(no subject)

[E. Bernardo]

Dear All,

I used Principal Axis Factoring using promax method in conducting EFA for the 81 items that utilized six-point ordinal scale.  The sample was n=381.  There is no indication of severe skewness on the data (skewness <3, kurtusis <10 and mardia coefficients >1000).  I used commonalities and factor loadings as criteria of dropping items.  Items with commonalities of <.40 were dropped.  Items with factor loadings of <.32 were also dropped. Crossloadings items were also dropped.  Finally, 35 items were left which loaded to six interpretable correlated factors.   The factors have the following number of items: 10, 7, 8, 4, 3 and 3.  After the factor analysis, the reliability coefficients were computed for each factor.  The Cronbach alpha are quite high.

After the EFA, a CFA was conducted using a separate sample of n=500 using amos.  Unfortunately, the chiquare has zero pvalue and no one of the fit indices were acceptable. I tried to improve the model  (guided by the modification indices).  I found out that the fit (at least the fit indices such as RMSEA, SRMR, cmin/df) of the model improved when I correlated the residuals/error terms.  Question:Is it appropriate to correlate the error terms?

Thank you in advance for your comments.

Eins

[Art Kendall]

What did you use as a stopping rule?
Why did you use promax?  Were you not interested in divergent validity?

That a set of variables be close to uncorrelated it a desirable property when you are going to use them as predictors in a GLM or clustering?



Art Kendall
Social Research Consultants

On 11/16/2011 5:02 AM, Eins Bernardo wrote:

Dear All,

I used Principal Axis Factoring using promax method in conducting EFA for the 81 items that utilized six-point ordinal scale.  The sample was n=381.  There is no indication of severe skewness on the data (skewness <3, kurtusis <10 and mardia coefficients >1000).  I used commonalities and factor loadings as criteria of dropping items.  Items with commonalities of <.40 were dropped.  Items with factor loadings of <.32 were also dropped. Crossloadings items were also dropped.  Finally, 35 items were left which loaded to six interpretable correlated factors.   The factors have the following number of items: 10, 7, 8, 4, 3 and 3.  After the factor analysis, the reliability coefficients were computed for each factor.  The Cronbach alpha are quite high.

After the EFA, a CFA was conducted using a separate sample of n=500 using amos.  Unfortunately, the chiquare has zero pvalue and no one of the fit indices were acceptable. I tried to improve the model  (guided by the modification indices).  I found out that the fit (at least the fit indices such as RMSEA, SRMR, cmin/df) of the model improved when I correlated the residuals/error terms.  Question:Is it appropriate to correlate the error terms?

Thank you in advance for your comments.

Eins

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

[Swank, Paul R]

CFA is a much more restricted model than EFA so often an EFA solution indicate lack of fit in a CFA. With respect to correlated residuals, this indicates that the correlations among the indicators is either higher than expected given the solution (positive residual correlations) or lower (negative residual correlations). This indicates that the factor structure is more complex than proposed. Most SEM analysts  do not like correlated residuals because they are a sort of hand-waving approach to dealing with the problem. Of more importance is to understand the data structure, not just to get a non-significant chi-square.

 

Dr. Paul R. Swank,

Children's Learning Institute

Professor, Department of Pediatrics, Medical School

Adjunct Professor, School of Public Health

University of Texas Health Science Center-Houston

 

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Eins Bernardo
Sent: Wednesday, November 16, 2011 4:03 AM
To: [hidden email]
Subject:

 

Dear All,

 

I used Principal Axis Factoring using promax method in conducting EFA for the 81 items that utilized six-point ordinal scale.  The sample was n=381.  There is no indication of severe skewness on the data (skewness <3, kurtusis <10 and mardia coefficients >1000).  I used commonalities and factor loadings as criteria of dropping items.  Items with commonalities of <.40 were dropped.  Items with factor loadings of <.32 were also dropped. Crossloadings items were also dropped.  Finally, 35 items were left which loaded to six interpretable correlated factors.   The factors have the following number of items: 10, 7, 8, 4, 3 and 3.  After the factor analysis, the reliability coefficients were computed for each factor.  The Cronbach alpha are quite high.

 

After the EFA, a CFA was conducted using a separate sample of n=500 using amos.  Unfortunately, the chiquare has zero pvalue and no one of the fit indices were acceptable. I tried to improve the model  (guided by the modification indices).  I found out that the fit (at least the fit indices such as RMSEA, SRMR, cmin/df) of the model improved when I correlated the residuals/error terms.  Question:Is it appropriate to correlate the error terms?

 

Thank you in advance for your comments.

 

Eins

[Maguin, Eugene]

Eins,

 

Don’t you actually mean that the chi –square value is very large/the p value is ver small. Yes, you can add residual covariances. But, how do you decide which ones to add and which ones not to add? Factor analysis allows every item to load on every factor. Conventional CFA allows each item to load on only one factor. The question is where does the item-factor covariance go for the non- dominant factors? Some items may need to load on multiple factors.

