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factor analysis of nominal data

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factor analysis of nominal data

For an analysis of 44 local parishes I have numerous nominal variables
(0/1 coded) that characterise the behaviour of a parish as an
institution. Correspondence analysis would be an appropriate method to
find a pattern but this method is not part of the base & regression
modules that I have access to. Any other idea ?

Thanks
F. Thomas

--
..........................................
Dr. Frank Thomas
FTR Internet Research
93110 Rosny-sous-Bois
France

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Hector Maletta

Re: factor analysis of nominal data

CATPCA is categorical factor analysis. It accepts nominal, ordinal and
interval variables.
Besides the method you use, I feel somewhat uncomfortable at the idea of
analyzing "numerous" variables with only 44 cases. I bet you may need more
cases for ANY such analysis to make any sense.

Hector

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Frank Thomas
Sent: 14 April 2008 20:06
To: [hidden email]
Subject: factor analysis of nominal data

For an analysis of 44 local parishes I have numerous nominal variables
(0/1 coded) that characterise the behaviour of a parish as an
institution. Correspondence analysis would be an appropriate method to
find a pattern but this method is not part of the base & regression
modules that I have access to. Any other idea ?

Thanks
F. Thomas

--
..........................................
Dr. Frank Thomas
FTR Internet Research
93110 Rosny-sous-Bois
France

=====================
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Dale Glaser

Re: factor analysis of nominal data

Another option that I use for binary factor analysis is Mplus.......however, as Hector mentioned with n = 44 parishes, though you may be able to obtain convergence in Mplus, I would question the stability of the solution............that being said, there is an interesting article in Psych. Methods (I don't have the issue in front of me) a few years back, that furnishes some evidence of relatively stable solutions with small sample sizes (e.g, n = 100) contingent on factor/variable ratio (i.e., under/over determination) and communalities (e.g, h^2 > .60).........but in Mplus I believe the default is WLSMV which requires n larger than n = 44....in fact, here is a quote from Bength Muthen from the Mplus discussion site indicating ULS is an option for small n:

"ULS is the Mplus default with EFA because there one typically has many items for which WLSMV would be slow. Muthen, Du Toit, Spisic finds that WLMSV works well for n as small as 200, but your sample is even smaller. The first things to go wrong are the chi-square and SEs, less so the parameter estimates. So since ULS does not give SEs or chi-square, it would seem that at your low sample sizes ULS would be just as good. "

.....dale

Hector Maletta <[hidden email]> wrote:
CATPCA is categorical factor analysis. It accepts nominal, ordinal and
interval variables.
Besides the method you use, I feel somewhat uncomfortable at the idea of
analyzing "numerous" variables with only 44 cases. I bet you may need more
cases for ANY such analysis to make any sense.

Hector

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Frank Thomas
Sent: 14 April 2008 20:06
To: [hidden email]
Subject: factor analysis of nominal data

For an analysis of 44 local parishes I have numerous nominal variables
(0/1 coded) that characterise the behaviour of a parish as an
institution. Correspondence analysis would be an appropriate method to
find a pattern but this method is not part of the base & regression
modules that I have access to. Any other idea ?

Thanks
F. Thomas

--
..........................................
Dr. Frank Thomas
FTR Internet Research
93110 Rosny-sous-Bois
France

=====================
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Dale Glaser, Ph.D.
Principal--Glaser Consulting
Lecturer/Adjunct Faculty--SDSU/USD/AIU
President, San Diego Chapter of
American Statistical Association
3115 4th Avenue
San Diego, CA 92103
phone: 619-220-0602
fax: 619-220-0412
email: [hidden email]
website: www.glaserconsult.com

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Ian Martin-2

Re: factor analysis of nominal data

In reply to this post by news

You could do the COA in ade4 if you don't have the facility in SPSS.

regards,
Ian Martin

Ian D. Martin, Ph.D.
Aquatic Ecologist

On 14 Apr, 2008, at 7:05 PM, Frank Thomas wrote:

> For an analysis of 44 local parishes I have numerous nominal variables
> (0/1 coded) that characterise the behaviour of a parish as an
> institution. Correspondence analysis would be an appropriate method to
> find a pattern but this method is not part of the base & regression
> modules that I have access to. Any other idea ?
>
> Thanks
> F. Thomas
>
> --
> ..........................................
> Dr. Frank Thomas
> FTR Internet Research
> 93110 Rosny-sous-Bois
> France
>
> =====================
> 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

=====================
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news

Re: factor analysis of nominal data

In reply to this post by Hector Maletta

Will have to buy the categories module in the future, I guess.

