Bias due to conditioning on a collider
Message/Author
 nata posted on Monday, March 10, 2014 - 2:22 am
Dear Mplus-Team,

I am running a full SEM Which I have 9 observed binary indicators (x1-x11), 3 latent factor (f1-f3), 1 mediating variable (m), 3 confounders (x12-x14) and 1 binary outcome (y) . The model is the Following:

BY f1 x1-x4;
f2-BY x5 x8;
f3-BY 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
 Bengt O. Muthen posted on Monday, March 10, 2014 - 11:49 am
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 x1-x4;
f2 BY x5-x8;
f3 BY x9-x11;

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
 Bengt O. Muthen posted on Wednesday, March 12, 2014 - 11:27 am
This model specification looks fine. Under the usual causal inference assumptions, the Mplus Model Indirect estimates of direct and indirect effects are consistent.