Dear all, I’m testing a model with multiple mediation. Theory suggests that mediators (MVs) influence the DV subsequently, i.e. IV -> MV1 -> MV2 -> DV. Accordingly, the total effect of IV is made up of the direct effect and three indirect effects. MV1 is binary. MV2 is continuous but not normally distributed. The DV is continuous and normally distributed. My questions are: (1)How can I compute the total effects of MV1 and MV2? Can I simply add the indirect effects in the case of a binary mediator? (2) How can I test whether the total effect of MV1 or MV2 is significant? (3) I'm using the WLSMV estimator (with parameterization theta) as this seems the estimator of choice if at least one IV/MV is categorical. Is there an alternative to WLSMV? I have two problems with it: (a) Probit coefficients are hardly interpretable. (b) Most indirect effects are significant while I use the max. number of respondents (N=3720). I would also like to analyze subgroups (168 to 502 respondents). In the single group models direct and indirect effects are mostly ns. Of course this is related to the smaller N but growth of the S.E. strikes me as pretty big. Could an alternative estimator yield more efficient estimates? If I’m right, bootstrapped S.E. should be more efficient and could be combined with an ML estimator. Correct? Any help and hints highly appreciated! Best Kai
(1) You use Model Constraint to express ind=a*b*c, where those are the 3 slopes involved.
(2) ind gets a SE and a z-test.
(3) WLSMV is appropriate because the binary MV1 is replaced by its underlying continuous latent response variable, say u*. This means that you have linear regressions in all 3 cases and can therefore consider a*b*c as the indirect effect. That would not be the case with ML because it does not consider u* but instead lets MV1 be the predictor. WLSMV is fine as far as SEs go, but you can also use Bayes which by default uses probit and u*, just like WLSMV, but is a full-information estimator.
Note that with a binary mediator, newer "causally-defined" effects are available as discussed in:
Muthén, B. (2011). Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus.
Dear Bengt, thank you very much for your helpful reply! (and sorry for the late reply - took me a while to digest this). The model constraint command worked very nicely and I was able to play with it and calculate coeffs & SE for various combinations of slopes. As often, some more questions emerged... (1) I understand that probit coeffs give the increase in predicted probabilities of a latent u* (underlying a binary MV1). But what could probit coeffs mean regarding a continous DV (the natural logarithm of income in my case)? (2) If I'm right I can compare the effect sizes of the different IVs/MVs using the StdXY coeffs. Correct? Is it also possible to get those standardised coeffs for parameters calculated with model constraint? (3) I understand I can neither compare probit coeffs nor StdXY coeffs across different groups, when calculating separate group models. However, would it be possible to compare effect sizes across groups in a group model? Or is there any other means of getting an idea of the differences in effect sizes between groups ("predicted probabilities" based on group means don't make much sense for a continous DV). (5) Thank you for the reference! Admittedly, heavy stuff for me but I will try to get my head around it (especially the transfer of your treatment of binary mediator/binary outcome to binary mediator/continous outcome).
(1) Ok, but how can I get other than probit coeffs? If I'm right I need to use WLSMV due to the binary mediator and WLSMV goes together with probit coeffs. What am I missing here? What would be the alternative(s) to WLSMV?
(2) Thus I would need to enter the standardization formula in model constraint 'by hand'. Correct?
Your answer brings me back to question of how to interpret the coefficients provided by WLSMV. I understand that related to the binary mv the coefficients are probit. Related to the continous y the weighted least squares coefficients are to be interpreted in the sense of one unit increase in x triggers beta units increase in y. Correct?