Concerning the limited no of cases : I shall get some more cases in the
near future but the upper limit will be 68 as this is the universe. So I
don't work with an sample but with the complete population. Numerous
variables and few cases is the standard in organisational analysis. Now
what can you do if you are limited in this way?

Frank

Hector Maletta wrote:

> CATPCA is categorical factor analysis. It accepts nominal, ordinal and
> interval variables.
> Besides the method you use, I feel somewhat uncomfortable at the idea of
> analyzing "numerous" variables with only 44 cases. I bet you may need more
> cases for ANY such analysis to make any sense.
>
> Hector
>
> -----Original Message-----
> From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
> Frank Thomas
> Sent: 14 April 2008 20:06
> To: [hidden email]
> Subject: factor analysis of nominal data
>
> For an analysis of 44 local parishes I have numerous nominal variables
> (0/1 coded) that characterise the behaviour of a parish as an
> institution. Correspondence analysis would be an appropriate method to
> find a pattern but this method is not part of the base & regression
> modules that I have access to. Any other idea ?
>
> Thanks
> F. Thomas
>
> --
> ..........................................
> Dr. Frank Thomas
> FTR Internet Research
> 93110 Rosny-sous-Bois
> France
>
> =====================
> 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
>
>
>
>
>

Kooij, A.J. van der

Re: factor analysis of nominal data

In reply to this post by Hector Maletta

When all variables are dichotomous, the result of CATPCA is equal to the result of standard PCA.
(A line fitted on 2 points will always be a straight line, so the transformations are linear, no matter the scaling level.)

Anita van der Kooij
Data Theory Group
Leiden University

________________________________

From: SPSSX(r) Discussion on behalf of Hector Maletta
Sent: Tue 15/04/2008 02:21
To: [hidden email]
Subject: Re: factor analysis of nominal data

CATPCA is categorical factor analysis. It accepts nominal, ordinal and
interval variables.
Besides the method you use, I feel somewhat uncomfortable at the idea of
analyzing "numerous" variables with only 44 cases. I bet you may need more
cases for ANY such analysis to make any sense.

Hector

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Frank Thomas
Sent: 14 April 2008 20:06
To: [hidden email]
Subject: factor analysis of nominal data

For an analysis of 44 local parishes I have numerous nominal variables
(0/1 coded) that characterise the behaviour of a parish as an
institution. Correspondence analysis would be an appropriate method to
find a pattern but this method is not part of the base & regression
modules that I have access to. Any other idea ?

Thanks
F. Thomas

--
..........................................
Dr. Frank Thomas
FTR Internet Research
93110 Rosny-sous-Bois
France

=====================
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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=====================
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Hector Maletta

Re: factor analysis of nominal data

In reply to this post by news

You can have lower sampling error (finite population correction), but anyway
the number of variables x categories cannot exceed the number of cases.
Hector

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Frank Thomas
Sent: 15 April 2008 07:50
To: [hidden email]
Subject: Re: factor analysis of nominal data

Will have to buy the categories module in the future, I guess.

Concerning the limited no of cases : I shall get some more cases in the
near future but the upper limit will be 68 as this is the universe. So I
don't work with an sample but with the complete population. Numerous
variables and few cases is the standard in organisational analysis. Now
what can you do if you are limited in this way?

Frank

Hector Maletta wrote:

--
..........................................
Dr. Frank Thomas
FTR Internet Research
93110 Rosny-sous-Bois
France

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

=====================
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Art Kendall

Re: factor analysis of nominal data

In reply to this post by news

I don't have the list of which procedures are available in Base, but am
very sure that Cluster is, and believe that Twostep is.
There are many similarity coefficients either in cluster or through
proximities.

How did the nominal variables arise? Were they used in previous
research as items in scales?
Are they intrinsic dichotomies or are they in sets representing several
levels of a multi-valued nominal level variable?

Are the 44 parishes a population of parishes in a region? a sample, a
conveniently obtained group, or volunteer respondents?

Are you interested in finding groups of variables or groups of parishes?

