Yes, I have two equations within my model. First equation has a continuous dependent variable and second equaiton has a binary variable (final dependent variable). I'm trying to run a path analysis with ML estimation. I need to get predicted probabilities and changes of predicted probabilities across varying independent variables (most of them are binary, too). I also need to robust standized error adjusted by clustering a certain variable with one-tailed test.
I would really appreciate it, if you can help me find the way out.
Thank you for your advice. However, what I really want to know is whether there are commands to get those statistics in M plus and the way of inputting coomands to get those in M plus, if any. Or should I calculate those by myself?
We don't calculate probabilities when covariates are involved because they depend on the value of the covariate that is chosen. You will need to calculate them yourself.
J Owens posted on Thursday, January 10, 2013 - 9:09 am
I was wondering how you would recommend calculating predicted scores for a path model in which the final dependent variable is continuous (GPA) but one of the two prior dependent variables is binary. The equations above are very helpful in terms of calculating the predicted probabilities for my intervening binary dependent variable, but I'm wondering how to use these probabilities or underlying logit values in calculating the final dependent variable, GPA.
My equations look like this: (v is a continuous dependent variable, u is a binary dependent variable, and y is a continuous dependent variable)
If you use estimation by WLSMV or Bayes, the continuous latent response variable u* is used instead of the binary u so that only linear relationships are considered and in this case you simply express the "reduced-form" inserting the v and u equations in the y equation so that y becomes a function of x.
If you use ML, things are more complex because the binary u is the predictor of y. For that case, see formulas in
Muthén, B. (2011). Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus.
which is on our web site.
J Owens posted on Thursday, January 10, 2013 - 12:20 pm
On May 7, 2007, you discussed how to calculate predicted probabilities, noting that this would be the solution:
"logit = -a2 + b1*a1 + b1*b*x + b2*x Note that Mplus estimates a threshold for a2. To make the threshold an intercept, the sign must change. With ML and the logit link which is the default, the probability of u=1 is: 1 / (1 + exp(-logit))"
My question: Is the above formula essentially the same as the below formula, which I've used with logistic regression?:
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).