Hi Sowan
This question is a little bit trickier than it sounds.
Your first order analysis is fine (that is, the first layer of latent
variables).
Think about the second order analysis though, in terms of degrees of
freedom (or estimated parameters, it's the same).
You have 3 latent variables, which correlate. You therefore have
three correlations that you want to try to explain, with your higher
order factor. If you add a higher order factor, that will require 3
factor loadings.
Because you are putting in 3 pieces of information, and are also
getting out three pieces of information, your higher order structure
has zero degrees of freedom, and it is therefore just-identified.
(Remember that we normally want models that are overidentified).
In other words, they are the same. It will make no difference which one you do.
However, a slight disclaimer on that: If you have that higher order
model being either a predictor or an outcome of some other measures,
then the model is overidentified, and it will make a difference. But
you might get identification problems.
Jeremy
P.S. I was asked a question about this in my PhD viva - the examiner
asked why I hadn't fitted a 2nd order model. As it was my viva, I
couldn't think of the answer, but the answer was - it wouldn't have
made a difference.
On 21/04/2008, So-Wan Wong <[log in to unmask]> wrote:
> hi all! i have a question regarding running CFA with a construct. hope i could get some ideas/advice from you all!
>
> i have a construct which includes 3 dimensions, the theory says that they all contribute to form a single construct. my question is, should i run a CFA with a higher ordre factor, and 3 first order factors, or just a single factor solution, with one first order factor? what's the difference between the two ways of analyses?
>
> would be great if i could get some help from you all! many thanks in advance! best, - sowan
>
>
> --
> ... like this insubstantial pageant faded,
> Leave not a rack behind. We are such stuff
> As dreams are made on; and our little life
> Is rounded with a sleep.
> - Shakespeare, Tempest, ActIV, SceneI
>
>
> Sowan Wong
> research student in psychology
> School of Social Sciences
> Brunel University, West London
>
> http://people.brunel.ac.uk/~hspgssw/sowan.htm <http://people.brunel.ac.uk/~hspgssw/sowan.htm>
>
>
--
Jeremy Miles
Learning statistics blog: www.jeremymiles.co.uk/learningstats
Psychology Research Methods Wiki: www.researchmethodsinpsychology.com
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