LTA with continuous indicators
Message/Author
 Xiao-min Li posted on Sunday, November 16, 2014 - 7:47 am
Dear Doctors:
I'm a Chinese student majoring in psychology in Beijing Normal University and now I am writing message to ask for help.
My graduate teacher wants me to analyze 2-wave longitudinal data (all variables are continuous) to explore behavior patterns and their transition across time. I have download data and syntax examples provided by official website but just found that all examples are about categorical variables. I¡®m wondering that whether I can run LTA with continuous variable. And if it is ok, following are some questions puzzling:
1. Whether estimation method or other specification should be changed in contrast to categorical data.
2. According to examples, number of category should be set in advance, which parameter in output can I use to test its appropriateness except for BIC and AIC for my graduate teacher ask me to provide more evidence;
3. In Latent Class Analysis, savedata syntax can save cprob to help researchers make sure the class each individual belongs to, so is it also possible in latent transition analysis? If possible, how to write the syntax?
Best regards!
 Bengt O. Muthen posted on Sunday, November 16, 2014 - 11:50 am
Yes, LTA can also use continuous variables as latent class indicators. In fact, all variable types are allowed, including latent variables, and combinations.

1. No.

2. Apart from BIC you can also use the RESIDUAL option of the OUTPUT command.

3. Try the same approach as for LCA.
 Xiao-min Li posted on Sunday, November 16, 2014 - 5:17 pm
ANALYSIS: ALGORITHM=INTEGRATION;
TYPE=MIXTURE;
MODEL:
%OVERALL%
c2 on c1;
MODEL c1: %c1#1%
[h11\$1] (1);
[h12\$1] (2);
[h13\$1] (3);
%c1#2%
[h11\$1] (6);
[h12\$1] (7);
[h13\$1] (8);
%c1#3%
[h11\$1] (11);
[h12\$1] (12);
[h13\$1] (13);

MODEL c2: %c2#1%
[h21\$1] (1);
[h22\$1] (2);
[h23\$1] (3);
%c2#2%
[h21\$1] (6);
[h22\$1] (7);
[h23\$1] (8);
%c2#3%
[h21\$1] (11);
[h22\$1] (12);
[h23\$1] (13);

OUTPUT: TECH1 TECH8 TECH11 TECH14 TECH15

But warning is output:
*** WARNING in MODEL command
All variables are uncorrelated with all other variables within class.
Check that this is what is intended.
*** ERROR
The following MODEL statements are ignored:
* Statements in Class %C1#1% of MODEL C1:
[ H11\$1 ]

Thanks!
 Bengt O. Muthen posted on Monday, November 17, 2014 - 7:56 am
You don't use the \$1 notation with continuous variables.
 Xiao-min Li posted on Monday, November 17, 2014 - 6:15 pm
Got it, and model executed successfully, thanks very much!
 Xiao-min Li posted on Monday, November 17, 2014 - 6:43 pm
One more question, I-state objects analysis (ISOA) can also be endorsed to explore transition of pattern across time? Is there any difference between ISOA and LTA? In assumption or output? Thanks!
 Linda K. Muthen posted on Tuesday, November 18, 2014 - 7:38 am
I don't know what ISOA is. Do you have a reference that describes it?
 Xiao-min Li posted on Tuesday, November 18, 2014 - 6:26 pm
L. R. Bergman, B. M. El-Khouri (1999) Studying Individual Patterns of Development Using I-States as Objects Analysis (ISOA)Biometrical Journal 41 (1999) 6, 753-770.
Thanks!
 Bengt O. Muthen posted on Wednesday, November 19, 2014 - 12:22 pm
I glanced at the article and although there are similarities in goals, there seems to be many differences in methodology between ISOA and LTA. For one, ISOA uses cluster analysis whereas LTA uses mixture modeling. But I can't say more about ISOA since I have not studied it.
 Xiao-min Li posted on Thursday, November 20, 2014 - 4:05 am
Thanks a lot!
 weiyi cheng posted on Wednesday, January 25, 2017 - 8:07 pm
Hi, I'm running a LTA model with 3 classes at two time points. Somehow, I got same transition probabilities for each time 1 class category. That can't be right I suppose? What might cause this then? I appreciate your insight!

C1 Classes (Rows) by C2 Classes (Columns)

1 2 3

1 0.369 0.403 0.228
2 0.369 0.403 0.228
3 0.369 0.403 0.228
 Bengt O. Muthen posted on Thursday, January 26, 2017 - 3:54 pm
 Anshuman Sharma posted on Saturday, October 07, 2017 - 8:15 am
Hi Dr. Muthen,

My objective is to carry out LTA with continuous variables as latent class indicators. I have performed all the three steps as per webnote 15 (Subheading - "Estimating latent transition analysis using the 3-step method"). I can't see any other model fit information except AIC and BIC in the output of the last step.

