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We need more documentation on heterogeneity = "homogeneous". panelSEM creates variances between the lagged time varying variables in a homogeneous model and covariances between contemporaneous variables. This corresponds to the "Linear Model without Unobserved Heterogeneity" in the document "The causalSEM package: An Illustration". However, the "homogeneous", linear = TRUE case does not make clear that this is the "Linear Model without Unobserved Heterogeneity". Which one is correct?

When adding product terms in case of linear = FALSE and use_definition_variables = FALSE, (co-) variances of all exogenous variables are automatically added. These are not freely estimated but set to the observed covariances. This should, in theory, be identical to an estimation.
Limitations:

• It is currently unclear if covariances between the residuals of x1, x2, ..., y1, y2, ... and the product terms should be added. These would have to be estimated, considerably increasing the number of model parameters
• Thoroughly test the current approach
• Adapt tests: We are now estimating fewer parameters