Laboratory for Affective Neuroscience
Waisman Laboratory for Brain Imaging & Behavior
University of Wisconsin-Madison
1202 West Johnson Street
Madison, Wisconsin 53706

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

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--
The University of Stirling (a charity registered in Scotland, number
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FK9 4LA.  Privileged/Confidential Information may be contained in this
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