Thresholds, Path Analysis with Probit...
Message/Author
 Qiana Brown posted on Wednesday, July 02, 2014 - 11:09 am
Hello,

Are the threshold values synonymous with constants in path analysis?

I've used path analysis with binary outcomes to assess mediation, and I want to estimate the values of my outcomes in Paths A and B if all covariates were equal to zero. Can I simply substitute the threshold value from the regression models for the constant term?

Thank you
 Qiana Brown posted on Wednesday, July 02, 2014 - 12:53 pm
Hello,

I have an additional question regarding the thresholds from my mediation analysis. Since my outcomes are binary, should I multiply the thresholds by -1 to obtain the constant value?

Thank you
 Bengt O. Muthen posted on Wednesday, July 02, 2014 - 5:28 pm
Thresholds are like intercepts in regression, except with opposite sign. Binary outcomes with mediation has been given a special treatment in Version 7.2 as discussed in

Muthén, B. & Asparouhov T. (2014). Causal effects in mediation modeling: An introduction with applications to latent variables. Forthcoming in Structural Equation Modeling.

See also the handout on our website from my May workshop at the UCONN M3 conference.
 Qiana Brown posted on Wednesday, July 02, 2014 - 10:16 pm
Thank you. The resources were helpful, and I want to make sure that I am applying the methods correctly with regard to the interpretation of my results.

The Muthen & Asparouhov paper explains that in the case of binary outcomes (and similarly for binary mediators), that the indirect effect is only valid for the underlying continuos latent variable Y*, and that the probit regressions relating Y to M are based off of a linear regression of Y* on M.

In my case the mediator (M), outcome (Y), and exposure (X) are all binary. Results from my probit regressions relating X to M, and M to Y are below:

Path A: M ON X = -0.589
Path B: Y ON M = -0.420

Is it incorrect to interpret the estimates with regard to the observed variables? For example, in Path A, is it incorrect to say that higher levels of the exposure relative to lower levels (reference group) were associated with a decrease in the predicted probability of the mediator?

Do I need to specify that the decreases in the probabilities in paths A and B are in regard to the underlying continuous latent variables M* and Y*, and do apply to changes in the actual observed variables M and Y?

Thank you
 Qiana Brown posted on Wednesday, July 02, 2014 - 10:24 pm
In the last sentence of the post above, I meant to say

"Do I need to specify that the decreases in the probabilities in paths A and B are in regard to the underlying continuous latent variables M* and Y*, and do not apply to changes in the actual observed variables M and Y? "

Thank you
 Bengt O. Muthen posted on Thursday, July 03, 2014 - 4:56 pm
Your statements are ok as far as they go, but I would recommend switching to the new "counterfactually-defined" effects - the all binary case is also covered by the new Version 7.2 Model Indirect options - see the Version 7.2 Mplus Language Addendum. Then you get the right answers automatically.

The all binary case is discussed in more detail in my 2011 causal effect paper.