SPSSX Discussion

categorical factor analysis?

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Ramzi Mabsout

categorical factor analysis?

Dear all:

I have numerical, ordinal and nominal data. I would like to run factor
analysis--not PCA--on contextually chosen groups of indicators.
However, as far as my understanfing informs me, CATPCA is a principle
component technique that maximises common variance. Whereas I am
interested in exploring the dimensions within the groups. Is there in
SPSS or other software a CategoricalAnalysisFactorAnalsysis method? Or
is CATPCA a good substitute for a categorical factor analysis?

Kind regards and thank you.

Ramzi Mabsout

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Zetu, Dan

Re: categorical factor analysis?

I think that what you intend to do is closely related to Multiple
Correspondence Analysis (MCA), which is supported by the SPSS Categories
module.

-------------------------------
Dan Zetu
Analytical Consultant
R. L. Polk & Co.
248-728-7278
[hidden email]

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Ramzi Mabsout
Sent: Tuesday, February 19, 2008 7:04 AM
To: [hidden email]
Subject: categorical factor analysis?

Dear all:

I have numerical, ordinal and nominal data. I would like to run factor
analysis--not PCA--on contextually chosen groups of indicators.
However, as far as my understanfing informs me, CATPCA is a principle
component technique that maximises common variance. Whereas I am
interested in exploring the dimensions within the groups. Is there in
SPSS or other software a CategoricalAnalysisFactorAnalsysis method? Or
is CATPCA a good substitute for a categorical factor analysis?

Kind regards and thank you.

Ramzi Mabsout

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Hector Maletta

Re: categorical factor analysis?

CATPCA is, strictly speaking, categorical factor analysis. It elicits the
underlying factor structure of a set of variables which could be
categorical, ordinal or interval, or any combination thereof. It uses the
Principal Component specification of factor analysis. In the case of ordinal
and categorical variables, it further estimates a numerical value for each
category of the variables.
In my humble opinion it is vastly superior, both computationally and
theoretically, to Multiple Correspondence Analysis.
I do not understand what Ramzi means when he says that CATPCA " maximises
common variance. Whereas I am interested in exploring the dimensions within
the groups". What CATPCA does is extracting factors, with the assumption
that all variance in the variables can be represented by underlying factors
(the usual assumption of Principal Component Analysis). This elicits (for K
variables) as many as K factors. The analyst can then analyze which factors
are more important, which factors are more closely associated with each
variable, and (if factor scores are saved) how factor scores vary across
groups of subjects (e.g. between males and females, or between different
socioeconomic groups).
Hector

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Zetu, Dan
Sent: 19 February 2008 14:45
To: [hidden email]
Subject: Re: categorical factor analysis?

I think that what you intend to do is closely related to Multiple
Correspondence Analysis (MCA), which is supported by the SPSS Categories
module.

-------------------------------
Dan Zetu
Analytical Consultant
R. L. Polk & Co.
248-728-7278
[hidden email]

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Ramzi Mabsout
Sent: Tuesday, February 19, 2008 7:04 AM
To: [hidden email]
Subject: categorical factor analysis?

Dear all:

I have numerical, ordinal and nominal data. I would like to run factor
analysis--not PCA--on contextually chosen groups of indicators.
However, as far as my understanfing informs me, CATPCA is a principle
component technique that maximises common variance. Whereas I am
interested in exploring the dimensions within the groups. Is there in
SPSS or other software a CategoricalAnalysisFactorAnalsysis method? Or
is CATPCA a good substitute for a categorical factor analysis?

Kind regards and thank you.

Ramzi Mabsout

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Hector Maletta

Re: categorical factor analysis?

Ramzi,
Exploratory factor analysis (EFA) is not opposed to Principal Component
Analysis (PCA).
EFA is opposed to Confirmatory Factor Analysis (CFA), which is a different
stage in the analysis of the underlying factors of a set of variables.
EFA and CFA can be performed through a number of mathematical procedures,
depending on assumptions about the underlying structure. One of those
procedures is Principal Component Analysis, where the essential assumption
is that underlying factors cover the entire variance of the observed
variables (i.e. commonality = 1). Other procedures assume that only part of
the variable's variance is to be explained by underlying factors, while the
remainder is specific or unique variance that remains outside the scope of
factor analysis (commonality < 1).
In your case you would perform an EFA by means of CPA, and (since your data
set includes categorical variables) the algorithm for CPA should be CATCPA.

