Latent Transition Analysis with Covar...
Message/Author
 Kerry M Green posted on Wednesday, June 25, 2008 - 8:34 am
I'm trying to run an LTA with 4 time points and 3 classes for each time point and a single covariate (3 level variable modeled with dummy variables)influencing the transitions, which I modeled as an interaction. I can't seem to figure out if the transition probabilities average over the covariate or are calculated without the covariate. My goal is to determine if the transition probabilities differ by level of the covariate. Can I get this matrix by each level of the covariate?

Also, how do I interpret the estimate given for regression of the classes (e.g., C1#1, C1#2) on the covariate?

 Linda K. Muthen posted on Wednesday, June 25, 2008 - 9:45 am
They average over the covariates. There is not automatic way to get this matrix for each level of the covariate. See the Nylund dissertation on the website for detailed information about LTA.
 Kerry M. Green posted on Tuesday, July 22, 2008 - 8:50 am
Thanks for your help. I'm now having trouble with setting my reference class. I tried changing the starting values, but that didn't work. I want no alcohol use to be the reference class (coded as 0 for all the alcohol variables), but with the output below Class 3 is the problem alcohol class (1s on all the alcohol variables). It is a 3 class model with 4 time points.

CLASSES = c1(3) c2(3) c3 (3) c4 (3);
ANALYSIS: TYPE = MIXTURE MISSING;
MODEL:
%OVERALL%
c2 on c1;
c3 on c2;
c4 on c3;
MODEL c1:
%c1#1%
[alcopp6r\$1 - alcsoc6\$1*15] (1-7);
%c1#2%
[alcopp6r\$1 - alcsoc6\$1*1] (8-14);
%c1#3%
[alcopp6r\$1 - alcsoc6\$1*-15] (15-21);

MODEL c2:
%c2#1%
[alcopp7r\$1 - alcsoc7\$1*15] (1-7);
%c2#2%
[alcopp7r\$1 - alcsoc7\$1*1] (8-14);
%c2#3%
[alcopp7r\$1 - alcsoc7\$1*-15] (15-21);

MODEL c3:
%c3#1%
[alcopp8r\$1 - alcsoc8\$1*15] (1-7);
%c3#2%
[alcopp8r\$1 - alcsoc8\$1*1] (8-14);
%c3#3%
[alcopp8r\$1 - alcsoc8\$1*-15] (15-21);

MODEL c4:
%c4#1%
[alcopp9r\$1 - alcsoc9\$1*15] (1-7);
%c4#2%
[alcopp9r\$1 - alcsoc9\$1*1] (8-14);
%c4#3%
[alcopp9r\$1 - alcsoc9\$1*-15] (15-21);
 Bengt O. Muthen posted on Tuesday, July 22, 2008 - 7:09 pm
For u = 0, 1 a threshold of -15 ensures u = 1 and a threshold of +15 u = 0. Looks like class 1 and 3 should be switched.
 Louise Lafortune posted on Tuesday, August 05, 2008 - 12:02 pm
Hi,
I'm running a LTA with 2 time points and would like to know whether transition probabilities vary by gender while controlling for age; and vice versa. Age is categorical (65-74; 75-84;85+ years).

I tried regressing on both age and gender but then I can only estimate gender specific transition probabilities one age group at a time and not across age groups. Yes I read chapter 13...a thousand times. Did I miss something?

Instead, would it make sense to use a "known class" for gender and regress on knownclass and age to get my gender transition probabilities while controlling for age?

Here's what I have in mind:

CLASSES = cg (2) c1(4) c2(5);
KNOWNCLASS = cg (sex=0 sex=1);

ANALYSIS: TYPE = MIXTURE;

MODEL:
%OVERALL%
c2#1-c2#4 on c1#1-c1#3 cg age;

Thanks! I'm running out of ideas here...and the reviewers will be asking for this!
 Bengt O. Muthen posted on Tuesday, August 05, 2008 - 7:05 pm
It sounds like you want the marginal transition effect for a certain covariate from a model with several covariates. If you create a gender knownclass, a transition probability table for c1 x c2 would give you what you want. I don't recall if this is what the output provides, but do try. Otherwise, perhaps you have to estimate say the gender effect at each age and then weight the transitions probabilities with the frequencies of the ages.
 Louise Lafortune posted on Tuesday, August 05, 2008 - 7:42 pm
Exactly, I want the marginal transition effect. I did run the model and the output gives me the mean Cg#1 and the regression coefficients for each (C2#. on Cg#1) and (C1#. on Cg#1). It also gives me the overall transition probabilities (c1 x c2) and the (Cg classes x C1 classes).

