factor analysis with dichotomous (yes/no) and ordinal variables

[Phil Higgins, MSW, LICSW]

Hello,

I know there have already been a number of posts related to FA with
dichotomous variables, but in reviewing them I'm still left unclear about
the best approach for my situation.

I am working with a dataset from which I have extracted 18 items, some of
which are dichotomous (Yes/No responses) and some of which are ordinal (5-
or 7-point Likert).  All of these are related to caregiver opinions on end-
of-life care for their loved one.

My research focus is on a larger phenomenon which isn't addressed directly
in the dataset, but which I believe may be a latent construct represented
by these 18 items.

I would like to test my hypothesis and see whether or not these
items "hang together" in factor analysis, but I am not sure about the best
approach.  I have access to LISREL/PRELIS and SPSS (as well as STATA, but
I haven't used it before). I understand that the necessary steps involve
computing a correlation matrix, and then "plugging" that into a program
for analysis. My questions:

1. In attempting to compute a correlation matrix on LISREL, it gives me
the option for classical and ordinal. Do I select ordinal? If so, will
LISREL automatically know which are dichotomous and which are ordinal, and
choose the correct type of correlation?  I have read about tetrachoric and
polychoric correlation - - does LISREL/PRELIS calculate these on its own?

2. Do I need to transform my Yes/No items to dummy variables? At present,
they are designated as 1=yes, 2=no

3. Once I have the matrix, what is the best approach to analyzing it via
SPSS?  Or is there a better readily accessible program?

4. Is classic factor analysis the best approach? As opposed to PCA or
Latent Class Factor Analysis?

I apologize for the elementary level of my questions - I am a 3rd year
doctoral student and we didn't cover this in my coursework thus far. Does
anyone know of a good online resource that could guide me through this
whole process in step-by-step fashion...??

Thanks for any guidance. I'm sure I missed some key questions to consider,
please feel free to set me back onto the right path!

Phil Higgins, MSW, LICSW

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[Art Kendall]

 Single Likert items are conventionally treated as not very discrepant from interval level of measurement.  Their scores based on them even more so.

Dichotomies may be the only instance in which all intervals between values are perfectly equal to each other. There is only one interval and it is necessarily equal to itself.  For factoring it makes no difference what two values you use for a dichotomy.  However, it may improve readability of your syntax and output to use 0 for no and 1 for yes.

If you end up with factors that contain both kinds of items, you would have to standardize them before summing (averaging).

In SPSS it is not necessary to create the correlation matrix as a separate procedure.  The correlation matrix is computed as part of the FACTOR process.
For this kind of situation, you would only be interested in what is common among items that group together.  So in factor specify /extraction=PAF.
Also in order of aid divergent validity use /rotate=varimax.
I suggest that you use "parallel analysis" to ballpark the number of factors to retain.
Your solution is unlikely to have every item end up in the final scoring.  Some items may load nowhere and some items may not load cleanly on a single factor.

If you are more advanced in statistics you may want to run  CATPCA  and see if it makes any substantive difference in the final scoring keys to treat the Likert items as ordinal vs interval.


On 3/20/2012 8:55 AM, Phil Higgins, MSW, LICSW wrote:

Hello,

I know there have already been a number of posts related to FA with
dichotomous variables, but in reviewing them I'm still left unclear about
the best approach for my situation.

I am working with a dataset from which I have extracted 18 items, some of
which are dichotomous (Yes/No responses) and some of which are ordinal (5-
or 7-point Likert).  All of these are related to caregiver opinions on end-
of-life care for their loved one.

My research focus is on a larger phenomenon which isn't addressed directly
in the dataset, but which I believe may be a latent construct represented
by these 18 items.

I would like to test my hypothesis and see whether or not these
items "hang together" in factor analysis, but I am not sure about the best
approach.  I have access to LISREL/PRELIS and SPSS (as well as STATA, but
I haven't used it before). I understand that the necessary steps involve
computing a correlation matrix, and then "plugging" that into a program
for analysis. My questions:

1. In attempting to compute a correlation matrix on LISREL, it gives me
the option for classical and ordinal. Do I select ordinal? If so, will
LISREL automatically know which are dichotomous and which are ordinal, and
choose the correct type of correlation?  I have read about tetrachoric and
polychoric correlation - - does LISREL/PRELIS calculate these on its own?

2. Do I need to transform my Yes/No items to dummy variables? At present,
they are designated as 1=yes, 2=no

3. Once I have the matrix, what is the best approach to analyzing it via
SPSS?  Or is there a better readily accessible program?

4. Is classic factor analysis the best approach? As opposed to PCA or
Latent Class Factor Analysis?

I apologize for the elementary level of my questions - I am a 3rd year
doctoral student and we didn't cover this in my coursework thus far. Does
anyone know of a good online resource that could guide me through this
whole process in step-by-step fashion...??

