Hi,
a number of allstaters have asked me for a copy of the replies I
received to my question on Factor Analysis - please find this below.
Many thanks to all those who took the time to reply. As you can see
below there was a range of opinions on the approach to analysing likert
data.
Best Wishes to you all
Graham
Original Question:
I have undertaken some factor analysis on a set of data derived from
Likert type (5 point ordinal) questions. Other papers on the topic in
question have used FA however a reviewer has pointed out FA requires the
data to be at least interval in nature.
What do members of the list feel - is it ever acceptable to use FA on
likert scale variables (if so when, is there any diagnostic tests?) any
references to acceptability of use would be most appreciated.
If not acceptable what would be the prefered way of undertaking a FA
type analysis on ordinal data? I've heard of 'optimal scaling' though
I've never used it.
--------------------------------------------------
Responses – truncated in places for brevity:
I'd agree with your reviewer, though to an extent it depends on how
well-behaved your data are. As to this having been a commonly used
methodology for such data in your topic area, my experience has been
(and I appreciate that this will sound snooty) to have very little faith
in most of the factor analyses I have seen: they tend to have absurdly
small sample sizes, to violate basic assumptions, and to have
constructed "meaningful" factors from what appears to me to be random
variation. To return to the point, you might find it possible to employ
polychoric correlations. See, for example,
http://flash.lakeheadu.ca/~boconno2/itemanalysis.html
---------------------------------------------
It's completely appropriate, and rarely done on anything else. The
reviewer is talking nonsense. Useful books on factor analysis may be:
Making Sense of Factor Analysis in Health Care Research: A Practical Guide
http://www.amazon.co.uk/exec/obidos/ASIN/0761919503
A first course in factor analysis
http://www.amazon.co.uk/exec/obidos/ASIN/0805810625/
An easy guide to factor analysis
http://www.amazon.co.uk/exec/obidos/ASIN/0415094909
Papers, things like:
Briggs, S. R., & Cheek, J. M. (1986). The role of factor analysis in the
development and evaluation of personality scales. Journal of
Personality, 54, 106-148.
Journals like Personality and Individual Differences, or Journal of
Personality and Social Psychology will have lots of examples of factor
analysis done on Likert scales (and rarely done on anything else).
----------------------------------------------------
Yes FA is meant for interval data, however it is common practice to use
FA for Likert scales. However to strengthen your results you should look
into RASCH analysis, which has been used a lot in education and is
starting to appear in other fields http://www.rasch-analysis.com/. You
can do RASCH analysis in Stata, though I believe it is tricky to
program, ideally you would need a specific package for it (RUMM). The
other option is to look into confirmatory FA. Programs like lisrel and
AMOS do this. AMOS is very user friendly, lisrel on the other hand is a
bit more tricky. A great text is "scale development" by Robert F DeVellis.
RASCH can be tricky, but once you see what it can do for scale
development, you'll see why it is such a great skill to have.
What about confirmatory FA? AMOS is easy to use (like SPSS) and I found
the best way to learn was to replicate other people's studies. In papers
that have used CFA you'll see they provide a correlation matrix, you can
enter that into excel or some other spreadsheet program and then copy
the model they have in the paper to see if you can re-produce the
results (not always the case!). This would be easier than RASCH as you
already have the model from your exploratory FA, so you would start by
testing that and looking at the statistics to confirm/reject the EFA.
That would certainly add validity to your results along with all the
other validity tests you can use.
-----------------------------------------------------------
Muthen's 'MPlus' program can perform factor analysis with ordinal data.
Probably Vermunt's 'Latent Gold' software can also do it.
You can try Muthen's software. There is a free download, which can do
factor analysis for 6 variables, I think. It is at -
http://www.statmodel.com/
The model you need is example 4.2 in the User's Guide examples, which
you can get at http://www.statmodel.com/ugexcerpts.shtml.
Mplus is very handy, because you can easily perform confirmatory factor
Analysis and factor analysis with covariates that affect the latent
variables and/or the indicator variables. You can check through the
other examples to see what is possible.