Hector

-----Original Message-----
From: Ramzi Mabsout [mailto:[hidden email]]
Sent: 19 February 2008 15:35
To: Hector Maletta
Subject: Re: categorical factor analysis?

Dear Hector Maletta:

Many thanks for your answer. It is helpful in clarifying many things.

However, the following quote got me into a slight state of confusion
hence my query:

"When researchers have collected a data set, and wish to explore the
correlational
structure among the variables (i.e., without starting from a specific
theory), principal components analysis (PCA) or exploratory factor analysis
(EFA) may be the method of choice. When the goal of a study is to model
the structure in the observed data set, incorporating the relationships
between
the variables (common variance) as well as the unique contribution of
separate
variables (unique variance), EFA is the most appropriate method. When
the goal is data reduction, that is, reducing a large number of
observed variables
to a smaller number of composite variables, without considering each
variable's unique contribution, PCA is more suitable (see Fabrigar, Wegener,
MacCallum, & Strahan, 1999). This thesis will be focused on PCA, the most
popular of the two approaches (Fabrigar et al., 1999)."

This is taken from Mariëlle Linting's thesis entitled "Nonparametric
inference in nonlinear principal components analysis : exploration and
beyond"

And since I am not interested in data reduction as such, and at a
later stage I plan to move to CFA, I thought PCA would not be
suitable.

Thank you again,

best wishes

Ramz

On 2/19/08, Hector Maletta <[hidden email]> wrote:
> CATPCA is, strictly speaking, categorical factor analysis. It elicits the
> underlying factor structure of a set of variables which could be
> categorical, ordinal or interval, or any combination thereof. It uses the
> Principal Component specification of factor analysis. In the case of
ordinal
> and categorical variables, it further estimates a numerical value for each
> category of the variables.
> In my humble opinion it is vastly superior, both computationally and
> theoretically, to Multiple Correspondence Analysis.
> I do not understand what Ramzi means when he says that CATPCA " maximises
> common variance. Whereas I am interested in exploring the dimensions
within
> the groups". What CATPCA does is extracting factors, with the assumption
> that all variance in the variables can be represented by underlying
factors
> (the usual assumption of Principal Component Analysis). This elicits (for
K
> variables) as many as K factors. The analyst can then analyze which
factors

> are more important, which factors are more closely associated with each
> variable, and (if factor scores are saved) how factor scores vary across
> groups of subjects (e.g. between males and females, or between different
> socioeconomic groups).
> Hector
>
>
>
> -----Original Message-----
> From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
> Zetu, Dan
> Sent: 19 February 2008 14:45
> To: [hidden email]
> Subject: Re: categorical factor analysis?
>
> I think that what you intend to do is closely related to Multiple
> Correspondence Analysis (MCA), which is supported by the SPSS Categories
> module.
>
> -------------------------------
> Dan Zetu
> Analytical Consultant
> R. L. Polk & Co.
> 248-728-7278
> [hidden email]
>
> -----Original Message-----
> From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
> Ramzi Mabsout
> Sent: Tuesday, February 19, 2008 7:04 AM
> To: [hidden email]
> Subject: categorical factor analysis?
>
> Dear all:
>
> I have numerical, ordinal and nominal data. I would like to run factor
> analysis--not PCA--on contextually chosen groups of indicators.
> However, as far as my understanfing informs me, CATPCA is a principle
> component technique that maximises common variance. Whereas I am
> interested in exploring the dimensions within the groups. Is there in
> SPSS or other software a CategoricalAnalysisFactorAnalsysis method? Or
> is CATPCA a good substitute for a categorical factor analysis?
>
> Kind regards and thank you.
>
> Ramzi Mabsout
>
> =====================
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> *****************************************************************
> This message has originated from R. L. Polk & Co.,
> 26955 Northwestern Highway, Southfield, MI 48033.
> R. L. Polk & Co. sends various types of email
> communications. If this email message concerns the
> potential licensing of a Polk product or service, and
> you do not wish to receive further emails regarding Polk
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>
> The email and any files transmitted with it are confidential
> and intended solely for the individual or entity to whom they
> are addressed.
>
> If you have received this email in error, please delete this
> message and notify the Polk System Administrator at
> [hidden email].
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>
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stace swayne

Correlation & Sample Size

Dear list,

I am interested in finding out what impact sample size has on correlation size ...if any? Can someone suggest a resource for me to read or share what you know about this relationship.

