Factor Analysis and dichotomous data

[Katina Dimoulias]

Hi,

I understand that questions related to factor analysis and dichotomous data
have been raised on this list in the past.  I have read through all of the
responses to those questions and if I understand these correctly, factor
analysis can be used with dichotomous data.  However, I would like to
clarify this issue as I have been receiving conflicting advice from my
supervisor and statistical consultants.  I have also found that a number of
references on factor analysis state that it is not an appropriate procedure
for dichotomous data.

Could this issue please be clarified?  Can I use factor analysis to find
the underlying factors on the below instrument or should I be using CATPCA?
Or can I use either?

I have used an instrument in my research that is made up of 10 subscales, 4
items per subscale.  The items are measured on a true/false scale coded 0
and 1. However, the results of reliability tests on each subscale were
cronbach alphas ranging from .2 to .6.  One reason maybe that it was
applied to a new type of environment, so I would like to identify the
underlying factors.

I appreciated your advice.

Katina

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[Dale Glaser]

Hi Katrina.....assuming you don't have a theoretical structure to your instrument, binary factor analysis is fine though not with the default 'data reduction' option in SPSS....I do know some have worked around this in SPSS by importing the matrix of tetrachoric correlations, however I can't speak to if that results in a similar fit as opposed to using software specifically geared to binary factor analysis, such as the Mplus software which uses the robust weighted least squares estimator......also, I don't know if the EFA option in the CATEGORIES module also results in similar fit to Mplus........another option is an IRT approach via Bilog.............


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: [phone]
fax: [phone]
email: [hidden email]
website: www.glaserconsult.com

--- On Fri, 10/31/08, Katina Dimoulias <[hidden email]> wrote:

From: Katina Dimoulias <[hidden email]>
Subject: Factor Analysis and dichotomous data
To: [hidden email]
Date: Friday, October 31, 2008, 3:40 PM

Hi,

I understand that questions related to factor analysis and dichotomous data
have been raised on this list in the past.  I have read through all of the
responses to those questions and if I understand these correctly, factor
analysis can be used with dichotomous data.  However, I would like to
clarify this issue as I have been receiving conflicting advice from my
supervisor and statistical consultants.  I have also found that a number of
references on factor analysis state that it is not an appropriate procedure
for dichotomous data.

Could this issue please be clarified?  Can I use factor analysis to find
the underlying factors on the below instrument or should I be using CATPCA?
Or can I use either?

I have used an instrument in my research that is made up of 10 subscales, 4
items per subscale.  The items are measured on a true/false scale coded 0
and 1. However, the results of reliability tests on each subscale were
cronbach alphas ranging from .2 to .6.  One reason maybe that it was
applied to a new type of environment, so I would like to identify the
underlying factors.

I appreciated your advice.

Katina

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

First of all, for dichotomous data CATPCA and classical FA give the same
results. This is because CATPCA works by assigning optimum numerical values
to each category of categorical variables, but for a dichotomy any pair of
numerical values is equivalent to any other pair, because the variable has
only two possible values and thus only one interval will be ever observed.
Second, you can compute linear correlation coefficients between dichotomous
variables, which can rigorously be treated as (discrete) interval-scale
variables. The phi association coefficient is equivalent to the linear
correlation coefficient when both variables are dichotomous. A matrix of
linear correlation coefficients is enough to compute a factor analysis
solution.
Third, linear REGRESSION is not entirely appropriate for dichotomous data,
since predicted values can be fractional, and fall either within or without
the interval 0,1, while observed values can only be 0 or 1. Moreover,
residuals (actual values minus predicted values) would not usually have a
normal distribution around predicted values: if the predicted value is a
fraction between 0 and 1, such as 0.40, all observed values will be at the
extremes or "tails" of the residual distribution, at values 0 and 1, and no
observed value will be in the vicinity of the predicted value, i.e. the
residual distribution will be almost the exact opposite of a normal
distribution; since a normal distribution of residuals is an assumption of
linear regression, you may not sustain certain consequences or inferences of
linear regression if you use dichotomous predictors. By the way, this
affects the very common habit of using dummies, e.g. in econometrics. But
few people give this problem a second thought. Dummies are used everywhere
in regression, objectionable as this might be to purists. If you ever used a
split infinitive, you are daring enough to use dummies in regression.

Hector


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Katina Dimoulias
Sent: 31 October 2008 20:41
To: [hidden email]
Subject: Factor Analysis and dichotomous data

Hi,

I understand that questions related to factor analysis and dichotomous data
have been raised on this list in the past.  I have read through all of the
responses to those questions and if I understand these correctly, factor
analysis can be used with dichotomous data.  However, I would like to
clarify this issue as I have been receiving conflicting advice from my
supervisor and statistical consultants.  I have also found that a number of
references on factor analysis state that it is not an appropriate procedure
for dichotomous data.

Could this issue please be clarified?  Can I use factor analysis to find
the underlying factors on the below instrument or should I be using CATPCA?
Or can I use either?

I have used an instrument in my research that is made up of 10 subscales, 4
items per subscale.  The items are measured on a true/false scale coded 0
and 1. However, the results of reliability tests on each subscale were
cronbach alphas ranging from .2 to .6.  One reason maybe that it was
applied to a new type of environment, so I would like to identify the
underlying factors.

I appreciated your advice.

