Open Maximilian-Stefan-Ernst opened 1 year ago
The goal of Taxonomy is to obtain a sample of actually used models to build simulations on. In this context it is important to know if we are working with standardized or unstandardized parameters, because they provide different and mutually exclusive information:
\hat{\lambda}^s_{ij} = \hat{\lambda}_{ij}(\frac{\hat{\sigma}^2_{jj}}{\hat{\sigma}^2_{ii}})^{1/2}
with:
\hat{\sigma}^2_{ii}
$ and $\hat{\sigma}^2_{jj}
$ are the model-predicted/model-implied variances of the $i
$th and $j
$th variables. It is possible to standardize all paramters (more common), or only the latent variables (less common).
Optimally, we would be able to standardize paramters by ourselves, but it can happen that the model implied variances are not reported. Also, it does not always seem to be clear whether the loadings have been standardized or not.
I recommend computing the model-implied covariance matrix from a given model. If this covariance matrix has a unit diagonal (up to some slack because of numerical imprecision), I guess we can assume that factor loadings and regressions and covariances were standardized. Usually, the model-implied matrix is only computed for observed variables but for this test, one should compute the covariance matrix between all latent and all observed variables.
We decided to assume everything is standardized. This means we have to recode all records that a standardized at the moment to check if we coded the raw or standardized stuff.
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