Thanks,

Stace

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David Greenberg

Re: Correlation & Sample Size

The two have nothing to do with one another. David Greenberg, Sociology Department, New York University

----- Original Message -----
From: stace swayne <[hidden email]>
Date: Thursday, February 21, 2008 11:16 am
Subject: Correlation & Sample Size
To: [hidden email]

> Dear list,
>
> I am interested in finding out what impact sample size has on
> correlation size ...if any? Can someone suggest a resource for me to
> read or share what you know about this relationship.
>
> Thanks,
>
> Stace
>
>
> ---------------------------------
> Be a better friend, newshound, and know-it-all with Yahoo! Mobile.
> Try it now.
>
> =====================
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A Seifert

Re: Correlation & Sample Size

In reply to this post by stace swayne

Hi Stace,

The correlation's size won't be impacted by the sample size, but the sample size will factor in to whether a correlation of a given size reaches statistical significance.

April

----- Original Message ----
From: stace swayne <[hidden email]>
To: [hidden email]
Sent: Thursday, February 21, 2008 10:15:22 AM
Subject: Correlation & Sample Size

Dear list,

I am interested in finding out what impact sample size has on correlation size ...if any? Can someone suggest a resource for me to read or share what you know about this relationship.

Thanks,

Stace

---------------------------------
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SR Millis-3

Re: Correlation & Sample Size

In reply to this post by David Greenberg

Are you certain? With 2 data points, r=1.00.

SR Millis

--- David Greenberg <[hidden email]> wrote:

> The two have nothing to do with one another. David
> Greenberg, Sociology Department, New York University
>
> ----- Original Message -----
> From: stace swayne <[hidden email]>
> Date: Thursday, February 21, 2008 11:16 am
> Subject: Correlation & Sample Size
> To: [hidden email]
>
>
> > Dear list,
> >
> > I am interested in finding out what impact
> sample size has on
> > correlation size ...if any? Can someone suggest a
> resource for me to
> > read or share what you know about this
> relationship.
> >
> > Thanks,
> >
> > Stace
> >
> >
> > ---------------------------------
> > Be a better friend, newshound, and know-it-all
> with Yahoo! Mobile.
> > Try it now.
> >
> > =====================
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> no body text except the
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>
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David Greenberg

Re: Correlation & Sample Size

For that special case, you are right. It is so unusual for someone to work with a data set with just two observations that I was not thinking of that special circumstance. David Greenberg

----- Original Message -----
From: SR Millis <[hidden email]>
Date: Thursday, February 21, 2008 6:25 pm
Subject: Re: Correlation & Sample Size
To: [hidden email]

> Are you certain? With 2 data points, r=1.00.
>
> SR Millis
>
>
> --- David Greenberg <[hidden email]> wrote:
>
> > The two have nothing to do with one another. David
> > Greenberg, Sociology Department, New York University
> >
> > ----- Original Message -----
> > From: stace swayne <[hidden email]>
> > Date: Thursday, February 21, 2008 11:16 am
> > Subject: Correlation & Sample Size
> > To: [hidden email]
> >
> >
> > > Dear list,
> > >
> > > I am interested in finding out what impact
> > sample size has on
> > > correlation size ...if any? Can someone suggest a
> > resource for me to
> > > read or share what you know about this
> > relationship.
> > >
> > > Thanks,
> > >
> > > Stace
> > >
> > >
> > > ---------------------------------
> > > Be a better friend, newshound, and know-it-all
> > with Yahoo! Mobile.
> > > Try it now.
> > >
> > > =====================
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aandreou

Re: Correlation & Sample Size

In reply to this post by stace swayne

April, is there a formula that calculates the min. sample size for a given significance level of correlation?

