In my recent question to Andrew Hayes on testing the indirect effect with the following model with Cs are control variables, Xs are the antecedents, M is the mediator and Y is the outcome.
MODEL: Y ON M; M ON C1 C2 C3 X1 X2 X3 X4;
MODEL INDIRECT: Y IND M X1; Y IND M X2; Y IND M X3; Y IND M X4;
This is what Andrew's response and I quote "In this model, your indirect effects would be biased. You should never estimate indirect effects without the corresponding direct effects also in the model. If you do so, then your indirect effects will include both indirect and direct components, as per standard tracing rules."
I notice that your example 3.16 is similar to mine and you did not include the direct path from x1 to y3 (i.e., y3 on x1)
MODEL: y1 y2 ON x1 x2 x3; y3 ON y1 y2 x2;
MODEL INDIRECT: y3 IND y1 x1; y3 IND y2 x1;
I'd appreciate your take on Andrew's response and my model. Thanks.
Typically, you want to allow for all direct effects in the model, particularly if you have little prior knowledge so that you can study what's indirect and what's direct. But in some other cases you may want to test a theory that some direct effects are zero - that is what is done in UG ex 3.16.