# Assumptions for SEM

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Joined: 11/08/2011 - 12:23
Assumptions for SEM

Hello everybody,

I looked trough the two papers indicated by citation('OpenMx') and could not find the assumptions on the data (indicators). Do they need to be centered around Zero and/or have variance of One? Where is that written down? I found literature with and without the above mentioned assumptions.

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Joined: 07/31/2009 - 15:14
It depends

If you are using the MLObjective (means and covariances) or the mxFIMLObjective() fit functions then the assumption is that the data are continuous and marginally distributed as multivariate normal. When I say marginally, I mean that conditional on any definition variables or covariates specified in the model, the data are distributed according to a multivariate normal distribution.

If you are using the FIMLObjective with binary or ordinal data, the assumption is that the conditional multivariate normality exists at the level of the underlying latent distribution, and that abrupt thresholds distinguish between the ordered categories that are observed.

If you are using an mxRowObjective or an mxRObjective, you can specify the likelihood of the data (or any other fit function that it is possible to program) in any way you choose. The assumptions then depend on the function you have specified. There are various forms of weighted least squares functions, for example, which involve less stringent assumptions than normal theory ML.

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Joined: 11/08/2011 - 12:23
Estimate of polychoric correlations and thresholds by OpenMx

With ordinal data: I would like to know how the FIMLObjective estimates the thresholds and polychoric correlations. I found the paper of Olsson (1979, p. 446ff.) explaining that there are two ways: a formally correct one and one that yields similar estimates. The latter is not as computationally expensive as the first. He calls it
Case 1: All Parameters Are Estimated Simultaneously;
Case 2: The Thresholds are Computed from the Marginal.

Which of the two methods does OpenMx use?
If the question is not detailed enough I will write more.

Sophia

Full citation:
Olsson, U. (1979). Maximum Likelihood Estimation of the Polychoric Correlation Coeffcient. Psychometrika 44(4), 443-460.

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Joined: 07/31/2009 - 15:12
In FIML estimation in OpenMx,

In FIML estimation in OpenMx, we do everything simultaneously. When WLS is supported, weight matrices will be calculated using a variation of the second method.