[R] SEM model testing with identical goodness of fits

[John Fox]

Dear hyena,

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
> Behalf Of hyena
> Sent: March-14-09 5:07 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] SEM model testing with identical goodness of fits
> 
> HI,
> 
>    I am testing several models about three latent constructs that
> measure risk attitudes.
> Two models with different structure obtained identical of fit measures
> from chisqure to BIC.
> Model1 assumes three factors are correlated with  each other and model
> two assumes a higher order factor exist and three factors related to
> this higher factor instead of to each other.
> 
> Model1:
> model.one <- specify.model()
> 	tr<->tp,e.trtp,NA
> 	tp<->weber,e.tpweber,NA
> 	weber<->tr,e.webertr,NA
> 	weber<->weber, e.weber,NA
> 	tp<->tp,e.tp,NA
> 	tr <->tr,e.trv,NA
> 	....
> 
> Model two
> model.two <- specify.model()
> 	rsk->tp,e.rsktp,NA
> 	rsk->tr,e.rsktr,NA
> 	rsk->weber,e.rskweber,NA
> 	rsk<->rsk, NA,1
> 	weber<->weber, e.weber,NA
> 	tp<->tp,e.tp,NA
> 	tr <->tr,e.trv,NA
> 	 ....
> 
> the summary of both sem model gives identical fit indices, using same
> data set.
> 
> is there some thing wrong with this mode specification?

>From your verbal description, I would have thought that the second model is
more restrictive than the first, but that doesn't seem to be the case -- if
the two models have identical log-likelihoods and degrees of freedom, as you
seem to imply, then it's a good bet that the models are observationally
indistinguishable. On the other hand, you don't provide a whole lot of
information; it would have been much more informative had you shown the
input and output for both models.

John

> 
> Thanks
> 
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