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 Julian Wienert posted on Wednesday, June 15, 2016 - 1:56 am

I have a quick question regarding indirect effects. I have a model with interval scaled IV and M, but the DV is nominal scaled (binary). Besides odds ratios Mplus provides standardized and unstandardized coefficients for the b path (using MLR). Using model indirect displays an indirect effect based on a*b, however, I am not sure if Mplus already transforms standardized and unstandardized coefficients for b so that model indirect comes to a valid result. If this is not the case, how do I transform coefficients for b appropriately?

Thank you very much in advance for your help!

 Bengt O. Muthen posted on Wednesday, June 15, 2016 - 12:54 pm
Not sure what you are asking so let me state a few facts to see if they help.

Mplus gives the a*b indirect effect in unstand. and stand. form. The stand. value is the same as the product of a stand. and b stand. With a binary outcome you should use the counterfactually-based effects.
 Julian Wienert posted on Monday, August 15, 2016 - 6:16 am
Dear Prof. Muthén,

thank you for your help. However, I am not very firm with counterfactuals and have problems interpreting the output. Any help would be very welcome!

Kind regards

Estimate S.E. Est./S.E. P-Value

Effects from Var1 to Var2

Pure natural DE 0.000 0.000 0.581 0.561
Tot natural IE 0.000 0.000 0.872 0.383
Total effect 0.000 0.000 0.876 0.381

Odds ratios for binary Y

Pure natural DE 1.102 0.157 7.039 0.000
Tot natural IE 1.441 0.068 21.329 0.000
Total effect 1.588 0.219 7.240 0.000

Other effects

Tot natural DE 0.000 0.000 0.584 0.559
Pure natural IE 0.000 0.000 0.853 0.394
Total effect 0.000 0.000 0.876 0.381

Odds ratios for other effects for binary Y

Tot natural DE 1.102 0.157 7.040 0.000
Pure natural IE 1.442 0.068 21.330 0.000
Total effect 1.588 0.219 7.240 0.000
 Bengt O. Muthen posted on Monday, August 15, 2016 - 8:15 am
This is described in our new book at

See also counterfactual papers at posted on Wednesday, October 19, 2016 - 11:37 am

I would like to calculate a path model with 1 continuous IV, 3 continuous mediators (in parallel), 1 sequential continuous mediator and 3 DVs (2 are continuous, 1 is binary). I am using ML estimation (I am thus calculating a logistic regression) and defined the binary outcome as categorical. Using MODEL CONSTRAINT, I calculated all possible indirect effects (BOOTSTRAP = 10000; CINT(bcbootstrap)). To obtain the the correct estimates of the indirect effect involving the binary DV I exponentiated the indirect effects (e.g., ORa1b1 = exp(a1*b1); ORa1b1d1=exp (a1*b1*d1). Is this approach correct? What about direct effect involving the binary DV - is the estimation a B coefficient in the output based on logistic regression? When looking at the output, I also get the odds ratio in case of the direct effect but I don't not the CIs (however, I do get those for these indirect effects). How do I get the CIs of the odds rations for the direct effects? What would be the best way to run the same analyses if the DVs would be ordinal with 4 categories (e.g., which estimator, bcbootstrap or other approaches to calculate the significance of indirect effects)? Many thanks for your help.
 Bengt O. Muthen posted on Wednesday, October 19, 2016 - 5:53 pm
Using ORa1b1 = exp(a1*b1) is only correct assuming that the binary outcome is rare and only for a 1-unit change in the continuous x. See Section 8.1.5 in our new book.

Estimating path-specific indirect effects with a binary outcome and several mediators is more complex as mentioned in our book and discussed further in the VanderWeele (2015) book.
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