 

Gene Maguin

 

 

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Eins Bernardo
Sent: Wednesday, November 16, 2011 5:03 AM
To: [hidden email]
Subject:

 

Dear All,

 

I used Principal Axis Factoring using promax method in conducting EFA for the 81 items that utilized six-point ordinal scale.  The sample was n=381.  There is no indication of severe skewness on the data (skewness <3, kurtusis <10 and mardia coefficients >1000).  I used commonalities and factor loadings as criteria of dropping items.  Items with commonalities of <.40 were dropped.  Items with factor loadings of <.32 were also dropped. Crossloadings items were also dropped.  Finally, 35 items were left which loaded to six interpretable correlated factors.   The factors have the following number of items: 10, 7, 8, 4, 3 and 3.  After the factor analysis, the reliability coefficients were computed for each factor.  The Cronbach alpha are quite high.

 

After the EFA, a CFA was conducted using a separate sample of n=500 using amos.  Unfortunately, the chiquare has zero pvalue and no one of the fit indices were acceptable. I tried to improve the model  (guided by the modification indices).  I found out that the fit (at least the fit indices such as RMSEA, SRMR, cmin/df) of the model improved when I correlated the residuals/error terms.  Question:Is it appropriate to correlate the error terms?

 

Thank you in advance for your comments.

 

Eins

[Rich Ulrich]

You are using Promax, which produces correlated factors.  Your sample
size is not necessarily large enough for a good construction from 81 items.
That suggests you would get a lot of cross-loaded items.  Varimax is
the most common tool, for various reasons, including the clearer delineation
of loadings.

You use Promax, and then you eliminate items that are cross-loaded?  That
sounds like it might be a formula for getting rid of the best items. When you
read the items that were dropped for low communalities, I assume you can
infer (somewhat) why these are inferior to the rest -- unclear items or not
on-topic.  I expect that is not the case for cross-loaded items.

Poor replication/confirmation could owe to a poor choice of items from the
original set.

--
Rich Ulrich

---

Date: Wed, 16 Nov 2011 18:02:43 +0800
From: [hidden email]
To: [hidden email]

Dear All,

I used Principal Axis Factoring using promax method in conducting EFA for the 81 items that utilized six-point ordinal scale.  The sample was n=381.  There is no indication of severe skewness on the data (skewness <3, kurtusis <10 and mardia coefficients >1000).  I used commonalities and factor loadings as criteria of dropping items.  Items with commonalities of <.40 were dropped.  Items with factor loadings of <.32 were also dropped. Crossloadings items were also dropped.  Finally, 35 items were left which loaded to six interpretable correlated factors.   The factors have the following number of items: 10, 7, 8, 4, 3 and 3.  After the factor analysis, the reliability coefficients were computed for each factor.  The Cronbach alpha are quite high.

After the EFA, a CFA was conducted using a separate sample of n=500 using amos.  Unfortunately, the chiquare has zero pvalue and no one of the fit indices were acceptable. I tried to improve the model  (guided by the modification indices).  I found out that the fit (at least the fit indices such as RMSEA, SRMR, cmin/df) of the model improved when I correlated the residuals/error terms.  Question:Is it appropriate to correlate the error terms?

Thank you in advance for your comments.

Eins

[E. Bernardo]

Dear Gene and all,

 

Gene wrote:

>>>>>Don’t you actually mean that the chi –square value is very large/the p value is ver small.

      Yes, very large chi –square value / very small pvalue would mean ill-fit model.  

>>>>>>Yes, you can add residual covariances. But, how do you decide which ones to add and which ones not to add?

       I am using modification indices to decide which residual covariances can be added.

>>>>> Factor analysis allows every item to load on every factor. Conventional CFA allows each item to load on only one factor. The question is where does the item-factor covariance go for the non- dominant factors? Some items may need to load on multiple factors.

     In the CFA, I expect that each item would load on only one factor because in the EFA the  "crossloading" items were removed. When I look at the modification indices, i found no item would load on other factors.

Thank you.

J

---

From: Gene Maguin <[hidden email]>
To: [hidden email]
Sent: Thursday, November 17, 2011 10:28 PM
Subject:

Eins,

 

Don’t you actually mean that the chi –square value is very large/the p value is ver small. Yes, you can add residual covariances. But, how do you decide which ones to add and which ones not to add? Factor analysis allows every item to load on every factor. Conventional CFA allows each item to load on only one factor. The question is where does the item-factor covariance go for the non- dominant factors? Some items may need to load on multiple factors.

 

Gene Maguin

 

 

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Eins Bernardo
Sent: Wednesday, November 16, 2011 5:03 AM
To: [hidden email]
Subject:

 

Dear All,

 

I used Principal Axis Factoring using promax method in conducting EFA for the 81 items that utilized six-point ordinal scale.  The sample was n=381.  There is no indication of severe skewness on the data (skewness <3, kurtusis <10 and mardia coefficients >1000).  I used commonalities and factor loadings as criteria of dropping items.  Items with commonalities of <.40 were dropped.  Items with factor loadings of <.32 were also dropped. Crossloadings items were also dropped.  Finally, 35 items were left which loaded to six interpretable correlated factors.   The factors have the following number of items: 10, 7, 8, 4, 3 and 3.  After the factor analysis, the reliability coefficients were computed for each factor.  The Cronbach alpha are quite high.

 

After the EFA, a CFA was conducted using a separate sample of n=500 using amos.  Unfortunately, the chiquare has zero pvalue and no one of the fit indices were acceptable. I tried to improve the model  (guided by the modification indices).  I found out that the fit (at least the fit indices such as RMSEA, SRMR, cmin/df) of the model improved when I correlated the residuals/error terms.  Question:Is it appropriate to correlate the error terms?

 

Thank you in advance for your comments.

