factoring dichotomous response

[Johnny Amora]

I have 70 dichotomous variables (coded 0 and 1) with n>550 cases.  I want to reduce the variables into few factors (if possible).  Can I use the classical approach (e.g., principal axis factoring) in extracting the factors considering the type of variables I have? Your thoughts are very important.


Johnny T. Amora
Center for Learning and Performance Assessment
De La Salle-College of Saint Benilde
Manila, Philippines

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[Hector Maletta]

You may, although it is not totally kosher. You should try CATPCA,
categorical principal component analysis, available in the Categories module
of SPSS. It accepts variables of any measurement level (interval, ordinal or
nominal). In the case of ordinal or nominal variables, it estimates also
optimal numerical values for each category.
The main objection to the use of ordinary factor analysis with dichotomous
variables is not the fact that they are not continuous: a binary variable
can be construed as an interval measurement (with only one interval present,
you do not have problems with measuring different intervals); the problem is
that factor analysis is subsidiary to linear regression, and linear
regression requires a normal distribution of residues around the regression
line; it is easy to see that a regression like Y=a+bX where Y and X are
binary cannot have a normal distribution of residues around the predicted
value of Y. However, many people use ordinary factor analysis for binary
variables in spite of this shortcoming.
Hector
-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Johnny Amora
Sent: 24 April 2008 01:57
To: [hidden email]
Subject: factoring dichotomous response

I have 70 dichotomous variables (coded 0 and 1) with n>550 cases.  I want to
reduce the variables into few factors (if possible).  Can I use the
classical approach (e.g., principal axis factoring) in extracting the
factors considering the type of variables I have? Your thoughts are very
important.


Johnny T. Amora
Center for Learning and Performance Assessment
De La Salle-College of Saint Benilde
Manila, Philippines

---------------------------------
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now.

=====================
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[Hector Maletta]

In addition to my previous message, notice also that 550 cases are very few
for a factor analysis involving 70 variables. A prudent minimum is 30 cases
per variable, and the traditionally considered extreme minimum is 10 cases
per variable. You do not reach either. You better reduce the number of
variables, perhaps segmenting the analysis by grouping similar items
together and factoring these groups of variables separately.

Hector

-----Original Message-----
From: Hector Maletta [mailto:[hidden email]]
Sent: 24 April 2008 02:27
To: 'Johnny Amora'; '[hidden email]'
Subject: RE: factoring dichotomous response

You may, although it is not totally kosher. You should try CATPCA,
categorical principal component analysis, available in the Categories module
of SPSS. It accepts variables of any measurement level (interval, ordinal or
nominal). In the case of ordinal or nominal variables, it estimates also
optimal numerical values for each category.
The main objection to the use of ordinary factor analysis with dichotomous
variables is not the fact that they are not continuous: a binary variable
can be construed as an interval measurement (with only one interval present,
you do not have problems with measuring different intervals); the problem is
that factor analysis is subsidiary to linear regression, and linear
regression requires a normal distribution of residues around the regression
line; it is easy to see that a regression like Y=a+bX where Y and X are
binary cannot have a normal distribution of residues around the predicted
value of Y. However, many people use ordinary factor analysis for binary
variables in spite of this shortcoming.
Hector
-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Johnny Amora
Sent: 24 April 2008 01:57
To: [hidden email]
Subject: factoring dichotomous response

I have 70 dichotomous variables (coded 0 and 1) with n>550 cases.  I want to
reduce the variables into few factors (if possible).  Can I use the
classical approach (e.g., principal axis factoring) in extracting the
factors considering the type of variables I have? Your thoughts are very
important.


Johnny T. Amora
Center for Learning and Performance Assessment
De La Salle-College of Saint Benilde
Manila, Philippines

---------------------------------
Be a better friend, newshound, and know-it-all with Yahoo! Mobile.  Try it
now.

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