Now, I’m not certain how to calculate the transition probabilities with a known class (e.g. gender). For example, to estimate transition probabilities from C1#1 to C2#1 when female=1. Do I just add the following terms to calculate the log odds (referring to your 2x2 table in chapter 13): a1 + b11 + (Cg#1) + (C2#1 on Cg#1)? For male, I would just use the table as it is since male=0.

Thank you for your precious help.
LL
 Bengt O. Muthen posted on Wednesday, August 06, 2008 - 5:29 pm
The LTA dissertation by Karen Nylund on our web site under Papers, Latent Transition Analysis gives details on how to compute transition probabilities as a function of covariates.
 xybi2006 posted on Tuesday, February 24, 2015 - 6:39 pm
Dear Dr. Muthen,
I used latent class analysis to look at how individuals cluster into distinctive groups based on a set of symptoms. Besides only looking at it cross-sectionally, I wanted to know how consistent these clusters are over time (I have five waves data). Should I use latent transition analysis to modeling this question?
Thank you,
 Bengt O. Muthen posted on Wednesday, February 25, 2015 - 1:32 pm
Yes, that would be natural. But start with 2 timepoints to get into it.
 Raghav Ramachandran posted on Tuesday, May 05, 2015 - 4:05 pm
Dr. Muthen,

I am running a power simulation for my LTA study with multiple covariates. As a result, I ran MC example 8.14 (LTA with a continuous covariate) with multiple covariates. I fixed the mean and variance of the other covariates. I also estimated the regression of c1 on all covariates and the regression of the c1-c2 transition (c2 regression under class-specific c1 commands) on all covariates. Apart from those changes in the model and model population statements, I did not make any other changes to the example.

However, when I run the program, it ignores the model population statements regressing the c1-c2 transition on any covariates except for the first and throws this as an error. Please let me know if you have any thoughts on what might be causing this error and thanks for understanding.

Thanks,
Raghav
 Linda K. Muthen posted on Tuesday, May 05, 2015 - 4:35 pm
 Alvin  posted on Monday, August 10, 2015 - 11:48 pm
Hi Bengt/Linda, I wanted to do a subsidary analysis of crude predictors of the transitional classes. I did a three-model LTA across two time points with full measurement invariance. Then looked at covariates using the three-step approach, all within Mplus. My question is would be possible to extract class memberships of the transitional classes (I am particularly interested in those who transitioned from T1 asymptomatic to comorbid at T2). I tried to do this using (save cprob) but didn't work. Should I look at class memberships at each time point and then derive transition patterns (e.g. subset those who are in class 2 at T1 and class 3 at T1, assuming that class 2=asymptomatic and class 3=comorbid). Or is there a better way to do this? Your advice much appreciated.
 Bengt O. Muthen posted on Tuesday, August 11, 2015 - 1:59 pm
The cprobs should come out for the combination of all the classes, so you can get the transition values you want.

If you have problems, send relevant output and license number to support.
 Angela Sorgente posted on Friday, November 11, 2016 - 3:17 pm
Hi Bengt/Linda,
I'm running a LTA model. I have two time points. At each time 3 classes. I have some concerns about the auto-regressive path "C2 on C1", for two reasons:

1. Why "C2 on C1" results in 6 coefficients when the model is unconditional, while 4 coefficients when covariates are added?

UNCONDITIONAL MODEL

C2#1 ON
C1#1 0.569 0.063 8.959 0.000
C1#2 0.293 0.041 7.109 0.000
C1#3 0.000 0.044 0.002 0.998

C2#2 ON
C1#1 0.094 0.043 2.207 0.027
C1#2 0.195 0.031 6.308 0.000
C1#3 0.014 0.131 0.107 0.915

CONDITIONAL MODEL

C2#1 ON
C1#1 14.186 8.637 1.643 0.100
C1#2 13.027 8.638 1.508 0.132

C2#2 ON
C1#1 6.313 3.175 1.988 0.047
C1#2 6.309 3.127 2.017 0.044

2. In the unconditional model, the coefficients seems too high (and consequently their ORs). Is this normal? What could be wrong?

Thanks,
Angela
 Bengt O. Muthen posted on Friday, November 11, 2016 - 4:57 pm
 Angela Sorgente posted on Sunday, July 15, 2018 - 2:34 am
Hi,
I'm studying how to include covariates and distal outcomes in a LTA model using a 3-step approach. I actually succeeded in it (also requiring measurement invariance).

My only concern is about auxiliar variables.
Am I correct in affirming that specifications about auxiliar variables like:
(R)
(E)
(R3STEP)
(DU3STEP)
(DE3STEP)
(DCON)
(DCAT)
have to be used only for LCA?