 

Eins

[E. Bernardo]

Dear Rich and all,

Rich said: Poor replication/confirmation could owe to a poor choice of items from the
original set.

Would you able to suggest a method that will produce good items from the original test in order to have good replication/confirmation?

Thank you.

---

From: Rich Ulrich <[hidden email]>
To: [hidden email]
Sent: Friday, November 18, 2011 2:08 AM
Subject:

You are using Promax, which produces correlated factors.  Your sample
size is not necessarily large enough for a good construction from 81 items.
That suggests you would get a lot of cross-loaded items.  Varimax is
the most common tool, for various reasons, including the clearer delineation
of loadings.

You use Promax, and then you eliminate items that are cross-loaded?  That
sounds like it might be a formula for getting rid of the best items. When you
read the items that were dropped for low communalities, I assume you can
infer (somewhat) why these are inferior to the rest -- unclear items or not
on-topic.  I expect that is not the case for cross-loaded items.

Poor replication/confirmation could owe to a poor choice of items from the
original set.

--
Rich Ulrich

---

Date: Wed, 16 Nov 2011 18:02:43 +0800
From: [hidden email]
To: [hidden email]

Dear All,

I used Principal Axis Factoring using promax method in conducting EFA for the 81 items that utilized six-point ordinal scale.  The sample was n=381.  There is no indication of severe skewness on the data (skewness <3, kurtusis <10 and mardia coefficients >1000).  I used commonalities and factor loadings as criteria of dropping items.  Items with commonalities of <.40 were dropped.  Items with factor loadings of <.32 were also dropped. Crossloadings items were also dropped.  Finally, 35 items were left which loaded to six interpretable correlated factors.   The factors have the following number of items: 10, 7, 8, 4, 3 and 3.  After the factor analysis, the reliability coefficients were computed for each factor.  The Cronbach alpha are quite high.

After the EFA, a CFA was conducted using a separate sample of n=500 using amos.  Unfortunately, the chiquare has zero pvalue and no one of the fit indices were acceptable. I tried to improve the model  (guided by the modification indices).  I found out that the fit (at least the fit indices such as RMSEA, SRMR, cmin/df) of the model improved when I correlated the residuals/error terms.  Question:Is it appropriate to correlate the error terms?

Thank you in advance for your comments.

Eins

[Rich Ulrich]

How to better produce a set of items for the next step?
I already suggested the easiest change: Varimax in place of Promax.

Getting rid of some items for their low achieved-communality is a
good idea, cross-loaded or not, since you have too many items
for your N.  Then, re-do the factoring.  The structure matrix is what
you look at for the loadings.

I've always been worried about getting rid of cross-loaded items.
I know that Varimax will give me theoretically-uncorrelated factors
as defined by proper weights on *every* item on the scale, but the
pragmatic factors will indeed be correlated after I compute them as
averages of the best-loaded items.  I always kept an item for its
better-loaded scale when it was .15 or .20 higher on that scale.  That
seems like a useful rule for your next step, too.

I sometimes want to keep an item for only the too-short scale when
there are equal loadings for two scales, but that is something that
can be argued in both directions.  And it is not unspeakable to keep
one item for both scales.  Since your total N is small for the number
of items, you are apt to see quite a few split loadings, even with
Varimax.  If you are throwing out more than a few items because of
split loadings - and they aren't ambiguous items when you read them -
you should adjust your rules about what to keep.

This will produce results that are *better*.  Whether they are really
pleasing results will depend on whether this sample does own and display
some latent traits that were successfully captured by the test.

--
Rich Ulrich

---

Date: Fri, 18 Nov 2011 16:57:51 +0800
From: [hidden email]
Subject: EFA to CFA( was Re: )
To: [hidden email]

Dear Rich and all,

Rich said: Poor replication/confirmation could owe to a poor choice of items from the
original set.

Would you able to suggest a method that will produce good items from the original test in order to have good replication/confirmation?

Thank you.

[snip, previous]

[Art Kendall]

You use of promax specifically allows items to be cross loaded.  but the you dropped cross loaded items.  This is contradictory to the purpose of promax.

See what happens if you go back and 1) use varimax rotation and 2) use parallel analysis to ball park the number of factors to retain.
In my experience the number I have finally retained is at least 1 "variable's worth" more than that obtained from purely random data (or random permutations).


Art Kendall
Social Research Consultants

On 11/16/2011 5:02 AM, Eins Bernardo wrote:

Dear All,

I used Principal Axis Factoring using promax method in conducting EFA for the 81 items that utilized six-point ordinal scale.  The sample was n=381.  There is no indication of severe skewness on the data (skewness <3, kurtusis <10 and mardia coefficients >1000).  I used commonalities and factor loadings as criteria of dropping items.  Items with commonalities of <.40 were dropped.  Items with factor loadings of <.32 were also dropped. Crossloadings items were also dropped.  Finally, 35 items were left which loaded to six interpretable correlated factors.   The factors have the following number of items: 10, 7, 8, 4, 3 and 3.  After the factor analysis, the reliability coefficients were computed for each factor.  The Cronbach alpha are quite high.

After the EFA, a CFA was conducted using a separate sample of n=500 using amos.  Unfortunately, the chiquare has zero pvalue and no one of the fit indices were acceptable. I tried to improve the model  (guided by the modification indices).  I found out that the fit (at least the fit indices such as RMSEA, SRMR, cmin/df) of the model improved when I correlated the residuals/error terms.  Question:Is it appropriate to correlate the error terms?

