SPSSX Discussion

What communalities and matrice to report ?

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Mbaye Fall Diallo

What communalities and matrice to report ?

Hi dear all,
1. I am using factor analysis (ML extraction). I would like to know what communality to report : initial or extraction ?
2. I used a Promax rotation. I would like to know what matrice to report : pattern matrix or structure matrix ?

Thanks in advance for your help. I would appreciate if you can provide some references.

Best,

Mbaye.

Art Kendall

Re: What communalities and matrice to report ?

Just curious. What is the goal of your factor analysis?

Are there specific reason to choose ML and Promax?

Do you find that the results differ in substantive conclusions from conventional approaches?

Art Kendall
Social Research Consultants

On 2/17/2011 4:03 PM, Mbaye Fall Diallo wrote:

Hi dear all,
1. I am using factor analysis (ML extraction). I would like to know what communality to report : initial or extraction ?
2. I used a Promax rotation. I would like to know what matrice to report : pattern matrix or structure matrix ?

Thanks in advance for your help. I would appreciate if you can provide some references.

Best,

Mbaye.

===================== 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
Social Research Consultants

Swank, Paul R

Re: What communalities and matrice to report ?

Are you suggesting that maximum likelihood and oblique solutions are unconventional?

Dr. Paul R. Swank,

Professor and Director of Research

Children's Learning Institute

University of Texas Health Science Center-Houston

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Art Kendall
Sent: Saturday, February 19, 2011 6:31 AM
To: [hidden email]
Subject: Re: What communalities and matrice to report ?

Mbaye Fall Diallo

Re: What communalities and matrice to report ?

In reply to this post by Art Kendall

Hi Art,
My objective is to assess the factorial structure of some scales adapted from previous research. I will subsequently use ML in CFA. So I was advised to use ML in EFA so as to have the Chi-2 test. I am using Promax because previous research showed the the dimensions of my construts were correleted.
Results do not have great differences but as I am using ESEM (exploratory structural equation modeling), I have to use ML I think.
Best,

Mbaye

Date: Sat, 19 Feb 2011 07:30:48 -0500
From: [hidden email]
Subject: Re: What communalities and matrice to report ?
To: [hidden email]

Just curious. What is the goal of your factor analysis?

Are there specific reason to choose ML and Promax?

Do you find that the results differ in substantive conclusions from conventional approaches?

Art Kendall
Social Research Consultants

On 2/17/2011 4:03 PM, Mbaye Fall Diallo wrote:

Hi dear all,
1. I am using factor analysis (ML extraction). I would like to know what communality to report : initial or extraction ?
2. I used a Promax rotation. I would like to know what matrice to report : pattern matrix or structure matrix ?

Thanks in advance for your help. I would appreciate if you can provide some references.

Best,

Mbaye.

Swank, Paul R

Re: What communalities and matrice to report ?

I would report both the pattern and structure matrices, since they impart different information, as well as the factor intercorrelations.

Dr. Paul R. Swank,

Professor and Director of Research

Children's Learning Institute

University of Texas Health Science Center-Houston

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Mbaye Fall Diallo
Sent: Saturday, February 19, 2011 11:48 AM
To: [hidden email]
Subject: Re: What communalities and matrice to report ?

Art Kendall

Re: What communalities and matrice to report ?

In reply to this post by Swank, Paul R

I seemed to recall that the OP had talked about working with summative scales, but was not sure.
I did not mean unconventional with the connotation that there was something wrong with it. New to an audience is not the same thing as "wrong".

If one reporting in the context of scale construction there is nothing wrong with using newer forms of factor analysis. However, I would usually ask for some explication to an audience why the newer way was used. How is it different? Did it make a substantive difference to use it? Different communities are used to seeing different approaches. When one does something novel-to-an-audience I believe it is helpful to tie what you are doing to what that audience is familiar with.

In scale construction based on the multi-trait multi-method approach it is conventional to allow an item to be unit weighted on only one scale (zero in the others). This is in interest of divergent validity. Oblique rotation is not consistent with that particular use. Items that have split loading are usually not used in the scoring key derived from the factor analysis. There are uses of factor analysis other than getting distinct interpretable measures of constructs.
The goals and context of an analysis make a lot of difference in communicating to an audience.

Perhaps my last question would have been clearer if I had asked if the OP found substantive differences in the scoring keys derived via ML vs PAF (aka PA2).

Without an intense interest, I kind of keep an eye out for actual instances where it makes a substantive difference what kind of extraction was used.
Offhand I cannot recall, for instance, an actual application in scale construction where it made much difference whether one use the principal components or the principal axes type of extraction. YMMV.

Art Kendall

On 2/19/2011 10:34 AM, Swank, Paul R wrote:

Are you suggesting that maximum likelihood and oblique solutions are unconventional?

Dr. Paul R. Swank,

Professor and Director of Research

Children's Learning Institute

University of Texas Health Science Center-Houston

From: SPSSX(r) Discussion [[hidden email]] On Behalf Of Art Kendall
Sent: Saturday, February 19, 2011 6:31 AM
To: [hidden email]
Subject: Re: What communalities and matrice to report ?