Art Kendall
Social Research Consultants

Frank Thomas wrote:

> For an analysis of 44 local parishes I have numerous nominal variables
> (0/1 coded) that characterise the behaviour of a parish as an
> institution. Correspondence analysis would be an appropriate method to
> find a pattern but this method is not part of the base & regression
> modules that I have access to. Any other idea ?
>
> Thanks
> F. Thomas
>
> --
> ..........................................
> Dr. Frank Thomas
> FTR Internet Research
> 93110 Rosny-sous-Bois
> France
>
> =====================
> 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

news

Re: factor analysis of nominal data

Hi Art,
I answer using your questions.
Art Kendall wrote:
> I don't have the list of which procedures are available in Base, but
> am very sure that Cluster is, and believe that Twostep is.
Right, I could do a typology of cases but not of variables.
>
> How did the nominal variables arise? Were they used in previous
> research as items in scales?
No, the nominal variables have not been used as items in scales. Most of
them are ad hoc lists of mission statements, activities, resource
availability, demands, that were created during the collaborative
creation of the questionnaire.
> Are they intrinsic dichotomies or are they in sets representing
> several levels of a multi-valued nominal level variable?
They are intrinsic dichotomies : activity present/not present.
>
> Are the 44 parishes a population of parishes in a region? a sample, a
> conveniently obtained group, or volunteer respondents?
The 44 parishes are not the complete universe but nearly. In the next
weeks nearly all of the 68 parishes will have returned the
questionnaire. The survey is an official one organised by the regional
church. So as parishes have some leeway in participating they are
volunteer respondents.
>
> Are you interested in finding groups of variables or groups of parishes?
I am interested in both : understanding the pattern of responses and
using the pattern for categorizing the parishes.
I think it necessary not to use the raw data for clustering the parishes
since some dimensions (religious orientation) is treated by one item set
whereas activities are described with several item sets. If I would use
the raw data the result would be too much influenced by the pattern with
the larhest number of items.

Thanks
Frank Thomas

>
> Art Kendall
> Social Research Consultants
>
> Frank Thomas wrote:
>> For an analysis of 44 local parishes I have numerous nominal variables
>> (0/1 coded) that characterise the behaviour of a parish as an
>> institution. Correspondence analysis would be an appropriate method to
>> find a pattern but this method is not part of the base & regression
>> modules that I have access to. Any other idea ?
>>
>> Thanks
>> F. Thomas
>>
>> --
>> ..........................................
>> Dr. Frank Thomas
>> FTR Internet Research
>> 93110 Rosny-sous-Bois
>> France
>>
>> =====================
>> 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

Re: factor analysis of nominal data

replies interspersed.

Frank Thomas wrote:
> Hi Art,
> I answer using your questions.
> Art Kendall wrote:
>> I don't have the list of which procedures are available in Base, but
>> am very sure that Cluster is, and believe that Twostep is.
> Right, I could do a typology of cases but not of variables.

Flip i.e., transpose. the data matrix

>>
>> How did the nominal variables arise? Were they used in previous
>> research as items in scales?
> No, the nominal variables have not been used as items in scales. Most
> of them are ad hoc lists of mission statements, activities, resource
> availability, demands, that were created during the collaborative
> creation of the questionnaire.
>> Are they intrinsic dichotomies or are they in sets representing
>> several levels of a multi-valued nominal level variable?
> They are intrinsic dichotomies : activity present/not present.
>>
>> Are the 44 parishes a population of parishes in a region? a sample, a
>> conveniently obtained group, or volunteer respondents?
> The 44 parishes are not the complete universe but nearly. In the next
> weeks nearly all of the 68 parishes will have returned the
> questionnaire. The survey is an official one organised by the regional
> church. So as parishes have some leeway in participating they are
> volunteer respondents.

if you get (almost) all 68 you should have no problem generalizing to
all 68.
>>
>> Are you interested in finding groups of variables or groups of parishes?
> I am interested in both : understanding the pattern of responses and
> using the pattern for categorizing the parishes.
> I think it necessary not to use the raw data for clustering the
> parishes since some dimensions (religious orientation) is treated by
> one item set whereas activities are described with several item sets.
> If I would use the raw data the result would be too much influenced by
> the pattern with the larhest number of items.
You might try clustering all items on one run and clustering items and
scale scores in another. Then create new composite scores and cluster them.

Art Kendall
Social Research Consultants

>
> Thanks
> Frank Thomas
>
>>
>> Art Kendall
>> Social Research Consultants
>>
>> Frank Thomas wrote:
>>> For an analysis of 44 local parishes I have numerous nominal variables
>>> (0/1 coded) that characterise the behaviour of a parish as an
>>> institution. Correspondence analysis would be an appropriate method to
>>> find a pattern but this method is not part of the base & regression
>>> modules that I have access to. Any other idea ?
>>>
>>> Thanks
>>> F. Thomas
>>>
>>> --
>>> ..........................................
>>> Dr. Frank Thomas
>>> FTR Internet Research
>>> 93110 Rosny-sous-Bois
>>> France
>>>
>>> =====================
>>> 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