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Arbuckle's coverage of PD begins on page 249. He compared PD, LD, and ML.
I have used Schafer's data augmentation technique with some success; it
has the advantage of ML imputation but adds an end step that reproduces
randomization in the residual. His NORM software is free. There is a bit
of a learning curve but you can find plenty of documentation on the web.
Mark
***************************************************************************************************************************************************************
Mark A. Davenport Ph.D.
Asst. to the Vice Chancellor for Student Affairs
Office of Student Affairs Research and Evaluation
The University of North Carolina at Greensboro
336.334.5582
M_Davenport@uncg.edu
'An approximate answer to the right question is worth a good deal more
than an exact answer to an approximate question.' -- J. W. Tukey
King Douglas <King.Douglas@aa.com>
Sent by: "SPSSX(r) Discussion" <SPSSX-L@VM.MARIST.EDU>
02/03/2005 06:03 PM
Please respond to
King Douglas <King.Douglas@aa.com>
To
SPSSX-L@VM.MARIST.EDU
cc
Subject
Re: Problem with factor analysis
Hey, Marcos,
It might be helpful to know how many cases you have in your data.
Just a hunch, but the pairwise deletion/not positive definite problem may
lie in the large number of missing values per case and/or
the exact way the attributes were distributed (i.e. randomized) among
respondents. You can read more on this (so I'm told) in Arbuckle, J. L.
(1996). Full information estimation in the presence of incomplete data. In
G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced structural equation
modeling: Issues and techniques (pp. 243-78). Mahwah, NJ: Lawrence
Erlbaum.
You may have no choice but to replace (with care) the missing values
before running your analysis. As far as reliability is concerned, there
is no way to tell if you would get exactly the same factors and similar
factor scores if you had no missing data.
King Douglas
>>> Marcos Sanches <marcos.sanches@IPSOS.COM.BR> 02/03/05 04:49AM >>>
Hi all,
I am performing a factor analysis with 60 attributes. Each one were
rated in a importance scale - 0 for Not Important to 10 for Very
Important. As there are so many attributes each respondent rated only a
random subset of 39 attributes. That means I have 60 - 39 = 21 missing
values for each case. I want to run a factor analysis with this data.
If I select the listwise method of missing values deletion, of
course I end up with no case left.
If I select the pairwise method of missing values deletion, I
get na error message - "The matrix is not positive definite. This may be
due to pairwise deletion of missing values.".
If I select the "replace with means" method of missing values
substitution, then it sorks well.
My questions are:
1) Why does the pairwise method does not work? Even when I select a
subsample it does not work. I know what is a 'not positive definete
matrix', but why this happens? Is there a way to handle this?
Before the enterview had been done, I made a simulation using another
study. I deleted randomly some values for every case so that every cases
had some missing values, then I ran a factor analysis with pairwise
deletion. It worked pretty well, in fact the final factor were almost
the same these one got with the complete data. So I didn't hope this
problem could happen.
2) In such a case, would the factor analysis done with missing values
replaced with means be reliable?
Thanks in advance,
Marcos
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