Thank you in advance for your comments.

Eins

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

[Swank, Paul R]

How can you justify forcing factors to be uncorrelated if in fact they are correlated?

 

Paul

 

Dr. Paul R. Swank,

Children's Learning Institute

Professor, Department of Pediatrics, Medical School

Adjunct Professor, School of Public Health

University of Texas Health Science Center-Houston

 

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Rich Ulrich
Sent: Friday, November 18, 2011 9:52 AM
To: [hidden email]
Subject: Re: EFA to CFA( was Re: )

 

How to better produce a set of items for the next step?
I already suggested the easiest change: Varimax in place of Promax.

Getting rid of some items for their low achieved-communality is a
good idea, cross-loaded or not, since you have too many items
for your N.  Then, re-do the factoring.  The structure matrix is what
you look at for the loadings.

I've always been worried about getting rid of cross-loaded items.
I know that Varimax will give me theoretically-uncorrelated factors
as defined by proper weights on *every* item on the scale, but the
pragmatic factors will indeed be correlated after I compute them as
averages of the best-loaded items.  I always kept an item for its
better-loaded scale when it was .15 or .20 higher on that scale.  That
seems like a useful rule for your next step, too.

I sometimes want to keep an item for only the too-short scale when
there are equal loadings for two scales, but that is something that
can be argued in both directions.  And it is not unspeakable to keep
one item for both scales.  Since your total N is small for the number
of items, you are apt to see quite a few split loadings, even with
Varimax.  If you are throwing out more than a few items because of
split loadings - and they aren't ambiguous items when you read them -
you should adjust your rules about what to keep.

This will produce results that are *better*.  Whether they are really
pleasing results will depend on whether this sample does own and display
some latent traits that were successfully captured by the test.

--
Rich Ulrich

---

Date: Fri, 18 Nov 2011 16:57:51 +0800
From: [hidden email]
Subject: EFA to CFA( was Re: )
To: [hidden email]

Dear Rich and all,

 

Rich said: Poor replication/confirmation could owe to a poor choice of items from the
original set.

 

Would you able to suggest a method that will produce good items from the original test in order to have good replication/confirmation?

 

Thank you.

[snip, previous]

[Rich Ulrich]

[see below]

---

From: [hidden email]
To: [hidden email]; [hidden email]
Date: Fri, 18 Nov 2011 11:11:14 -0600
Subject: RE: EFA to CFA( was Re: )

How can you justify forcing factors to be uncorrelated if in fact they are correlated?

 

[snip previous; my recommendation of Varimax over Promax.]
 - thanks for asking -


It works. 

In more detail:  It works a lot better than the alternatives.

Explanation:  Since we are intending to compute factors from
items using equal weights, we will end up with factors that are
correlated, just as expected.  And they will have just about as
much correlation as we expected, judging from my own experience. 

If we start with an oblique rotation, we pile correlation (from selecting
items) on top of allowed-correlation (oblique solution).  That is,
we are faced with factors that have a lot of double-loaded items.
Either we end up suffering from too much induced correlation from
using non-exclusive scale definitions; or else we drop entirely (as our
OP did) many items which are central to our universe of items.

The situation is different if we were preserving and using the
theoretical factors, but there are good reasons (interpretation,
generalizability) that that practice is rare.

If we look at the geometrical representation in plots, we will see
that a varimax solution does a pretty decent job of describing
factors as correlated as, say,  0.60.  And varimax does a much
better job that any oblique solution in separating out the variables
into non-overlapping sets.

By the way, Promax is what I did most of my experimenting with,
after it seemed superior (to several other oblique rotations)
for the sort of scaled data I've regularly reduced to factors.

--
Rich Ulrich

[Swank, Paul R]

My experience and that of other’s (eg. Preacher and MacCallum) is that most factors in behavioral sciences and many in biomedical sciences are in fact correlated. And in that case, allowing the factors to be correlated gives a cleaner solution. When factors are truly correlated, forcing them to be uncorrelated is what gives crossloadings.

 

Paul

 

Dr. Paul R. Swank,

Children's Learning Institute

Professor, Department of Pediatrics, Medical School

Adjunct Professor, School of Public Health

University of Texas Health Science Center-Houston

 

From: Rich Ulrich [mailto:[hidden email]]
Sent: Friday, November 18, 2011 11:55 AM
To: Swank, Paul R; SPSS list
Subject: RE: EFA to CFA( was Re: )

 

[see below]

---

From: [hidden email]
To: [hidden email]; [hidden email]
Date: Fri, 18 Nov 2011 11:11:14 -0600
Subject: RE: EFA to CFA( was Re: )

How can you justify forcing factors to be uncorrelated if in fact they are correlated?

 

[snip previous; my recommendation of Varimax over Promax.]
 - thanks for asking -


It works. 

In more detail:  It works a lot better than the alternatives.

Explanation:  Since we are intending to compute factors from
items using equal weights, we will end up with factors that are
correlated, just as expected.  And they will have just about as
much correlation as we expected, judging from my own experience. 

If we start with an oblique rotation, we pile correlation (from selecting
items) on top of allowed-correlation (oblique solution).  That is,
we are faced with factors that have a lot of double-loaded items.
Either we end up suffering from too much induced correlation from
using non-exclusive scale definitions; or else we drop entirely (as our
OP did) many items which are central to our universe of items.