Instead for LTA models covariates are specified as:
c1 ON x;
c2 ON c1;
while outcome are tested using model constraint in order to test means equality?

thanks, Angela
 Bengt O. Muthen posted on Sunday, July 15, 2018 - 2:41 pm
Right. For LTA, see

Asparouhov, T. & Muthén, B. (2014). Auxiliary variables in mixture modeling: Using the BCH method in Mplus to estimate a distal outcome model and an arbitrary second model. Web note 21.
 Macarena Larrain posted on Thursday, August 09, 2018 - 12:33 am
Dear Dr. Muthén,
I am running a LTA using the three-step approach according to Web Note 13 and Nylund-Gybson et al (2014) paper. I have three classes at each of both times. I am specially interested in the interactions of the covariates on the transition probabilities and would also need to try out the model with other covariates.

I obtain the following message:
ONE OR MORE MULTINOMIAL LOGIT PARAMETERS WERE FIXED TO AVOID SINGULARITY
OF THE INFORMATION MATRIX....

Moreover, the output give estimates only for latent class patterns 1 1, 2 1 and 3 1.
I am not sure why this happens, if my syntax is correct and how should I interpret the results.

My syntax is:

%OVERALL%
T2 ON T1;
T1 ON PIPRE MATCOUR;
T2 ON PIPRE MATCOUR MKT;
Model T1:
%T1#3%
[T1CLASS#1@3.621];
[T1CLASS#2@0.883];
T2 ON PIPRE MATCOUR MKT;
%T1#2%
[T1CLASS#1@1.646];
[T1CLASS#2@5.163];
T2 ON PIPRE MATCOUR MKT;
%T1#1%
[T1CLASS#1@-10.567];
[T1CLASS#2@-2.714];
T2 ON PIPRE MATCOUR MKT;
Model T2: ... (has also fixed values)
 Bengt O. Muthen posted on Thursday, August 09, 2018 - 2:08 pm
 Daniel Lee posted on Tuesday, February 12, 2019 - 8:58 pm
Hello, I too am having trouble with changing the reference class for an LTA model with covariate/interaction. In particular, I would like to set "C2#3" (in "C2#3 on rdea") as the reference class, not "C2#6" (which seems to be the default). Thank you for your help.

Model:
%OVERALL%
C2 on C1;
C1 on sex eduea rdea strsea;
Model C1:
%C1#1%
[centEA humEA pubEA prvEA assEA natEA minEA] (em1-em7);
centEA humEA pubEA prvEA assEA natEA minEA (ev1-ev7);
C2#1 ON rdea (g11);
C2#2 ON rdea (g21);
C2#3 ON rdea (g31);
C2#4 ON rdea (g41);
C2#5 on rdea (g51);
%C1#2%
[centEA humEA pubEA prvEA assEA natEA minEA] (em8-em14);
centEA humEA pubEA prvEA assEA natEA minEA (ev8-ev14);
C2#1 ON rdea (g12);
C2#2 ON rdea (g22);
C2#3 ON rdea (g32);
C2#4 ON rdea (g42);
C2#5 on rdea (g52);
%C1#3%
[centEA humEA pubEA prvEA assEA natEA minEA] (em15-em21);
centEA humEA pubEA prvEA assEA natEA minEA (ev15-ev21);
C2#1 ON rdea (g13);
C2#2 ON rdea (g23);
C2#3 ON rdea (g33);
C2#4 ON rdea (g43);
C2#5 on rdea (g53);
 Bengt O. Muthen posted on Wednesday, February 13, 2019 - 5:54 pm
You want to switch the estimates of the parameters that describe the relationships between the latent classes and the outcomes
 Daniel Lee posted on Thursday, February 14, 2019 - 8:32 am
Do you mean switching like this?

Model:
%OVERALL%
C2 on C1;
C1 on sex eduea rdea strsea;
Model C1:
%C1#1%
[centEA humEA pubEA prvEA assEA natEA minEA] (em1-em7);
centEA humEA pubEA prvEA assEA natEA minEA (ev1-ev7);
C2#1 ON rdea (g11);
C2#2 ON rdea (g21);
C2#4 ON rdea (g31); !class 3 reference
C2#5 ON rdea (g41);
C2#6 on rdea (g51);

*** ERROR in MODEL command
No reference to the slopes of the last class is allowed.

How would I switch estimates of the parameters that describe the effect of X on the transition
 Bengt O. Muthen posted on Thursday, February 14, 2019 - 5:27 pm
No I mean switch the parameters of the measurement model that give the classes their meaning, so the Y | C part of the model. E.g.

%C#1%
[y*1];
%C#2%
[y*-1];

Would be changed to

%C#1%
[y*-1];
%C#2%
[y*1];
 JuliaSchmid posted on Wednesday, January 15, 2020 - 8:54 am
Hi there

I'd like to run a LTA with a covariate. We have 5 patterns (with 6 indicators). I want to examine if the transition probabilities are influenced by a binary variable (= Interventiongroup vs. Controlgroup).