Just curious. What is the goal of your factor analysis?

Are there specific reason to choose ML and Promax?

Do you find that the results differ in substantive conclusions from conventional approaches?

Art Kendall
Social Research Consultants

On 2/17/2011 4:03 PM, Mbaye Fall Diallo wrote:

Hi dear all,
1. I am using factor analysis (ML extraction). I would like to know what communality to report : initial or extraction ?
2. I used a Promax rotation. I would like to know what matrice to report : pattern matrix or structure matrix ?

Thanks in advance for your help. I would appreciate if you can provide some references.

Best,

Mbaye.

===================== 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
Social Research Consultants

Swank, Paul R

Re: What communalities and matrice to report ?

The major advantage to maximum likelihood extraction is a test for the number of factors that account for most of th variance, which I believe is preferable to eigenvalues greater than one. Given the popularity of structural modeling and confirmatory factor analyses, I would suspect that ML is not that new. As for oblique factor solutions, I find that in most social science examples I have seen the existence of uncorrelated factors are the exception rather than the rule.

Dr. Paul R. Swank,

Professor and Director of Research

Children's Learning Institute

University of Texas Health Science Center-Houston

From: Art Kendall [mailto:[hidden email]]
Sent: Saturday, February 19, 2011 5:57 PM
To: Swank, Paul R
Cc: [hidden email]
Subject: Re: What communalities and matrice to report ?

Are you suggesting that maximum likelihood and oblique solutions are unconventional?

Dr. Paul R. Swank,

Professor and Director of Research

Children's Learning Institute

University of Texas Health Science Center-Houston

From: SPSSX(r) Discussion [[hidden email]] On Behalf Of Art Kendall
Sent: Saturday, February 19, 2011 6:31 AM
To: [hidden email]
Subject: Re: What communalities and matrice to report ?

Swank, Paul R

Re: What communalities and matrice to report ?

In reply to this post by Mbaye Fall Diallo

Also report the final communalities although they are different depending on whether you consider the correlation among factors or not. I usually reproduce the communalities associated with the pattern matrix but there is some disagreement as to whether the pattern or structure matrices are best. Be prepared to report both.

Dr. Paul R. Swank,

Professor and Director of Research

Children's Learning Institute

University of Texas Health Science Center-Houston

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Mbaye Fall Diallo
Sent: Thursday, February 17, 2011 3:03 PM
To: [hidden email]
Subject: What communalities and matrice to report ?

Mbaye Fall Diallo

Re: What communalities and matrice to report ?

Hi dear all,
Thanks again for all your comments. I agree with what Paul said.

@ Art : have a look on the following references for more details about why I used ESEM and oblique rotation :

Asparouhov, Tihomir and Muthén, Bengt (2009), 'Exploratory Structural Equation Modeling', Structural Equation Modeling: A Multidisciplinary Journal,16:3,397 — 438.

Sass, Daniel A. and Schmitt, Thomas A.(2010) 'A Comparative Investigation of Rotation Criteria Within Exploratory Factor Analysis', Multivariate Behavioral Research, 45: 1, 73 — 103.

Kristopher J. Preacher and Robert C. MacCallum (2003), Repairing Tom Swift’s Electric Factor Analysis Machine, UNDERSTANDING STATISTICS, 2(1), 13–43. See p.25-26.

Iacobucci, Dawn (ed.) (2001), Journal of Consumer Psychology’s Special Issue on Methodological and Statistical Concerns of the Experimental Behavioral Researcher,
10 (1&2), Mahwah, NJ: Lawrence Erlbaum Associates. See Factor Analysis, (See p.78).

Best,

Mbaye,

Date: Sat, 19 Feb 2011 21:11:25 -0600
From: [hidden email]
Subject: Re: What communalities and matrice to report ?
To: [hidden email]

Dr. Paul R. Swank,

Professor and Director of Research

Children's Learning Institute

University of Texas Health Science Center-Houston

Art Kendall

Re: What communalities and matrice to report ?

These all give good ideas. However, it helps your audience if you anticipate questions that might arise. By comparing and contrasting the approach you use to what others might use you help the audience understand.

Today's computer environments make it almost trivial to try different approaches. For example, running a parallel analysis would have been a laughable idea 40 years ago. Last week I did a 40,000 case parallel analysis with 1000 random permutations in 50 minutes, less time than it would have take to do a 400 case factor analysis in 1972.

Depending on your audience you still may want to put a few sentences in to point to these citations and briefly state your reasoning.

For example:

"ML was used because it gave an additional idea on the number of factors to retain (cite). Both ML and parallel analysis suggested retaining k factors."

"The substantive results did not depend on the choice of extraction method. The substantive results were the same using other methods of extraction."

"Using xyz gave clearer results than lmn in that ..."