The situation is different if we were preserving and using the
theoretical factors, but there are good reasons (interpretation,
generalizability) that that practice is rare.

If we look at the geometrical representation in plots, we will see
that a varimax solution does a pretty decent job of describing
factors as correlated as, say,  0.60.  And varimax does a much
better job that any oblique solution in separating out the variables
into non-overlapping sets.

By the way, Promax is what I did most of my experimenting with,
after it seemed superior (to several other oblique rotations)
for the sort of scaled data I've regularly reduced to factors.

--
Rich Ulrich

[Art Kendall]

Varimax is used rather than promax when the goal is to have measures that give a good operational definition of a construct that distinguish related  ideas.

Each item is considered an imperfect measure of a construct so we measure many times.  We have a firmer idea of a construct when we see what is common to a set of items.  An item has 3 parts: common variance, unique variance, and noise (aka error variance).  When we construct scales we want to do summative scoring that retains the common variance.  The unique variance is may be consistent sources that are related or or not.

One reason that it has long been conventional to have at least 50% more items written is that one wants divergent validity among the set of measures.
We assume that we are not perfect writers of items for constructs that are somewhat fuzzy even for the originator of the construct.
Often in practice we refine our constructs when we see how some items seem to be double barreled. When items are double barreled it becomes unclear just what is being measured. The next round of item writing attempts to find items that distinguish between scale measures so that the traits measured are divergent.

For instance in developing Lorr's liberalism-conservatism scale over time 3 factors arose. Lib-con was then used in analysis using three roughly uncorrelated scales as a set or using only that part of lib-con considered to some other phenomenon like favoring (or not) a particular bill.
1) general lib-con
2) equality
3) sexual freedom.

When I did my dissertation I added a few items that related to more current issues. Lo and behold endorsing "equal right for gay people"  loaded on both equality and sexual freedom.

This is analogous to including subgroups of cases on only one side of a t-test Or to using orthogonal designs in experiments.

There may be some circumstances where the population of items is measured and one simply wants to to collapse data but is not in the process of measurement development.  There may be no intent to see if different parts of a more general construct relate differently to other general constructs or if the parts of one construct relate differently to parts of another construct.  In those circumstances there may be no need to have divergent measures.


Art Kendall
Social Research Consultants


On 11/18/2011 3:33 PM, Swank, Paul R wrote:

My experience and that of other’s (eg. Preacher and MacCallum) is that most factors in behavioral sciences and many in biomedical sciences are in fact correlated. And in that case, allowing the factors to be correlated gives a cleaner solution. When factors are truly correlated, forcing them to be uncorrelated is what gives crossloadings.

 

Paul

 

Dr. Paul R. Swank,

Children's Learning Institute

Professor, Department of Pediatrics, Medical School

Adjunct Professor, School of Public Health

University of Texas Health Science Center-Houston

 

From: Rich Ulrich [[hidden email]]
Sent: Friday, November 18, 2011 11:55 AM
To: Swank, Paul R; SPSS list
Subject: RE: EFA to CFA( was Re: )

 

[see below]

---

From: [hidden email]
To: [hidden email]; [hidden email]
Date: Fri, 18 Nov 2011 11:11:14 -0600
Subject: RE: EFA to CFA( was Re: )

How can you justify forcing factors to be uncorrelated if in fact they are correlated?

 

[snip previous; my recommendation of Varimax over Promax.]
 - thanks for asking -


It works. 

In more detail:  It works a lot better than the alternatives.

Explanation:  Since we are intending to compute factors from
items using equal weights, we will end up with factors that are
correlated, just as expected.  And they will have just about as
much correlation as we expected, judging from my own experience. 

If we start with an oblique rotation, we pile correlation (from selecting
items) on top of allowed-correlation (oblique solution).  That is,
we are faced with factors that have a lot of double-loaded items.
Either we end up suffering from too much induced correlation from
using non-exclusive scale definitions; or else we drop entirely (as our
OP did) many items which are central to our universe of items.

The situation is different if we were preserving and using the
theoretical factors, but there are good reasons (interpretation,
generalizability) that that practice is rare.

If we look at the geometrical representation in plots, we will see
that a varimax solution does a pretty decent job of describing
factors as correlated as, say,  0.60.  And varimax does a much
better job that any oblique solution in separating out the variables
into non-overlapping sets.

By the way, Promax is what I did most of my experimenting with,
after it seemed superior (to several other oblique rotations)
for the sort of scaled data I've regularly reduced to factors.

--
Rich Ulrich

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

[Ryan]

Another, somewhat related point-- If one is truly interested in constructing an equal-interval measure (e.g., "ruler") of a unidimensional construct along a continuum ranging from the low end (e.g., low depression) through the upper end (e.g., severe depression) upon which both items and persons can be placed, Rasch modeling has been shown to prove quite useful. 

By fitting a Rasch model, one may examine various critical aspects of an equal-interval measure. First off, you can map items and persons on the "ruler," so to speak, (a.k.a. Wright map) to see the distribution of persons across the continuum of "severity", determine how well the items are covering the continuum of "severity" (a.k.a. bandwidth; that is, do your items adequately cover the lower end of depression?). One can also examine the extent to which the construct is unidimensional, how well the current sample of items are fitting the model, determine whether there are some persons who are not being placed as would be expected based on the model and potentially figure out why (e.g., atypical response patterns such as endorsement of suicide yet not endorsing "less severe" items), whether there is differential item function depending on the population (e.g., males versus females), and the list goes on and on. 