Thanks for any guidance. I'm sure I missed some key questions to consider,
please feel free to set me back onto the right path!

Phil Higgins, MSW, LICSW

=====================
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[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
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===================== 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

[John F Hall]

Phil

What's your disciplinary background and what discipline is your PhD for?
How many variables do you have altogether of Yes/No, 5-point and 7-point
Likert scales?  How many cases do you have?

I don't know what analysis you've done so far, but you can sometimes get a
pretty good idea of the structure of your data long before you resort to
factor analysis.  You can often tell al lot just from frequency
distributions, but in your case a glance at correlation matrices can be a
good place to start: these will give you some idea of how the variables hang
together.

I'm not a statistician, but I have seen and analysed many surveys such as
yours: in my experience psychologists were often guilty of heading straight
for multivariate inferential statistics instead of looking at simple
distributions.

Art has given you some sensible advice, but if you want to know a bit more
about measures of association, there are some useful notes on my website
written by Jim Ring.  They were specially written for non-numerate students:
you should find something in there, but not about factor analysis. (See:
http://surveyresearch.weebly.com/uploads/2/9/9/8/2998485/statistical_notes_2
012_draft.pdf )

If you need any specific help, I can always do this off-list, but I'd need a
copy, in confidence, of your instrument and (at least an extract from) your
SPSS data editor.

There is an example of a scale derived from Likert items in a set of SPSS
tutorials on COUNT and  COMPUTE.  The 9 items used to measure "Sexism" were
actually chosen from a list of 13, using factor analysis, a manual
elementary linkage analysis, and checked using alpha.  The selection is not
covered in the tutorials, but I'm happy to discuss with you how the final
list was derived.  (See:
http://surveyresearch.weebly.com/352-teenage-attitudes-tutorials.html )  My
site also has links to a range of useful on-line tutorials, some of which
may be relevant.

I also have data from the Quality of Life in Britain surveys conducted by
the late Dr Mark Abrams and myself in the early 1970s, in which various
scales were derived for domains and sub-domains, and also from semantic
differential scales.  Factor analysis was used to identify items measuring
the same underlying dimension and to reduce the number of items used in
subsequent waves.  Simply summing responses for selected items was as robust
as deriving complex factors. (See:
http://surveyresearch.weebly.com/subjective-social-indicators-quality-of-lif
e.html for the stack of material available on my site, including facsimile
questionnaires and (not easily available if at all) working papers, reports
etc.)

John Hall (Mr)


Email:    [hidden email]
Website: www.surveyresearch.weebly.com
Skype:    surveyresearcher1
Phone:    (+33) (0) 2.33.45.91.47



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Phil Higgins, MSW, LICSW
Sent: 20 March 2012 13:56
To: [hidden email]
Subject: factor analysis with dichotomous (yes/no) and ordinal variables

Hello,

I know there have already been a number of posts related to FA with
dichotomous variables, but in reviewing them I'm still left unclear about
the best approach for my situation.

I am working with a dataset from which I have extracted 18 items, some of
which are dichotomous (Yes/No responses) and some of which are ordinal (5-
or 7-point Likert).  All of these are related to caregiver opinions on end-
of-life care for their loved one.

My research focus is on a larger phenomenon which isn't addressed directly
in the dataset, but which I believe may be a latent construct represented by
these 18 items.

I would like to test my hypothesis and see whether or not these items "hang
together" in factor analysis, but I am not sure about the best approach.  I
have access to LISREL/PRELIS and SPSS (as well as STATA, but I haven't used
it before). I understand that the necessary steps involve computing a
correlation matrix, and then "plugging" that into a program for analysis. My
questions:

1. In attempting to compute a correlation matrix on LISREL, it gives me the
option for classical and ordinal. Do I select ordinal? If so, will LISREL
automatically know which are dichotomous and which are ordinal, and choose
the correct type of correlation?  I have read about tetrachoric and
polychoric correlation - - does LISREL/PRELIS calculate these on its own?

2. Do I need to transform my Yes/No items to dummy variables? At present,
they are designated as 1=yes, 2=no

3. Once I have the matrix, what is the best approach to analyzing it via
SPSS?  Or is there a better readily accessible program?

4. Is classic factor analysis the best approach? As opposed to PCA or Latent
Class Factor Analysis?

I apologize for the elementary level of my questions - I am a 3rd year
doctoral student and we didn't cover this in my coursework thus far. Does
anyone know of a good online resource that could guide me through this whole
process in step-by-step fashion...??

Thanks for any guidance. I'm sure I missed some key questions to consider,
please feel free to set me back onto the right path!

Phil Higgins, MSW, LICSW

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

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