Item response probabilites LTA
Message/Author
 Sebastian Daza posted on Sunday, April 24, 2011 - 5:53 pm
Hello,
I have just run a LTA model assuming invariance across time (3 waves). In order to understand better the meaning of the classes I have tried to obtain the estimated item-response probabilities for the respective observable variables categories (in my case 1 and 2). But, I haven't been able to find them. I have only got the class pattern thresholds. Is there any way to get those probabilities (item-response)?

Sebastian
 Sebastian Daza posted on Sunday, April 24, 2011 - 7:46 pm
What I am trying to get using MPLUS is something like this (for a LTA model):

Rho estimates (item-response probabilities):
(All times)
Response category: 1:
Status: 1 2 3
tab1 : 0.0191 0.9319 0.7290
alc1 : 0.1394 0.9419 0.7190
mar1 : 0.0050 0.9215 0.0224
coca1 : 0.0014 0.1752 0.0052

Response category: 2:
Status: 1 2 3
tab1 : 0.9809 0.0681 0.2710
alc1 : 0.8606 0.0581 0.2810
mar1 : 0.9950 0.0785 0.9776
coca1 : 0.9986 0.8248 0.9948

I got this output from SAS (PROC LTA).
Thank you.
 Linda K. Muthen posted on Monday, April 25, 2011 - 8:25 am
You would need to compute the probabilities yourself in this case:

prob = 1 / (1 + exp(threshold)
 Sebastian Daza posted on Wednesday, April 27, 2011 - 6:57 am
Thank you Linda for your reply. I am new in Mplus and now I am trying to explain the transition probabilities using covariates. Following the example 8.13 (covariate and interaction) in the UG, I have tried this model:
CLASSES = c1(3) c2(3);

MODEL:

%OVERALL%

c2 ON c1 male;
c1 ON male;

I assume measurement invariance across times (in my example two waves).

My problem is that I don't know how to exactly interpret the coefficients. I want for example to get the odds ratio of moving from class 1 (time 1) to class 2 (time 2) between males and females, but I am not sure which coefficient represents that figure in the output.

Could you give me any clues? Thank you in advance,
Sebastian
 Sebastian Daza posted on Wednesday, April 27, 2011 - 6:58 am
Here is the output:

Categorical Latent Variables

C2#1 ON
C1#1 4.377 0.408 10.729 0.000
C1#2 2.243 0.616 3.642 0.000

C2#2 ON
C1#1 0.081 0.197 0.412 0.680
C1#2 2.764 0.459 6.020 0.000

C2#1 ON
MALE 0.372 0.140 2.648 0.008

C2#2 ON
MALE 0.358 0.140 2.546 0.011

C1#1 ON
MALE 0.629 0.098 6.433 0.000

C1#2 ON
MALE 0.706 0.149 4.733 0.000

Intercepts
C1#1 0.628 0.072 8.686 0.000
C1#2 -1.340 0.141 -9.479 0.000
C2#1 -2.829 0.380 -7.455 0.000
C2#2 -1.427 0.147 -9.677 0.000
 Linda K. Muthen posted on Wednesday, April 27, 2011 - 9:13 am
See the Nylund dissertation on the website. Please keep your posts to one window.
 Sebastian Daza posted on Wednesday, April 27, 2011 - 9:42 pm
Thank you Linda. There is not an explanation of a model like 8.13 (UG) in the Nylund dissertation: LTA WITH A COVARIATE AND AN INTERACTION.

Regards.
 Linda K. Muthen posted on Thursday, April 28, 2011 - 10:20 am
In Example 8.13, the interaction is c ON x varying across the classes of c1. You need to use the information in the dissertation to generalize to other examples.