Ryan

On Sun, Nov 20, 2011 at 10:35 AM, Art Kendall <[hidden email]> wrote:

Varimax is used rather than promax when the goal is to have measures that give a good operational definition of a construct that distinguish related  ideas.

Each item is considered an imperfect measure of a construct so we measure many times.  We have a firmer idea of a construct when we see what is common to a set of items.  An item has 3 parts: common variance, unique variance, and noise (aka error variance).  When we construct scales we want to do summative scoring that retains the common variance.  The unique variance is may be consistent sources that are related or or not.

One reason that it has long been conventional to have at least 50% more items written is that one wants divergent validity among the set of measures.
We assume that we are not perfect writers of items for constructs that are somewhat fuzzy even for the originator of the construct.
Often in practice we refine our constructs when we see how some items seem to be double barreled. When items are double barreled it becomes unclear just what is being measured. The next round of item writing attempts to find items that distinguish between scale measures so that the traits measured are divergent.

For instance in developing Lorr's liberalism-conservatism scale over time 3 factors arose. Lib-con was then used in analysis using three roughly uncorrelated scales as a set or using only that part of lib-con considered to some other phenomenon like favoring (or not) a particular bill.
1) general lib-con
2) equality
3) sexual freedom.

When I did my dissertation I added a few items that related to more current issues. Lo and behold endorsing "equal right for gay people"  loaded on both equality and sexual freedom.

This is analogous to including subgroups of cases on only one side of a t-test Or to using orthogonal designs in experiments.

There may be some circumstances where the population of items is measured and one simply wants to to collapse data but is not in the process of measurement development.  There may be no intent to see if different parts of a more general construct relate differently to other general constructs or if the parts of one construct relate differently to parts of another construct.  In those circumstances there may be no need to have divergent measures.


Art Kendall
Social Research Consultants

On 11/18/2011 3:33 PM, Swank, Paul R wrote:

My experience and that of other’s (eg. Preacher and MacCallum) is that most factors in behavioral sciences and many in biomedical sciences are in fact correlated. And in that case, allowing the factors to be correlated gives a cleaner solution. When factors are truly correlated, forcing them to be uncorrelated is what gives crossloadings.

 

Paul

 

Dr. Paul R. Swank,

Children's Learning Institute

Professor, Department of Pediatrics, Medical School

Adjunct Professor, School of Public Health

University of Texas Health Science Center-Houston

 

From: Rich Ulrich [[hidden email]]
Sent: Friday, November 18, 2011 11:55 AM
To: Swank, Paul R; SPSS list
Subject: RE: EFA to CFA( was Re: )

 

[see below]

---

From: [hidden email]
To: [hidden email]; [hidden email]
Date: Fri, 18 Nov 2011 11:11:14 -0600
Subject: RE: EFA to CFA( was Re: )

How can you justify forcing factors to be uncorrelated if in fact they are correlated?

 

[snip previous; my recommendation of Varimax over Promax.]
 - thanks for asking -


It works. 

In more detail:  It works a lot better than the alternatives.

Explanation:  Since we are intending to compute factors from
items using equal weights, we will end up with factors that are
correlated, just as expected.  And they will have just about as
much correlation as we expected, judging from my own experience. 

If we start with an oblique rotation, we pile correlation (from selecting
items) on top of allowed-correlation (oblique solution).  That is,
we are faced with factors that have a lot of double-loaded items.
Either we end up suffering from too much induced correlation from
using non-exclusive scale definitions; or else we drop entirely (as our
OP did) many items which are central to our universe of items.

The situation is different if we were preserving and using the
theoretical factors, but there are good reasons (interpretation,
generalizability) that that practice is rare.

If we look at the geometrical representation in plots, we will see
that a varimax solution does a pretty decent job of describing
factors as correlated as, say,  0.60.  And varimax does a much
better job that any oblique solution in separating out the variables
into non-overlapping sets.

By the way, Promax is what I did most of my experimenting with,
after it seemed superior (to several other oblique rotations)
for the sort of scaled data I've regularly reduced to factors.

--
Rich Ulrich

===================== 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]

Good point. Unipolar (extent) scales are very useful. E.g., testing for unidimensionality can be very informative.
Sometimes scaling can also reveal when constructs that are considered single bipolar dimensions turn out to be two distinguishable dimensions. Bem found that conformity to masculine and feminine stereotype did not work as a single bipolar dimension. One can be low on both, high on both, or high on one and low on the other. This is analogous the the idea that position needs to be measured by both latitude and longitude.

Liberal-conservatism's 3 distinguishable factors are analogous to using longitude, latitude, and altitude.

The number of dimensions it takes to adequately measure a construct very much depends on the purposes of the research.

Art Kendall
Social Research Consultants




On 11/20/2011 12:18 PM, R B wrote:

Another, somewhat related point-- If one is truly interested in constructing an equal-interval measure (e.g., "ruler") of a unidimensional construct along a continuum ranging from the low end (e.g., low depression) through the upper end (e.g., severe depression) upon which both items and persons can be placed, Rasch modeling has been shown to prove quite useful.