VARIABLE:NAMES ARE y1-y8 cl1 cl2;
USEVARIABLES ARE cl1 cl2;
CLASSES = c1(3) c2(3);
Nominal are cl1 cl2;

(Only showing a part of model commands just to let you know about the classes)

My questions are:
How can I see any other model fit information?
Also, if you could please suggest, is it important to consider model fit information in step 3 when I have already assessed the model fit of latent classes (c1 and c2 separately) in previous steps.

Thanks and regards,
Anshuman
 Bengt O. Muthen posted on Saturday, October 07, 2017 - 12:50 pm
Q1: There are not really any very useful fit statistics for continuous mixture modeling like LTA. Instead you have to work with a series of model and compare them using BIC. That is, models that differ by e.g. the number of classes or differ by imposing and not imposing measurement invariance, etc.

Q2: It could be useful (by using neighboring models) but perhaps not necessary.
 Anshuman Sharma posted on Saturday, October 07, 2017 - 3:22 pm
Prof. Muthen.

Regards,
Anshuman
 Brittany Crawford posted on Wednesday, November 07, 2018 - 3:37 am
When conducting an LTA with categorical variables, response probabilities are generally set to be equal across time by placing \$1 after each parameter. I want to compare models with full invariance and full noninvariance, but my LTA has continuous indicators. How does one fix the item-response probabilities to be equal across two timepoints when working with continuous indicators? I'm assuming this is done using "@" rather than "\$", but I'm uncertain which value(s) should follow "@". Is it a single/standard value? Are there values that are output when running the freely estimated model? If so, where are these values in the output?
 Bengt O. Muthen posted on Wednesday, November 07, 2018 - 5:35 pm
Continuous indicators work with intercepts, so for one class:

[y1-y5] (1-5);
 Brittany Crawford posted on Thursday, November 08, 2018 - 8:14 pm
That worked well. Thank you for the quick response!
 EH posted on Monday, March 11, 2019 - 3:18 am
Dear Dr. Muthén,

I am running a 4-class LTA with two latent variables for two timepoints (CLASSES = T1(4) T2(4);) I tried to run the two LCA's in one script in order to check measurement invariance later on.

I defined the latent variables for Model T1 and for Model T2 (%OVERALL% MODEL T1: PET1 by 1T1, 2T1, 3T1; MWT1 by 4T1, 5T1, 6T1; %T1#1 (2,3 and 4)% [MWT1]; [PET1];
MODEL T2: PET2 by 1T2, 2T2, 3T2; MWT2 by 4T2, 5T2, 6T2; %T2#1 (2,3 and 4)% [MWT2]; [PET2];

Yet I always get the same warning: *** ERROR in MODEL command
No OVERALL or class label for the following MODEL statement(s):
PET1 BY

Yet I should define my latent variables under the MODEL T1 and T2 commands, right?

 Bengt O. Muthen posted on Tuesday, March 12, 2019 - 5:58 pm
After saying e.g.

Model T1:

%t1#1%

.....

%t1#2%

....

See UG examples.
 EH posted on Wednesday, March 13, 2019 - 11:55 am
Dear dr Muthén,

Thank you for your response. Unfortunately I cannot find a UG example using latent variables as indicators. To check for measurement invariance I specified my latent factors under the %overall% command.

Can I check measurement invariance over time and of classes over time?

Because running a model in which I specified (metric and scalar) measurement invariance for the variables and constrained the means of the classes per time indicated to be equal did not seem to work:

CLASSES = T1(4) T2(4);

%overall%

PET1 by 11U-14U (1-4);
MWT1 by 15U-17U (5-7);
PET2 by 21U-24U (1-4);
MWT1 by 25U-27U (5-7);
[11U - 21U] (111);
...

MODEL T1:

%T1#1%
[MWT1*] (A);
[PET1*] (B);
PET1 WITH MWT1*;

%T1#2%

[MWT1*] (C);
[PET1*] (D);
PET1 WITH MWT1*;

...

MODEL T2:

%T2#1%
[MWT3*](A);
[PET3*](B);
PET3 WITH MWT3*;

...
 Bengt O. Muthen posted on Wednesday, March 13, 2019 - 4:53 pm
This looks like a good start. Note, however, that for identification factor means need to be fixed at zero in at least one place - so in one class at one time point.