Published on *OpenMx* (http://openmx.psyc.virginia.edu)

By *carey*

Created *02/15/2011 - 22:10*

Tue, 02/15/2011 - 22:10 — carey [1]

the default likelihood function for observed data of type=cov or cor multiplies

log(det(predictedCov)) + trace(observedCov %*% inverse(predictedCov))

by (numObs - 1). my understanding is that both the derivations from the multivariate normal pdf and the wishart pdf lead to this being multiplied by numObs and not (numObs - 1). (note that math/stat treatment of the wishart talks of "degrees of freedom" but the actual algebra defines this quantity as numObs).

i stand to be corrected here.

greg

PS for most stuff in SEM, this is completely trivial. i am, however, in the process of writing an efficient algorithm for pedigree analysis in openmx (the genetic stuff) and want to know if i do or do not need to correct the likelihood function. also, if i am correct, the MLE will not be correct for the pedigree analysis.

**Links:**

[1] http://openmx.psyc.virginia.edu/users/carey

[2] http://openmx.psyc.virginia.edu/thread/813

[3] http://openmx.psyc.virginia.edu/thread/801

[4] http://openmx.psyc.virginia.edu/forums/openmx-help/openmx-general-help