By fitting a Rasch model, one may examine various critical aspects of an equal-interval measure. First off, you can map items and persons on the "ruler," so to speak, (a.k.a. Wright map) to see the distribution of persons across the continuum of "severity", determine how well the items are covering the continuum of "severity" (a.k.a. bandwidth; that is, do your items adequately cover the lower end of depression?). One can also examine the extent to which the construct is unidimensional, how well the current sample of items are fitting the model, determine whether there are some persons who are not being placed as would be expected based on the model and potentially figure out why (e.g., atypical response patterns such as endorsement of suicide yet not endorsing "less severe" items), whether there is differential item function depending on the population (e.g., males versus females), and the list goes on and on.

Ryan

On Sun, Nov 20, 2011 at 10:35 AM, Art Kendall <[hidden email]> wrote:

Varimax is used rather than promax when the goal is to have measures that give a good operational definition of a construct that distinguish related ideas.

Each item is considered an imperfect measure of a construct so we measure many times. We have a firmer idea of a construct when we see what is common to a set of items. An item has 3 parts: common variance, unique variance, and noise (aka error variance). When we construct scales we want to do summative scoring that retains the common variance. The unique variance is may be consistent sources that are related or or not.

One reason that it has long been conventional to have at least 50% more items written is that one wants divergent validity among the set of measures.
We assume that we are not perfect writers of items for constructs that are somewhat fuzzy even for the originator of the construct.
Often in practice we refine our constructs when we see how some items seem to be double barreled. When items are double barreled it becomes unclear just what is being measured. The next round of item writing attempts to find items that distinguish between scale measures so that the traits measured are divergent.

For instance in developing Lorr's liberalism-conservatism scale over time 3 factors arose. Lib-con was then used in analysis using three roughly uncorrelated scales as a set or using only that part of lib-con considered to some other phenomenon like favoring (or not) a particular bill.
1) general lib-con
2) equality
3) sexual freedom.

When I did my dissertation I added a few items that related to more current issues. Lo and behold endorsing "equal right for gay people" loaded on both equality and sexual freedom.

This is analogous to including subgroups of cases on only one side of a t-test Or to using orthogonal designs in experiments.

There may be some circumstances where the population of items is measured and one simply wants to to collapse data but is not in the process of measurement development. There may be no intent to see if different parts of a more general construct relate differently to other general constructs or if the parts of one construct relate differently to parts of another construct. In those circumstances there may be no need to have divergent measures.


Art Kendall
Social Research Consultants

On 11/18/2011 3:33 PM, Swank, Paul R wrote:

My experience and that of other’s (eg. Preacher and MacCallum) is that most factors in behavioral sciences and many in biomedical sciences are in fact correlated. And in that case, allowing the factors to be correlated gives a cleaner solution. When factors are truly correlated, forcing them to be uncorrelated is what gives crossloadings.

Paul

Dr. Paul R. Swank,

Children's Learning Institute

Professor, Department of Pediatrics, Medical School

Adjunct Professor, School of Public Health

University of Texas Health Science Center-Houston

From: Rich Ulrich [[hidden email]]
Sent: Friday, November 18, 2011 11:55 AM
To: Swank, Paul R; SPSS list
Subject: RE: EFA to CFA( was Re: )

[see below]

---

From: [hidden email]
To: [hidden email]; [hidden email]
Date: Fri, 18 Nov 2011 11:11:14 -0600
Subject: RE: EFA to CFA( was Re: )

How can you justify forcing factors to be uncorrelated if in fact they are correlated?

[snip previous; my recommendation of Varimax over Promax.]
- thanks for asking -


It works.

In more detail: It works a lot better than the alternatives.

Explanation: Since we are intending to compute factors from
items using equal weights, we will end up with factors that are
correlated, just as expected. And they will have just about as
much correlation as we expected, judging from my own experience.

If we start with an oblique rotation, we pile correlation (from selecting
items) on top of allowed-correlation (oblique solution). That is,
we are faced with factors that have a lot of double-loaded items.
Either we end up suffering from too much induced correlation from
using non-exclusive scale definitions; or else we drop entirely (as our
OP did) many items which are central to our universe of items.

The situation is different if we were preserving and using the
theoretical factors, but there are good reasons (interpretation,
generalizability) that that practice is rare.

If we look at the geometrical representation in plots, we will see
that a varimax solution does a pretty decent job of describing
factors as correlated as, say, 0.60. And varimax does a much
better job that any oblique solution in separating out the variables
into non-overlapping sets.

By the way, Promax is what I did most of my experimenting with,
after it seemed superior (to several other oblique rotations)
for the sort of scaled data I've regularly reduced to factors.

--
Rich Ulrich

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

[David Greenberg]

Let me just add an additional observation that in no way contradicts anything that Art Kendall says here. It can happen that a uni-dimensional Guttman scale, when subjected to exploratory factor analysis, will yield more than one factor. This is because the factor analysis algorithms impose a structure on the data that does not hold for a true Guttmann scale. In these circumstances, a naive researcher can mistakenly conclude that more dimensions are present than is actually the case.  Attitudes toward abortion in different circumstances, as revealed by the General Social Survey, reveal this phenomenon. David Greenberg, Sociology Department, New York University

On Sun, Nov 20, 2011 at 3:48 PM, Art Kendall <[hidden email]> wrote:

Good point. Unipolar (extent) scales are very useful. E.g., testing for unidimensionality can be very informative.
Sometimes scaling can also reveal when constructs that are considered single bipolar dimensions turn out to be two distinguishable dimensions. Bem found that conformity to masculine and feminine stereotype did not work as a single bipolar dimension. One can be low on both, high on both, or high on one and low on the other. This is analogous the the idea that position needs to be measured by both latitude and longitude.

