Example 7.14 question
Message/Author
 Judy Black posted on Tuesday, June 11, 2013 - 8:25 am
Dear Dr. Muthen,

I have a question about Latent class analysis.

I firstly examined trajectories of A, in which there were 4 classes. Secondly, I examined trajectories of B, in which there were 5 classes. Then, I examined the association between trajectories A and trajectories B. I used the example 7.14 as an example. Here is my syntax:

DATA: FILE IS X:\Data\Desktop\datasetjune.dat;
VARIABLE:
NAMES ARE T1CESD T1BF
T2CESD T2BF
T3CESD T3BF;
MISSING IS ALL(-99.00);
ClASSES = CESD(4) BF(5);

ANALYSIS: TYPE=MIXTURE;
PARAMETERIZATION = LOGLINEAR;

MODEL: %OVERALL%
CESD WITH BF;
MODEL CESD:
%CESD#1%
[T1CESD T2CESD T3CESD];
%CESD#2%
[T1CESD T2CESD T3CESD];
%CESD#3%
[T1CESD T2CESD T3CESD];
%CESD#4%
[T1CESD T2CESD T3CESD];

MODEL BF:
%BF#1%
[T1BF T2BF T3BF];
%BF#2%
[T1BF T2BF T3BF];
%BF#3%
[T1BF T2BF T3BF];
%BF#4%
[T1BF T2BF T3BF];
%BF#5%
[T1BF T2BF T3BF];
OUTPUT:TECH1 TECH8;
 Judy Black posted on Tuesday, June 11, 2013 - 8:25 am
However, in the output, regarding the association between trajectories of CESD and trajectories of BF, it is like this:

Categorical Latent Variables

CESD#1 WITH
BF#1 -26.431 2.486 -10.631 0.000

The number '-26.431' should be the correlation between CESD#1 and BF#1, right?

My question is , why the correlation coefficient is not between -1 and 1. I checked the output of your 7.14 example, under same part, all estimates are between -1 and 1.

Or, do I misunderstand what these estimates mean?

I realized my question is too long... I would really thank you in advance.

Kind regards,
Judy
 Bengt O. Muthen posted on Tuesday, June 11, 2013 - 10:34 am
This estimate is not a correlation. It is a logit coefficient describing part of the association between your two latent class variables. The way to understand how the two relate is to look at the model-estimated probabilities for the cross-classification between the two, which is shown at the top of the results.
 Judy Black posted on Monday, June 17, 2013 - 7:27 am
Dear Dr. Muthen,

I found three kinds of model-estimated probabilities in the output, which are: 'Average Latent Class Probabilities for Most Likely Latent Class Pattern (Row)by Latent Class Pattern (Column)', 'Classification Probabilities for the Most Likely Latent Class Pattern (Row)
by Latent Class Pattern (Column)', and 'Logits for the Classification Probabilities for the Most Likely Latent Class Pattern (Row)
by Latent Class Pattern (Column)'.

Which one is the one you indicated?

One further question, by using this kind of syntax, I actually examined the latent class pattern between two variables (BF and CESD). I still found there were 4 latent classes on CESD and 5 latent classes on BF. If I examine the latent class of CESD and latent class of BF separately, will the results of latent class the same as I examined CESD and BF at the same time?

Best,
 Bengt O. Muthen posted on Monday, June 17, 2013 - 1:14 pm
None of those. Look instead higher up, right below MODEL FIT INFORMATION where you see the heading:

FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL

To answer your last question, no they won't be the same because the joint model has many more implications than either of the two separate ones. Only if all model parts fit perfectly would they be the same. To ensure no change, you can alternatively take a 3-step approach in line with web note 15 (the LTA section would be the most similar).
 Judy Black posted on Monday, June 24, 2013 - 1:42 am
Dear Dr.Muthen,

In my study, I would like to (1) identify latent classes of variable A at Time 1, Time 2 and Time 3,(2) identify latent classes of variable B at Time 1, Time 2, and Time 3, and (3) examine the association between latent class A and latent class B.

After reading the LTA section in the web note 15. I am not sure whether I should use the simple LTA or LTA with measurement invariance.

Thanks.

Best,
Judy
 Bengt O. Muthen posted on Monday, June 24, 2013 - 7:24 am
If you are using the same measure at the 3 time points, I would use the 3-step version of LTA with measurement invariance.

Note also that you can do this in a 1-step analysis, although the class formation will change a bit. Because your two processes are correlated, each helps in the estimation of the other. If the classes change compared to estimating each process separately, there may be useful things to learn about why that happens. I am saying this to encourage not always jumping into 3-step modeling.
 Judy Black posted on Tuesday, June 25, 2013 - 4:17 am
If I examine the latent classes together in 1-step in the joint model,I actually examine the latent class pattern on variable A and variable B, right? Then I may lose information regarding the latent class of each variable? Am I right about this?

My research question is to examine latent class of variable A first, and then examine latent class of Variable B secondly, and then examine the association between latent class A and latent class B. Variable A and Variable B are two different measures, but at the same 3 time points.

A 1-step procedure or a 3-step procedure?
 Bengt O. Muthen posted on Tuesday, June 25, 2013 - 8:44 am
Regarding the questions in your first paragraph, the 1-step method does not lose any information, but gives the same information as the 3-step method.

Both procedures answer your research question. But they do it a bit differently.

If you want to make sure that the A classes and the B classes obtained by separate analyses stay intact when you look at the association between the two types of classes, then you use 3-step.
 Judy Black posted on Thursday, July 04, 2013 - 5:47 am
Dear Dr. Muthen,

I finally decided to do a 3-step LTA. In the output, we found this:

LATENT TRANSITION PROBABILITIES BASED ON THE ESTIMATED MODEL

BF Classes (Rows) by CD Classes (Columns)

1 2 3 4

1 0.366 0.247 0.132 0.256
2 0.349 0.294 0.183 0.173
3 0.207 0.694 0.032 0.067
4 0.206 0.565 0.053 0.176
5 0.249 0.698 0.053 0.000

I am wondering how do these probabilities calculated? Is it possible in Mplus to compare these probabilities to see whether one probability is significantly different from the others?

Thanks.
 Bengt O. Muthen posted on Thursday, July 04, 2013 - 1:38 pm
These probabilities are computed from the model-estimated logit values in line with the chapter 14 discussion of logits.

You can created tests of probabilities using Model Constraint. For an example, see slides 48-50 of our Topic 6 handout.