fixed.x = TRUE as the default

[Shu Fai Cheung]

The option fixed.x has been discussed a while ago:

https://groups.google.com/g/lavaan/c/Gk93Vp3o5Z0/m/3dWwhLVWBQAJ

This issue came back to me again when working on something else. I understand that, for incremental fit indices such as CFI and TLI, it makes sense to set the covariances between exogenous "x" variables to be free in the baseline model.

However, this can be done without fixed.x = TRUE. Just fit a model with those exogenous "x" variable covariances freely estimated and use this model as the baseline model. There is no need to treat the exogenous "x" variables as fixed variables in the model itself.

Actually, fixed.x = TRUE may not be consistent with other commonly reported results, such as the correlations among the exogenous variables, which researchers usually report their point estimates and p-values and/or confidence intervals. It rarely makes sense to treat these exogenous "x" variables as fixed.

Treating them as fixed can also result in incorrect standard errors for the standardized solution because the sampling error in estimating the population SDs (variances in the model) of the exogenous variables are ignored.

I am not sure about the default behavior of other SEM programs. For AMOS, this is not an issue because users have to manually specify all covariances between exogenous variables, although AMOS uses the independence model as the default. I don't use Mplus and so I have no idea about the default of Mplus.

-- Shu Fai

[Pat Malone]

Shu Fai,

To the last point, I'm pretty sure Mplus defaults to what fixed.x=TRUE does.

Pat

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Patrick S. Malone, PhD

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