Formula for Predicted Probability
Message/Author
 ABM posted on Tuesday, March 07, 2017 - 5:54 am
Can I use the formula below (which I've used for logistic regression data) to calculate predicted probabilities for the final mediation model (where all variables are dichotomous) by simply plugging in -threshold for a?

log (Pi / 1 – Pi) = a + b1X1 + b2X2 + . . . + bkXk to determine the log odds, exp(logit) to determine the estimated odds, which I then converted into probabilities using the formula odds / (1 + odds).

 Bengt O. Muthen posted on Tuesday, March 07, 2017 - 5:32 pm
Are you saying that X, M, and Y are all dichotomous? And you are applying a logit link for the M and for the Y regressions? And are you using ML?
 ABM posted on Tuesday, March 07, 2017 - 8:35 pm
Thanks for the message. Yes, x m and y are dichotomous.

Here's the analysis/commands I ran:
ANALYSIS: estimator=WLSMV;
BOOTSTRAP = 1000
OUTPUT: samp stand residual CINTERVAL(bcbootstrap)
Estimator WLSMV
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Number of bootstrap draws
Requested 1000
Completed 1000
Parameterization DELTA

I'm wondering if I can insert the unstandardized coefficients and the negative threshold from the full model (x, m1, m2) into the formula I listed before.

Or, if not...what would be the simplest method of calculating predicted probabilities (to create scenarios based on values of m and x)?
Thank you!
 Bengt O. Muthen posted on Wednesday, March 08, 2017 - 6:02 pm
WLSMV does probit, not logit. So the model is not for log (Pi / 1 – Pi). The probability is also a function of the residual variance of the mediator equation. Details are in our new book. This also explains why you need special direct and indirect formulas when the mediator and the outcome are binary.