SEM: Checking the Linearity Assumption

Before interpreting the results of Linear Structural Equation Models (SEM), it is important to check the assumptions of the procedure, as with all statistical techniques. One crucial assumption for SEM is that the latent constructs being analyzed are linearly related. However, it is often overlooked to check for this assumption of linearity.
This tutorial will demonstrate how to check linearity using factor scores and the potential impact of violating this assumption on the results (example based on R / lavaan). Additionally, it will briefly discuss potential solutions if the linearity assumption is found to be invalid.
How to get factor scores in AMOS or in MPlus:
www.ibm.com/su...
stats.oarc.ucl...
R package for non-linear SEM:
cran.r-project...

[@user-vu9fy7by9p]

Hi Mr Regorz, thank you very much for the video. It's very helpful! I was wondering if a few paths in the path analysis (not SEM as there isn't any latent variable) do NOT have linear relationships, but other paths (i.e., most of the paths in the model) do have linear relationships, can I still run a regular path analysis that assumes linear relationship? The paths that do not have linear relationships are between a predictor and two mediators. I am interested to test the indirect effects that involve these variables. Thank you for your help in advance.

[@RegorzStatistik]

The question of linearity should be assessed and dealt with for each path. If you have non-linear relationships then I would use polynomial modeling (e.g. including IV² in addition to IV). However, for indirect effects I haven't read how to model that, yet.