Question about fixing a factor loading to 1 in hierarchical Genomic SEM

[Linlin Jia]

Hi all：

I am currently fitting a hierarchical (second-order) Genomic SEM model with four first-order factors and a higher-order factor. During model estimation, one of the first-order factors (F4) showed instability and extremely large standard errors when all higher-order loadings were freely estimated.
To improve model identification and numerical stability, I constrained the loading of F4 on the higher-order factor to 1 (i.e., using a marker-variable approach to set the scale of the second-order factor).

Is fixing one higher-order loading to 1 an appropriate identification strategy in hierarchical Genomic SEM?

Thank you very much for your time and for developing such a valuable method.

[Elliot Tucker-Drob]

For a hierarchical factor model, I agree that the most sensible identification strategy is to fix the loading of a single indicator of each factor to 1.0 and freely estimate the (residual) variance. That applies to both the first order factors and the higher-order factor. You should not fix both the variance and a loading, as the results produced will not be sensible.

If you are using a traditional identification strategy (either unit variance or unit loadings, but not both) for each factor and you get an unstable solution with very large SEs, there are a few possible explanations that come to mind: 1) a coding error/misspecified model, 2) one of the phenotypes has trivial SNP heritability and/or a very low N, 3) the rG between at least one pair of indicators of a factor is extremely close to zero, 4) you have fewer than 3 indicators for a factor.  I'm sure there are other possible reasons, but those are the ones that come to mind.

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