Predicted probabilities, etc.
Message/Author
 Choong-Nam Kang posted on Thursday, May 03, 2007 - 2:02 pm
I'm trying to run two-stage path analysis with one categorical dependent variable in M plus.

I need to get predicted proabilites and changes of predicted probabilities. I also need robust standized errors adjusted by clustering a variable Z.

I could not find the ways of doing those.

Could you kindly help me to be able to those?
 Linda K. Muthen posted on Friday, May 04, 2007 - 8:19 am
By two stage, do you mean a model with two equations? Is the final dependent variable binary?
 Choong-Nam Kang posted on Monday, May 07, 2007 - 10:55 am
Dear Linda,

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.
 Linda K. Muthen posted on Monday, May 07, 2007 - 3:16 pm

y = a1 + b*x

u = a2 + b1*y + b2*x

therefore

u = a2 + b1 (a1 +b*x) +b2*x

u = a2 + b1*a1 + b1*b*x + b2*x

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))

You can vary the values of x.

For standard errors that take clustering into account, use TYPE = COMPLEX;
 Choong-Nam Kang posted on Wednesday, May 09, 2007 - 1:24 pm
Dear Linda

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?

Thank you very much for your help.
 Linda K. Muthen posted on Wednesday, May 09, 2007 - 2:19 pm
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
Hi There,

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)

v = a1 + b1*x
u = a2 + b2*v
y = a3 + b3*v + b4*u

Thank you very much!
 Bengt O. Muthen posted on Thursday, January 10, 2013 - 10:47 am
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
Thank you very much, Bengt!
 ABM posted on Sunday, March 05, 2017 - 4:22 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).

Thanks!
 ABM posted on Sunday, March 05, 2017 - 4:46 pm
And just to clarify my question about predicted probabilities, the 2007 question was about two equations. I only have one. Thanks.
 rgm smeets posted on Friday, July 26, 2019 - 12:56 am
I am running a LCA with some nominal indicators. I would like to calculate the probabilities for these nominal variables and found a formula online. Is it correct that I only need the estimated means for each level within the nominal variables to calculate the probabilities?
 Bengt O. Muthen posted on Friday, July 26, 2019 - 6:43 am
Yes, the logit means for each class. Using the UG chapter 14 formula.
 rgm smeets posted on Friday, July 26, 2019 - 9:35 am
Ok thank you. When Mplus gives the mean in the MODEL RESULTS, this is actually already the logit mean right?
 Bengt O. Muthen posted on Friday, July 26, 2019 - 9:42 am
right