Katina

=====================
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[E. Bernardo]

Hi all,

  Can you cite articles that used tetrachoric correlation as input data to do binary factor analysis.

  When we do CFA (continuous, not binary), means and standard deviations are added to the matrix?  Are means and standard deviations are the ones added to the tetrachoric correlation matrix when we do binary CFA?

  Binary Exploratory Factor Analysis as well as Binary CFA are always asked in this list, but the answers are not yet clear.  I hope experts on this field would provide direct advice.

  Thanks.
  Eins


Dale Glaser <[hidden email]> wrote:
  Hi Katrina.....assuming you don't have a theoretical structure to your instrument, binary factor analysis is fine though not with the default 'data reduction' option in SPSS....I do know some have worked around this in SPSS by importing the matrix of tetrachoric correlations, however I can't speak to if that results in a similar fit as opposed to using software specifically geared to binary factor analysis, such as the Mplus software which uses the robust weighted least squares estimator......also, I don't know if the EFA option in the CATEGORIES module also results in similar fit to Mplus........another option is an IRT approach via Bilog.............


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: [phone]
fax: [phone]
email: [hidden email]
website: www.glaserconsult.com

--- On Fri, 10/31/08, Katina Dimoulias wrote:

From: Katina Dimoulias
Subject: Factor Analysis and dichotomous data
To: [hidden email]
Date: Friday, October 31, 2008, 3:40 PM

Hi,

I understand that questions related to factor analysis and dichotomous data
have been raised on this list in the past. I have read through all of the
responses to those questions and if I understand these correctly, factor
analysis can be used with dichotomous data. However, I would like to
clarify this issue as I have been receiving conflicting advice from my
supervisor and statistical consultants. I have also found that a number of
references on factor analysis state that it is not an appropriate procedure
for dichotomous data.

Could this issue please be clarified? Can I use factor analysis to find
the underlying factors on the below instrument or should I be using CATPCA?
Or can I use either?

I have used an instrument in my research that is made up of 10 subscales, 4
items per subscale. The items are measured on a true/false scale coded 0
and 1. However, the results of reliability tests on each subscale were
cronbach alphas ranging from .2 to .6. One reason maybe that it was
applied to a new type of environment, so I would like to identify the
underlying factors.

I appreciated your advice.

Katina

=====================
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[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
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INFO REFCARD

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

I would advise using the phi coefficient, not the tetrachoric. The phi
coefficient is exactly the same as the Pearson linear correlation
coefficient when both variables are dichotomous.
In SPSS, the phi coefficient is produced by CROSSTABS, but you can produce
it also with CORRELATION if you want to generate a correlation matrix. If
you simply want to apply factor analysis with raw data, just use FACTOR.

Hector

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Eins Bernardo
Sent: 01 November 2008 01:13
To: [hidden email]
Subject: Re: Factor Analysis and dichotomous data

Hi all,

  Can you cite articles that used tetrachoric correlation as input data to
do binary factor analysis.

  When we do CFA (continuous, not binary), means and standard deviations are
added to the matrix?  Are means and standard deviations are the ones added
to the tetrachoric correlation matrix when we do binary CFA?

  Binary Exploratory Factor Analysis as well as Binary CFA are always asked
in this list, but the answers are not yet clear.  I hope experts on this
field would provide direct advice.

  Thanks.
  Eins


Dale Glaser <[hidden email]> wrote:
  Hi Katrina.....assuming you don't have a theoretical structure to your
instrument, binary factor analysis is fine though not with the default 'data
reduction' option in SPSS....I do know some have worked around this in SPSS
by importing the matrix of tetrachoric correlations, however I can't speak
to if that results in a similar fit as opposed to using software
specifically geared to binary factor analysis, such as the Mplus software
which uses the robust weighted least squares estimator......also, I don't
know if the EFA option in the CATEGORIES module also results in similar fit
to Mplus........another option is an IRT approach via Bilog.............


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: [phone]
fax: [phone]
email: [hidden email]
website: www.glaserconsult.com

--- On Fri, 10/31/08, Katina Dimoulias wrote:

From: Katina Dimoulias
Subject: Factor Analysis and dichotomous data
To: [hidden email]
Date: Friday, October 31, 2008, 3:40 PM

Hi,

I understand that questions related to factor analysis and dichotomous data
have been raised on this list in the past. I have read through all of the
responses to those questions and if I understand these correctly, factor
analysis can be used with dichotomous data. However, I would like to
clarify this issue as I have been receiving conflicting advice from my
supervisor and statistical consultants. I have also found that a number of
references on factor analysis state that it is not an appropriate procedure
for dichotomous data.

Could this issue please be clarified? Can I use factor analysis to find
the underlying factors on the below instrument or should I be using CATPCA?
Or can I use either?

I have used an instrument in my research that is made up of 10 subscales, 4
items per subscale. The items are measured on a true/false scale coded 0
and 1. However, the results of reliability tests on each subscale were
cronbach alphas ranging from .2 to .6. One reason maybe that it was
applied to a new type of environment, so I would like to identify the
underlying factors.

I appreciated your advice.

Katina

=====================
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command. To leave the list, send the command
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For a list of commands to manage subscriptions, send the command
INFO REFCARD

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---------------------------------
 Yahoo! Toolbar is now powered with Search Assist.   Download it now!

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