When doing regressions, if we are testing multiple hypotheses, there are traditional ways to deal with it (e.g. Bonferroni correction etc.)

And if we are also doing variable selection, there are modern ways such as regularisation and LASSO.

In structural equation modelling, we do both. Are there p-value corrections or variable selection procedures in SEM?


I have never heard of variable selection methods in SEM, probably because SEM tends to be very theory driven, and so variable selection is less of an issue; also because variable selection means that your ch-square tests of model fit cannot be interpreted in the same way.

When it comes to correction for multiple testing, the problem isn't so much variables as parameters - you can have a lot of parameters for a small number of variables. This paper: https://www.researchgate.net/publication/238865182_Multiplicity_Control_in_Structural_Equation_Modeling suggests using a false discovery rate (FDR) approach when examining a lot of parameters.


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