Andreas

-----Original Message-----
From: A Seifert
Sent: Thu, 21 Feb 2008 15:13:03 -0800
To: [hidden email]
Subject: Re: Correlation & Sample Size

Hi Stace,

The correlation's size won't be impacted by the sample size, but the sample size will factor in to whether a correlation of a given size reaches statistical significance.

April

----- Original Message ----
From: stace swayne
To: [hidden email]
Sent: Thursday, February 21, 2008 10:15:22 AM
Subject: Correlation & Sample Size

Dear list,

I am interested in finding out what impact sample size has on correlation size ...if any? Can someone suggest a resource for me to read or share what you know about this relationship.

Thanks,

Stace

---------------------------------
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Swank, Paul R

Re: Correlation & Sample Size

In reply to this post by David Greenberg

Isn't this the nature of overfit in regression? If the number of
variables approaches the number of subjects, the R squared gets larger.
So it would seem that with a single variable, the possibility of overfit
would get larger as the sample size got smaller.

Paul R. Swank, Ph.D.
Professor and Director of Research
Children's Learning Institute
University of Texas Health Science Center - Houston

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
David Greenberg
Sent: Thursday, February 21, 2008 6:25 PM
To: [hidden email]
Subject: Re: Correlation & Sample Size

For that special case, you are right. It is so unusual for someone to
work with a data set with just two observations that I was not thinking
of that special circumstance. David Greenberg

----- Original Message -----
From: SR Millis <[hidden email]>
Date: Thursday, February 21, 2008 6:25 pm
Subject: Re: Correlation & Sample Size
To: [hidden email]

the
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Granaas, Michael

Re: Correlation & Sample Size

In reply to this post by aandreou

The variability of the correlation will be impacted by sample size. The smaller the sample the more variable the sample correlation from sample to sample.

If rho = .5 in a very small sample you might get .15 < r < .85 while in a large sample you might get .45 < r < .55.

These intervals should be asymmetric, but the basic notion is correct. You are much more likely to get a misleading r in a small sample than in a large sample.

Michael
****************************************************
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Assoc. Prof. Phone: 605 677 5295
Dept. of Psychology FAX: 605 677 3195
University of South Dakota
414 E. Clark St.
Vermillion, SD 57069
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Richard Ristow

Re: Correlation & Sample Size

In reply to this post by aandreou

At 09:43 AM 2/22/2008, [hidden email] wrote:

>April, is there a formula that calculates the min. sample size for a
>given significance level of correlation?

There isn't, and never will be. It depends on the value of the
correlation in the underlying population.

There probably are formulae that give sample size for, say, 95%
probability of significance at the .05 level, for a specified
correlation in the population.

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A Seifert-2

Re: Correlation & Sample Size

In reply to this post by stace swayne

Hi Andreas,

If you look at a power table (http://www-class.unl.edu/psycrs/statpage/powertable.pdf), you can find an approximate sample size that will allow you to reach statistical significance for a given r.

For example, if you expect to get an r-value of about .30 and you want to make sure that your test is at 80% power (a good rule-of-thumb), you'd need N=82, according to the table.

April

----- Original Message ----
From: "[hidden email]" <[hidden email]>
To: [hidden email]
Sent: Friday, February 22, 2008 8:43:01 AM
Subject: Re: Correlation & Sample Size

April, is there a formula that calculates the min. sample size for a given significance level of correlation?

Andreas

-----Original Message-----
From: A Seifert
Sent: Thu, 21 Feb 2008 15:13:03 -0800
To: [hidden email]
Subject: Re: Correlation & Sample Size

Hi Stace,

The correlation's size won't be impacted by the sample size, but the sample size will factor in to whether a correlation of a given size reaches statistical significance.

April

----- Original Message ----
From: stace swayne
To: [hidden email]
Sent: Thursday, February 21, 2008 10:15:22 AM
Subject: Correlation & Sample Size

Dear list,

I am interested in finding out what impact sample size has on correlation size ...if any? Can someone suggest a resource for me to read or share what you know about this relationship.

Thanks,

Stace

---------------------------------
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