I created my input-file in accordance with the User Guide Chap. 8.13.:

usevar = CCPT1 INT1 Einst1 Kraft1 SR1 HrFK1 CCPT2 INT2 Einst2 Kraft2 SR2 HrFK2;

idvariable = ID;
missing = all(-99);
cluster = class;
classes = cg(2) c1(5) c2(5);
knownclass = cg (group = 0 group = 1);

analysis:
Processor = 3;
Type = mixture complex;
Starts = 10000 500;
STITERATIONS = 500;

model:

%Overall%
c1 c2 on cg;

model cg:

%cg#1%
c2 ON c1;
%cg#2%
c2 ON c1;

model c1:

%c1#1%
[CCPT1 INT1 Einst1 Kraft1 SR1 HrFK1] (m1-m6);
....

model c2:

%c2#1%
[CCPT2 INT2 Einst2 Kraft2 SR2 HrFK2] (m1-m6);
...

I have three questions:
1) is my input file correct?
2) Could you please explain the logic overall- and model-command?
3) I have hard times to understand the output. Where can I see, if the covariate has a significant influence on the transition probabilities?

Thank you very much in advance!
 Bengt O. Muthen posted on Wednesday, January 15, 2020 - 11:11 am
1) Looks correct

2) The Overall statements refer to model parameters that don't vary across classes. The Model C statements refer to model parameters that vary over classes but only the classes of the class variable mentioned in Model C. For instance, your Model c1 and Model c2 statements refer to parameters that vary over only those classes, not the cg classes. If you want full generality, you use the "dot" approach, for instance

%cg#1.c1#1.c2#1%
---

and so on for each combination of classes.

3) You have 2 sets of c2 ON c1 and if their difference is significant it tells you that the transition probabilities are different. You can express those difference using Model Constraint, either in the logit scale provided in the output or in the scale of transition probabilities. This is described in the Mplus Web Note 13:

Muthén, B. & Asparouhov, T. (2011). LTA in Mplus: Transition probabilities influenced by covariates. Mplus Web Notes: No. 13. July 27, 2011.
 shonnslc posted on Thursday, January 30, 2020 - 10:23 am
Hi,

I am doing latent transition probabilities influenced by covariates using Mplus. I have some questions:

1. If I understand the web notes correctly, using Parameterization 2, g11 actually is not the coefficient for the interaction term since g11 is the sum of g1 and g11 using Parameterization 1. Therefore, on page 21 of the notes, although the estimate 1.963 is statistically significant, it doesn't mean the interaction term is significant. Am I right?

2. Using Parameterizaton 1 (pg 7), is b11 a dummy variable (1 = first class in C1, 0 = third class in C1) and b12 (1 = second class in C1, 0 = third class)?

Thank you!
 Bengt O. Muthen posted on Friday, January 31, 2020 - 11:39 am
1. Right. The interaction is captured by the difference between g11, g12, and g13 and between g21, g22, g23, that is, the difference between the rows.

2. Right. So for a 2 x 2 case without x, you have

a+b 0
a 0

where b is C2#1 on C1#1.
 Nicole S posted on Thursday, April 02, 2020 - 6:12 pm
Hi there

I am working with a model based on LTA syntax for a 2 level categorical variable at two time points.

I'd like to examine covariates in this model. However, although I have a very large total N (more than 10,000) there is a very large difference in the ns for each category (e.g. n = 700 vs. n > 10000), and the transition ns between categories are (relatively speaking) very small (around n = 150 or less).
In other models, the situation is worse (e.g. transition n = 20).

Are there any clear guides on determining an appropriate number of covariates in these instances? or for LTA models in general? I've been looking myself but haven't come across anything, other than rules of thumb related to logistic regressions more generally.

Cheers.
 Bengt O. Muthen posted on Saturday, April 04, 2020 - 11:13 am
I am not aware of such written guidelines and your case is quite specific. You can do your own MonteCarlo study in Mplus to she light on it.
 shonnslc posted on Saturday, May 09, 2020 - 10:13 pm
Hi,

I have a question about LTA with transition probabilities influenced by a covarite X. I read the Webnotes and UG 8.14. It seems that there is an assumption that the covariate X will influence the latent class formation of C1 and C2. I am wondering if this is the default assumption or can I not to influence the latent class formation when including covariate x in UG 8.14 model. Thank you!
 Bengt O. Muthen posted on Monday, May 11, 2020 - 1:46 pm
Yes, X will influence class formation to some extent. We describe a multi-step procedure if you want to avoid this in the LTA section of Web note 15.