Liberal-conservatism's 3 distinguishable factors are analogous to using longitude, latitude, and altitude.

The number of dimensions it takes to adequately measure a construct very much depends on the purposes of the research.

Art Kendall
Social Research Consultants




On 11/20/2011 12:18 PM, R B wrote:

Another, somewhat related point-- If one is truly interested in constructing an equal-interval measure (e.g., "ruler") of a unidimensional construct along a continuum ranging from the low end (e.g., low depression) through the upper end (e.g., severe depression) upon which both items and persons can be placed, Rasch modeling has been shown to prove quite useful.

By fitting a Rasch model, one may examine various critical aspects of an equal-interval measure. First off, you can map items and persons on the "ruler," so to speak, (a.k.a. Wright map) to see the distribution of persons across the continuum of "severity", determine how well the items are covering the continuum of "severity" (a.k.a. bandwidth; that is, do your items adequately cover the lower end of depression?). One can also examine the extent to which the construct is unidimensional, how well the current sample of items are fitting the model, determine whether there are some persons who are not being placed as would be expected based on the model and potentially figure out why (e.g., atypical response patterns such as endorsement of suicide yet not endorsing "less severe" items), whether there is differential item function depending on the population (e.g., males versus females), and the list goes on and on.

Ryan

On Sun, Nov 20, 2011 at 10:35 AM, Art Kendall <[hidden email]> wrote:

Varimax is used rather than promax when the goal is to have measures that give a good operational definition of a construct that distinguish related ideas.

Each item is considered an imperfect measure of a construct so we measure many times. We have a firmer idea of a construct when we see what is common to a set of items. An item has 3 parts: common variance, unique variance, and noise (aka error variance). When we construct scales we want to do summative scoring that retains the common variance. The unique variance is may be consistent sources that are related or or not.

One reason that it has long been conventional to have at least 50% more items written is that one wants divergent validity among the set of measures.
We assume that we are not perfect writers of items for constructs that are somewhat fuzzy even for the originator of the construct.
Often in practice we refine our constructs when we see how some items seem to be double barreled. When items are double barreled it becomes unclear just what is being measured. The next round of item writing attempts to find items that distinguish between scale measures so that the traits measured are divergent.

For instance in developing Lorr's liberalism-conservatism scale over time 3 factors arose. Lib-con was then used in analysis using three roughly uncorrelated scales as a set or using only that part of lib-con considered to some other phenomenon like favoring (or not) a particular bill.
1) general lib-con
2) equality
3) sexual freedom.

When I did my dissertation I added a few items that related to more current issues. Lo and behold endorsing "equal right for gay people" loaded on both equality and sexual freedom.

This is analogous to including subgroups of cases on only one side of a t-test Or to using orthogonal designs in experiments.

There may be some circumstances where the population of items is measured and one simply wants to to collapse data but is not in the process of measurement development. There may be no intent to see if different parts of a more general construct relate differently to other general constructs or if the parts of one construct relate differently to parts of another construct. In those circumstances there may be no need to have divergent measures.


Art Kendall
Social Research Consultants

On 11/18/2011 3:33 PM, Swank, Paul R wrote:

My experience and that of other’s (eg. Preacher and MacCallum) is that most factors in behavioral sciences and many in biomedical sciences are in fact correlated. And in that case, allowing the factors to be correlated gives a cleaner solution. When factors are truly correlated, forcing them to be uncorrelated is what gives crossloadings.

Paul

Dr. Paul R. Swank,

Children's Learning Institute

Professor, Department of Pediatrics, Medical School

Adjunct Professor, School of Public Health

University of Texas Health Science Center-Houston

From: Rich Ulrich [[hidden email]]
Sent: Friday, November 18, 2011 11:55 AM
To: Swank, Paul R; SPSS list
Subject: RE: EFA to CFA( was Re: )

[see below]

---

From: [hidden email]
To: [hidden email]; [hidden email]
Date: Fri, 18 Nov 2011 11:11:14 -0600
Subject: RE: EFA to CFA( was Re: )

How can you justify forcing factors to be uncorrelated if in fact they are correlated?

[snip previous; my recommendation of Varimax over Promax.]
- thanks for asking -


It works.

In more detail: It works a lot better than the alternatives.

Explanation: Since we are intending to compute factors from
items using equal weights, we will end up with factors that are
correlated, just as expected. And they will have just about as
much correlation as we expected, judging from my own experience.

If we start with an oblique rotation, we pile correlation (from selecting
items) on top of allowed-correlation (oblique solution). That is,
we are faced with factors that have a lot of double-loaded items.
Either we end up suffering from too much induced correlation from
using non-exclusive scale definitions; or else we drop entirely (as our
OP did) many items which are central to our universe of items.

The situation is different if we were preserving and using the
theoretical factors, but there are good reasons (interpretation,
generalizability) that that practice is rare.

If we look at the geometrical representation in plots, we will see
that a varimax solution does a pretty decent job of describing
factors as correlated as, say, 0.60. And varimax does a much
better job that any oblique solution in separating out the variables
into non-overlapping sets.

By the way, Promax is what I did most of my experimenting with,
after it seemed superior (to several other oblique rotations)
for the sort of scaled data I've regularly reduced to factors.

--
Rich Ulrich

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