Alternatively, the MCMCordfactanal procedure in the "MCMCpack" package
in the open-source 'R' statistical programming language can make 'Markov
Chain Monte Carlo for Ordinal Data Factor Analysis Models'. You can
down-load R (and MCMCPack) free from http://www.r-project.org/
--------------------------------------------
I thought the Likert-like wording was supposed to give roughly
interval-scaled results. Certainly, ten years ago FA on likert scales
was 'industry-standard' in the social sciences
I've occasional tried correspondence analysis (one type of optimal
scaling) as an alternative. You end up with a map (similar to a biplot)
showing how each category/point on each scale relates. If
* all the points on the scale are being used fairly often
* you don't have too many scales to keep track of (coz you've got
(5*number of scales) points scatterd over the map), and
* you're lucky
it can work out quite neatly.
Michael Greenacre has written a couple of books on the technique
--------------------------------------------------
IMHO, any method for doing factorial analysis using Likert scales would
first treat them as ordinal, then slide that into interval scales.
Whether they said as much or not, would depend on the author. That is
how they do the analysis, like it or not.
So my suggestion is as follows: set the middle point of the 5 point
scale to 'neutral' and not to 'no response.' Treat the scale as an
interval scale, and say so out loud. BTW, you can't report averages
unless you do this. You can't take an average on an ordinal scale.
"does not compute."
Also, an interval scale means that a response halfway between 'strongly
disagree' and 'disagree' means just that - 1.5 on the scale.
If you have some very good data, and you really want to examine cases
of averages near the extremes, you can do a conversion that 'expands'
the scale near the extremes. It is related to the logit conversion, if
I get my names right, and is also used by Taguchi only he calls it
Omega transform.
y' = ln (y-y[low])/(y[high] - y) If some y's = y[low] or y[high],
adjust by shifting the extreme values slightly to get no -inf or +inf.
At very low values of y this goes to - infinity. at very high values
it goes to + infinity.
Whether your data is strong enough (low measurement variance) to
support such games, is up to you.
As for results: If you wish to draw a medical conclusion, then a
Likert scale survey is not your cup of tea anyway, but the ordinal-
interval conversion may not fly past the reviewers.
If you wish to learn trends and directions and you are not concerned
whether the result has a p value of 1.5 or 0.9, but only whether p<
0.1, then this will get you home. It has for me a couple times.
------------------------------------------------------
To be blunt, I think that the reviewer is grossly misinformed. One can
do factor analysis with any "type" of data, but special estimation
procedures may be required. For ordered categorical data with about 5-7
or more categories, and with the data roughly symmetrically distributed
across those categories, maximum likelihood estimation (mle) generally
works ok. With fewer categories and/ or non-symmetrically distributed
data (e.g., floor effects), special estimation procedures are required
to obtain good standard errors and model fit statistics. (Simulation
research suggests that the parameter estimates obtained from mle are
quite robust, so you might be able to get away with using mle with
bootstrapped confidence intervals.) You can find a bunch of references
on this topic on these two websites:
http://www.upa.pdx.edu/IOA/newsom/semrefs.htm
http://www.statmodel.com/references.shtml
More generally, on the topic of "types" of data "required" for certain
statistical analyses, see
Lord, F. (1953). On the statistical treatment of football numbers.
American Psychologist, 8(12), 750-751.
Lord, F. (1954). Further comment on "football numbers." American
Psychologist, 9(6), 264-265.
Velleman, P. F., & Wilkinson, L. (1993). Nominal, ordinal,
interval, and ratio typologies are misleading. The American
Statistician, 47(1), 65-72.
--
Dr G.S.Clarke
Lecturer in Physiology & Biometry
Faculty of Health Studies
University of Wales, Bangor
Fron Heulog
Ffriddoedd Road
Bangor
Gwynedd LL57 2EF
Tel: 01248 383157
e-mail: [log in to unmask]
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