Jonika Hash posted on Tuesday, October 10, 2017 - 1:09 pm
Hello! I am a PhD student looking for help with predicted probabilities.
I have a path model with a latent mediator and a final dichotomous outcome (u2). I would like to calculate predicted probabilities of u2 at different levels of two predictors (x3 & x4), holding all else constant. I am using ML with Monte Carlo integration and the logit link function. The model is:
It is tempting to think of that as the answer, but what's not taken into account is the residual variance in i which has to be "integrated out". With a logistic link and a normal i residual, this calls for numerical integration so not something done by hand. But with a probit link the expression simplifies to using a standard univariate normal distribution function using as argument the expectation that you have on the right-hand side of logit, divided by the square root of a residual variance expression. This is shown on page 310 of our book Regression and Mediation Analysis using Mplus. You can also figure it out adding residuals to both of your 2 equations where the probit residual variance is 1.
Jonika Hash posted on Tuesday, October 10, 2017 - 3:21 pm
Hi Dr. Muthen,
Thank you so much for your help! I am so glad I asked. I am not as familiar with probit regression as I am with logit, so I am hoping I understand. Does this now look correct?:
Using the probit link function and taking residuals into account, I think my equations would now be: