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non-normal SEM (third moment)

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tbates's picture
Joined: 07/31/2009 - 14:25
non-normal SEM (third moment)

Did anyone see this paper:

Koken Ozaki, Hideki Toyoda, Norikazu Iwama, Saori Kubo and Juko Ando (2011). Using Non-Normal SEM to Resolve the ACDE Model in the Classical Twin Design

Thoughts? They argue that estimating skewness (3rd moment of a distribution) in addition to mean and variance, the extra degree of freedom makes ACDE models identified...

This seems over value: Can we do it in OpenMx?


carey's picture
Joined: 10/19/2009 - 15:38
tim, have seen this but not


have seen this but not gone over it in detail, so the following gives my first thoughts.

unless i seriously misunderstand OpenMx, the answer to your query "Can we do it in OpenMx?" is "yes" as long as it pertains to writing the relevant code for the current OpenMx and does not pertain to adding features to OpenMx to deal with higher moments.

note that ozaki et al deal with one phenotype. hence, one can construct MxData objects with a (1 x 1) "observed=
". (of course, this is in addition to the MxData objects dealing with (optionally) means and a (2 x 2) covariance matrix.)

then use MxAlgebra objects to program their equations (3) through (10) and use these as the predicted values of the higher moments.

finally, use an MxAlgebraObjective object (along with many intermediate MxAlgebra calculations) to implement their equation (11).

note that this model assumes that at least one of the variables A, C, D, or E is not normal and any non-normality in the phenotype is a result of non-normality of these latent variables. this is a very strong assumption for behavioral phenotypes, many of which are measured on an ordinal scale.


carey's picture
Joined: 10/19/2009 - 15:38
opps. for some reason, this

opps. for some reason, this post eliminated a phrase.
should read
observed=formulas at the right hand, bottom of p. 331
pardonne moi

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