The article by Bullmore et al. that Will mentions addresses the issues about
whether how good a fit an SEM model should be.
The second point raised by Hector-Gabriel -- should one use an anatomical
model fit the data -- is more complicated. One must remember that SEM is
modeling. This means that you are trying to account for the important
variance in the data, not all the variance. If a task is complicated, as
most are, a good model may help elucidate part of what is going on, but it
will have trouble fitting all the functional brain imaging data because a
lot of that data will be related to things outside what the model is trying
to explain. Thus, a fine balance must be drawn between how well the SEM
model fits the experimental data, and what the model is trying to explain.
In other words, a reasonable fit of model to data is desired, but having
some arbitrary threshold that one always uses may be unwarranted.
As the risk of boring everyone, one SEM PET study that we performed several
years ago illustrates this point. We looked at a face matching task in
normal elderly and in mildly demented Alzheimer Disease (AD) patients. We
used a model based on young subjects and found that the old subjects' data
fit the model fairly well, but the AD didn't, even though they performed the
task normally. The point is that using the stacked model approach and
including the AD patients, we could never get a good fit (remember -- in the
stacked model approach, the goodness of fit is determined by all the data),
but the SEM told us something interesting.
Ref. B. Horwitz et al., NeuroImage 6: 2287-92 (1995).
Cheers,
Barry
----------------------------------------------------------------------------
------
Barry Horwitz, Ph.D.
Senior Investigator
Language Section
Voice, Speech and Language Branch
National Institute on Deafness and other Communication Disorders
National Institutes of Health
Bldg. 10, Rm. 6C420
MSC 1591
Bethesda, MD 20892
USA
Tel. 301-594-7755
FAX 301-480-5625
[log in to unmask]
http://www.nidcd.nih.gov/intram/scientists/horwitzb.htm
> -----Original Message-----
> From: Will Penny [mailto:[log in to unmask]]
> Sent: Wednesday, August 29, 2001 9:46 AM
> To: [log in to unmask]
> Subject: Re: Goodness of fit
>
>
> Hector-Gabriel wrote:
>
> > Dear SPM'ers:
> >
> > Looking among some fMRI/SEM studies I realised that the
> stacked model
> > approach has been used to compare a specific anatomical model under
> > different experimental conditions but most of the time the authors
> > don't
> > say anything about the goodness of fit (p value for example) of the
> > base
> > model. My questions are:
> >
> > 1) Is it possible to use SEM to evaluate not only the significant
> > difference across different conditions but also the goodness of fit
> > of the
> > model?
> >
> >
> >
> >
> > 2) Is it valid to use, in a stacked model approach, an anatomical
> > model
> > that is not statistically significant (p value < 0.05 for example)?
> >
>
> 1. The goodness of fit of the base model can be
> assessed using a Chi^2 criterion. For details of the
> derivation of this
> criterion
> see Bollen (1989) and for a description of it in action in a
> neuroimaging context
> see Bullmore et al. (2000).
>
> 2. In my opinion the base model *should be* statistically significant.
> But there
> is, I believe, some disagreement among researchers on this
> issue. On the
>
> second and third pages of the Bullmore paper, for example,
> they provide
> reasons
> why absolute (as opposed to relative) assessment of models should be
> made with caution. Maybe others would like to comment.
>
> Hope this helps,
>
> Will.
>
> References:
>
> @Article{bullmore_sem,
> author = {E. Bullmore and B. Horwitz and G. Honey and
> M. Brammer and S. Williams and T. Sharma},
> title = {How good is good enough in path analysis of fMRI
> data ?},
> journal = {Neuro{I}mage},
> year = 2000,
> volume = 11,
> pages = {289-301}
> }
>
> @Book{bollen_sem,
> author = {K.A. Bollen},
> title = {Structural Equations with Latent Variables},
> publisher = {John Wiley, New York},
> year = 1989
> }
> --
>
|