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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.
 Anna MacKinnon posted on Wednesday, January 29, 2020 - 11:46 am
Dear Drs. Muthen,

I have used the code, from the link you provide to Chris Stride's webpage, for Model 4d where I have a dichotomous X, continuous M, and dichotomous Y.

How do I interpret the OR of the indirect effect vs. A1B1:
- the indirect effect A1B1 is not significant (p=.394)
- but the odds ratio of the indirect effect ORA1B1 is significant (p = .001)

Also, why would the OR become non-significant when I add Bootstrap = 10000; to the Analysis?
- SE = ****** p = 1.000

Thank you kindly,

 Bengt O. Muthen posted on Wednesday, January 29, 2020 - 5:32 pm
With ORs, you should use non-symmetric confidence intervals to decide on significance - use confidence intervals from bootstrapping. The printed p-values assume that symmetric confidence intervals are relevant.
 Anna MacKinnon posted on Thursday, January 30, 2020 - 10:14 am
When I add bootstrapping, the 95% CI for A1B1 (-0.593, 0.752) crosses 0, but not for the OR (0.553, 2.121). These are not labeled in the output as non-symmetric - is there a different command to request those?

Also, I'm not sure what the difference is between A1B1 and ORA1B1? If the indirect effect is not significant, why would I interpret the OR?

Thanks again!
 Bengt O. Muthen posted on Friday, January 31, 2020 - 10:43 am
For OR, the question is if the interval crosses 1, not 0. So both indicate non-significance. When you request confidence intervals for ORs, they are non-symmetric (the correct choice).
 Anna MacKinnon posted on Monday, February 24, 2020 - 9:52 am
Hi Dr. Muthen,

Thank you for your response!

I'm still wondering what the difference is between the estimate of the indirect effect (A1B1) and the OR for the indirect effect? Which should I interpret/report?


 Bengt O. Muthen posted on Monday, February 24, 2020 - 5:11 pm
The OR is the most natural to report.
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