Exploratory versus confirmatory factor analysis
Sara Mottram
Apologies for the cross-posting.
I have ten variables, each with a three-level ordinal response. My
hypothesis is that these variables form a single factor.
Initially, I used exploratory factor analysis (EFA) to assess whether
this was true and found that I got only one factor with an eigenvalue
greater than 1 and this explained almost 70% of the variance. I was
happy that my original hypothesis was reasonable. I used SPSS 14 for
this analysis.
However, I then discovered that confirmatory factor analysis (CFA) was
probably more appropriate to my problem and used Amos 6 to specify a
model with ten items and one factor. The goodness of fit tests for
this model showed that there was poor fit. Here I am confused. My
understanding was that EFA fitted the 'best' model to the data whereas
CFA assessed whether the suggested model was good enough, even if it
wasn't the 'best'. So surely if I get the model I expected using EFA,
I should also get it using CFA?
I have thought about the reasons for this and, I think, eliminated
them one-by-one:
The sample size is large (n=7878), so there is good power to pick up
even slight departures from what would be expected in the CFA.
However, in a similar sized dataset, this wasn't a problem.
There is an issue surrounding the specification of only one factor. I
have tested this idea using a dataset where I expected 3 factors and
Amos suggested a reasonable fit. I then took one of these factors
(also with three levels and ten items) and specified this model alone
(very similar to my original model and data) and there was no
indication that model was not appropriate.
I've also checked that I used only complete-case analysis in both EFA
and CFA so that they are comparable.
I've also tried to use the asymptotically distribution free estimation
method in Amos instead of maximum likelihood, but this didn't change
the model fit, also I don't think it's possible to compare this to an
equivalent estimation method in EFA in SPSS.
I'm aware that I am on thin ice with regard to the assumption of a
continuous outcome, but I don't see why EFA and CFA don't give the
same 'answer'. I'm left with the feeling that maybe CFA is more
sensitive to violations of modeling assumptions. Could anyone tell me
if this is the case, or is there another reason why the two methods of
factor analysis are apparently contradictory please?
Best wishes,
Sara
Swank, Paul R
CFA is a more stringent model thatn EFA. In EFA there are coefficients
generated for each indicator on each factor. Many of these may be near
zero but in fact most are not zero. The CFA forces the indicators that
are not associated with a factor to be exactly zero. Thus, there are
many more restrictions in this model. With only three levels, you may
also run into a problem with nonnormality which will tend to inflate the
chisquare. There are statistics meant to reduce the impact of
nonnormality on the chisquare but the variables are still quite
discrete. With your sample size, however, it would be possible to
generate an asymptotic matrix and use nonparametric solutions. Or you
could use Mplus which has a nice built in measurement model to handle
discrete data without resorting to asymptotic matrices and nonparametric
solutions.
Paul R. Swank, Ph.D. Professor
Director of Reseach
Children's Learning Institute
University of Texas Health Science Center-Houston
Sara Mottram
Thank you for your helpful suggestions.
Best wishes,
Sara