"Oblique rotation was used because a (cite), b(cite, cite),and c. The goals of this analysis stated above were distinct from scale creation uses of factor analysis in that divergent validity was not a concern. There was not a reason to disallow an item from being on more than one scale key."

Also, when you present the pattern and structure in formation, in many contexts you would want to do more than say "This is the pattern matrix." "This is the structure matrix."

P.S.
I had copies of these articles in a file that has been lost. Unfortunately, I no longer have access to replacement copies so I cannot take another look at them.

I certainly agree that the Kaiser criterion of 1.00 merely was used to minimize machine time which used to be very expensive. I usually describe it as "there is no way I would want more than 10 factors, usually many fewer, but certainly not more so why waste money."

Art Kendall
Social Research Consultants

On 2/20/2011 10:12 AM, Mbaye Fall Diallo wrote:

Hi dear all,
Thanks again for all your comments. I agree with what Paul said.

@ Art : have a look on the following references for more details about why I used ESEM and oblique rotation :

Asparouhov, Tihomir and Muthén, Bengt (2009), 'Exploratory Structural Equation Modeling', Structural Equation Modeling: A Multidisciplinary Journal,16:3,397 — 438.

Sass, Daniel A. and Schmitt, Thomas A.(2010) 'A Comparative Investigation of Rotation Criteria Within Exploratory Factor Analysis', Multivariate Behavioral Research, 45: 1, 73 — 103.

Kristopher J. Preacher and Robert C. MacCallum (2003), Repairing Tom Swift’s Electric Factor Analysis Machine, UNDERSTANDING STATISTICS, 2(1), 13–43. See p.25-26.

Iacobucci, Dawn (ed.) (2001), Journal of Consumer Psychology’s Special Issue on Methodological and Statistical Concerns of the Experimental Behavioral Researcher,
10 (1&2), Mahwah, NJ: Lawrence Erlbaum Associates. See Factor Analysis, (See p.78).

Best,

Mbaye,

Date: Sat, 19 Feb 2011 21:11:25 -0600
From: [hidden email]
Subject: Re: What communalities and matrice to report ?
To: [hidden email]

Also report the final communalities although they are different depending on whether you consider the correlation among factors or not. I usually reproduce the communalities associated with the pattern matrix but there is some disagreement as to whether the pattern or structure matrices are best. Be prepared to report both.

Dr. Paul R. Swank,

Professor and Director of Research

Children's Learning Institute

University of Texas Health Science Center-Houston

From: SPSSX(r) Discussion [[hidden email]] On Behalf Of Mbaye Fall Diallo
Sent: Thursday, February 17, 2011 3:03 PM
To: [hidden email]
Subject: What communalities and matrice to report ?

Hi dear all,
1. I am using factor analysis (ML extraction). I would like to know what communality to report : initial or extraction ?
2. I used a Promax rotation. I would like to know what matrice to report : pattern matrix or structure matrix ?

Thanks in advance for your help. I would appreciate if you can provide some references.

Best,

Mbaye.

Art Kendall
Social Research Consultants

Mbaye Fall Diallo

Re: What communalities and matrice to report ?

Hi Art,

These are some quotations for :

- ESEM :

"The ... ESEM approach has the full generality of regular SEM. From an EFA perspective, this implies that EFA can be performed while allowing correlated residuals, covariates including direct effects on the factor indicators, longitudinal EFA with across-time invariance testing, and multiple-group EFA with across-group invariance testing. Several factor loading rotation methods are available, including Geomin and Target rotation. (Asparouhov and Muthen, 2009, p.429).

"The main advantage of the ESEM model over existing modeling practices is that it seamlessly

incorporates the EFA and SEM models. In most applications with multiple factors the EFA is used to discover and formulate factors. Usually the EFA is followed by an ad-hoc

procedure that mimics the EFA factor definitions in an SEM model with a CFA measurement specification. The ESEM model accomplishes this task in a one-step approach and thus it is a simpler approach. In addition, the ESEM approach is more accurate because it avoids potential pitfalls due to the challenging EFA to CFA conversion. For example, an EFA-based CFA model may lead to poor fit when covariates are added to the model. The ESEM approach avoids this problem by estimating the measurement and structural model parts simultaneously." (Asparouhov and Muthen, 2009, 430).

- Oblique rotation :

"In general, if the researcher does not know how the factors are related to each other, there is no reason to assume that they are completely independent. It is almost

always safer to assume that there is not perfect independence, and to use oblique rotation instead of orthogonal rotation.8 Moreover, if optimal simple structure is exhibited by orthogonal factors, an obliquely rotated factor solution will resemble an orthogonal one anyway (Floyd&Widaman, 1995), so nothing is lost by using oblique rotation. Oblique rotation offers the further advantage of allowing estimation of factor correlations, which is surely a more informative approach than assuming that the factors are completely independent." (Preacher and MacCallum, 2003, p.26).

NB : I sent you the articles I posted in your personal e-mail. Thanks for your feedback.

Best,

Mbaye.