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factor analysis for binary variables

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E. Bernardo

factor analysis for binary variables

Hi everyone,

The 70 variables that will be subjected to factor analysis are binary(coded 0 and 1). May I know your thoughts regarding the methods to use in extracting the factors, as well as the rotation methods.

Thank you in advance for your help.

Eins

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Art Kendall

Re: factor analysis for binary variables

What do you want to accomplish by using factor analysis?

Are the variables designed ahead of time to belong to summative scales?
How many scales?
Is this the first time this set of items has been used?

Are you only interested in the common variance (e.g., with items
designed to measure a construct?) Or is there a reason you want to
include unique item variance in the variance accounted for?

It is traditional to go ahead with principal axis factoring on
dichotomous items when you are making scales. However, now that CATPCA
is available, I suggest that you use that. As an exercise, you might
want to run your analysis with CATPCA and with FACTOR and see how the
results compare on which items load cleanly together.

You would need to check the documentation to choose specifications for
CATPCA.

If you are trying to build scales, I suggest 1) using PAF since you
would only be interested in the common variance 2)using varimax rotation
so that the final scales have divergent validity, 3) use at least the
scree and preferably parallel analysis (see the archives of this list
for that) to ballpark the number of factors to retain, and 4) keep only
items that load with an absolute loading of . 4 or so, and not more than
.25 or so on another factor.

Art Kendall
Social Research Consultants

Eins Bernardo wrote:

> Hi everyone,
>
> The 70 variables that will be subjected to factor analysis are binary(coded 0 and 1). May I know your thoughts regarding the methods to use in extracting the factors, as well as the rotation methods.
>
> Thank you in advance for your help.
>
> Eins
>
>
> ---------------------------------
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Art Kendall
Social Research Consultants

Kooij, A.J. van der

Re: factor analysis for binary variables

>It is traditional to go ahead with principal axis factoring on
>dichotomous items when you are making scales. However, now that CATPCA
>is available, I suggest that you use that. As an exercise, you might
>want to run your analysis with CATPCA and with FACTOR and see how the
>results compare on which items load cleanly together.

If all variables are binary, the result of CATPCA is equal to standard PCA. For a binary variable the transformation is always linear. So, no matter which optimal scaling level you choose, the result is equal to result of numeric scaling level. (think of the transformation plot: there are 2 categories, you can only fit a straight line between 2 points)

Anita van der Kooij

Data Theory Group

Leiden University

________________________________

From: SPSSX(r) Discussion on behalf of Art Kendall
Sent: Sun 12/10/2008 16:56
To: [hidden email]
Subject: Re: factor analysis for binary variables

What do you want to accomplish by using factor analysis?

Are the variables designed ahead of time to belong to summative scales?
How many scales?
Is this the first time this set of items has been used?

Are you only interested in the common variance (e.g., with items
designed to measure a construct?) Or is there a reason you want to
include unique item variance in the variance accounted for?

It is traditional to go ahead with principal axis factoring on
dichotomous items when you are making scales. However, now that CATPCA
is available, I suggest that you use that. As an exercise, you might
want to run your analysis with CATPCA and with FACTOR and see how the
results compare on which items load cleanly together.

You would need to check the documentation to choose specifications for
CATPCA.

If you are trying to build scales, I suggest 1) using PAF since you
would only be interested in the common variance 2)using varimax rotation
so that the final scales have divergent validity, 3) use at least the
scree and preferably parallel analysis (see the archives of this list
for that) to ballpark the number of factors to retain, and 4) keep only
items that load with an absolute loading of . 4 or so, and not more than
.25 or so on another factor.

Art Kendall
Social Research Consultants

Eins Bernardo wrote:

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Art Kendall

Re: factor analysis for binary variables

Is there a way in CATPCA to separate the unique and common variance
analogous to using reliability estimates on the diagonal in principal
axes factoring?

Art

Kooij, A.J. van der wrote:

>> It is traditional to go ahead with principal axis factoring on
>> dichotomous items when you are making scales. However, now that CATPCA
>> is available, I suggest that you use that. As an exercise, you might
>> want to run your analysis with CATPCA and with FACTOR and see how the
>> results compare on which items load cleanly together.
>>
>
> If all variables are binary, the result of CATPCA is equal to standard PCA. For a binary variable the transformation is always linear. So, no matter which optimal scaling level you choose, the result is equal to result of numeric scaling level. (think of the transformation plot: there are 2 categories, you can only fit a straight line between 2 points)
>
> Anita van der Kooij
>
> Data Theory Group
>
> Leiden University
>
> ________________________________
>
> From: SPSSX(r) Discussion on behalf of Art Kendall
> Sent: Sun 12/10/2008 16:56
> To: [hidden email]
> Subject: Re: factor analysis for binary variables
>
>
>
> What do you want to accomplish by using factor analysis?
>
> Are the variables designed ahead of time to belong to summative scales?
> How many scales?
> Is this the first time this set of items has been used?
>
> Are you only interested in the common variance (e.g., with items
> designed to measure a construct?) Or is there a reason you want to
> include unique item variance in the variance accounted for?
>
> It is traditional to go ahead with principal axis factoring on
> dichotomous items when you are making scales. However, now that CATPCA
> is available, I suggest that you use that. As an exercise, you might
> want to run your analysis with CATPCA and with FACTOR and see how the
> results compare on which items load cleanly together.
>
> You would need to check the documentation to choose specifications for
> CATPCA.
>
> If you are trying to build scales, I suggest 1) using PAF since you
> would only be interested in the common variance 2)using varimax rotation
> so that the final scales have divergent validity, 3) use at least the
> scree and preferably parallel analysis (see the archives of this list
> for that) to ballpark the number of factors to retain, and 4) keep only
> items that load with an absolute loading of . 4 or so, and not more than
> .25 or so on another factor.
>
> Art Kendall
> Social Research Consultants
>
> Eins Bernardo wrote:
>
>> Hi everyone,
>>
>> The 70 variables that will be subjected to factor analysis are binary(coded 0 and 1). May I know your thoughts regarding the methods to use in extracting the factors, as well as the rotation methods.
>>
>> Thank you in advance for your help.
>>
>> Eins
>>
>>
>> ---------------------------------
>> New Email names for you!
>> Get the Email name you've always wanted on the new @ymail and @rocketmail.
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>> command. To leave the list, send the command
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>>
>>
>>
>
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>
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>
>
>
> ===================
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Art Kendall
Social Research Consultants

E. Bernardo

Re: factor analysis for binary variables

I received an off-list message advising that I have to obtain the tetrachoric correlation matrix of the 70 variables, then I will use that matrix to do EFA. What are your comments?

Eins

Art Kendall <[hidden email]> wrote:
Is there a way in CATPCA to separate the unique and common variance
analogous to using reliability estimates on the diagonal in principal
axes factoring?

Art

Kooij, A.J. van der wrote:

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Marta Garcia-Granero

Re: factor analysis for binary variables

Eins Bernardo wrote:
> I received an off-list message advising that I have to obtain the tetrachoric correlation matrix of the 70 variables, then I will use that matrix to do EFA. What are your comments?
>

It could be a good idea, assuming your binary variables are adequate for
tetrachoric correlation coefficient.

Check this page (near the end):

http://www2.jura.uni-hamburg.de/instkrim/kriminologie/Mitarbeiter/Enzmann/Software/Enzmann_Software.html

There's a program to compute a tetrachoric correlation matrix that can
be imported into an SPSS dataset and used with FACTOR.

HTH,
Marta García-Granero

>>
>>
>>> Hi everyone,
>>>
>>> The 70 variables that will be subjected to factor analysis are binary(coded 0 and 1). May I know your thoughts regarding the methods to use in extracting the factors, as well as the rotation methods.
>>>
>>>
--

For miscellaneous statistical stuff, visit:
http://gjyp.nl/marta/

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David Hitchin

Re: factor analysis for binary variables

In reply to this post by E. Bernardo

Factor analysis is employed for several different purposes. Some of them
are "statistical" in the sense of taking into account distributions and
sampling theory, while others are merely concerned with getting some
insight into data.

I remember many years ago when a student as a project investigated
superstitions held (or not) by other students. I think that there were
about 80 questions, each of them scored zero or one.

Before trying any analysis I thought that so few students would be
superstitious that most of the responses would be zero (leaving little
variance to analyse) or that some would just reply in a haphazard way.

I submitted the whole data set to SPSS for a principal factor analysis
followed by varimax rotation, and the results were extremely clear and
easy to interpret. There was one large general factor (whether people
were superstitious on the whole, or not). The remaining factors all made
sense. There were variables which loaded high on "religious" questions,
those that loaded high on "actions", e.g. crossing ones fingers for
luck, those loading high on "pseudoscientific", e.g. trailing a chain
from your car to earth static prevents travel sickness, and so on.

The moral of this story is that often one need not be too statistically
purist; crude methods can often find most of what is useful in data.
After many years of performing factor analyses by many different methods
I have come to the conclusion that results seem to fall into one of two
groups; those analyses which make no sense at all, however much you
tweak them, and those where the results are clear whatever method is
used, although a little tweaking helps to focus a little better.

David Hitchin

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E. Bernardo

Doing EFA using correlation matrix as input

In reply to this post by Art Kendall

How to do EFA using the correlation matrix as input? I think this is beyond the point-click in SPSS! Please help.

Eins

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Marta Garcia-Granero

Re: Doing EFA using correlation matrix as input

Eins Bernardo wrote:
> How to do EFA using the correlation matrix as input? I think this is beyond the point-click in SPSS! Please help.
>

FACTOR
/MATRIX = IN(cor=*)
/ANALYSIS ......

Marta

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