

Bias due to conditioning on a collider 

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nata posted on Monday, March 10, 2014  2:22 am



Dear MplusTeam, I am running a full SEM Which I have 9 observed binary indicators (x1x11), 3 latent factor (f1f3), 1 mediating variable (m), 3 confounders (x12x14) and 1 binary outcome (y) . The model is the Following: BY f1 x1x4; f2BY x5 x8; f3BY x9 x11; y ON m f1 f2 f3 x12 x13 x14; ON m f1 f2 f3 x12 x13 x14; f1 ON x12 x13 x14; ON f1 f2 f3 x12 x13 x14; ON f1 f3 x12 x13 x14; Now, if the model is correct from a syntactic point of view, the variable m should be a collider. I was wondering if the estimates of the direct and indirect effects on y that provides Mplus are biased or not? Thanks 


You have 3 statements starting with ON which does not translate to Mplus language. If the model is correctly specified, there is no bias. 

nata posted on Wednesday, March 12, 2014  3:53 am



Sorry, probably there was a problem in the copy&past process. Here is the exact formulation of the model: f1 BY x1x4; f2 BY x5x8; f3 BY x9x11; y ON m f1 f2 f3 x12 x13 x14; m ON f1 f2 f3 x12 x13 x14; f1 ON x12 x13 x14; f2 ON f1 f3 x12 x13 x14; f3 ON f1 x12 x13 x14; Thanks 


This model specification looks fine. Under the usual causal inference assumptions, the Mplus Model Indirect estimates of direct and indirect effects are consistent. 

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