LTA mover/stayer: thresholds PreviousNext
Mplus Discussion > Latent Variable Mixture Modeling >
 Luca Mariotti posted on Friday, October 12, 2007 - 6:12 am
dear Linda and Bengt,

I am working on a LTA and trying to include a mover/stayer variable in the model.
I am using the following paper as examples: Mplus User Guide (exp 8.14), Nylund 's dissertation (2007), and Kpaln (2006), which are all in your webpage.

I am a bit confuse bacause of the different threshold values used in these examples.
Nylund uses -15 for the intercepts and 30 and -45 for the "b" coefficients.
Muthen and Kaplan use 10 and -10 for the intercepts and 20 for the "b" coefficients.

I am modeling a 3 time points LTA with the following number of classes:
CLASSES c(2) c1(4) c2(4) c3(4)

could you please help me to understand the meaning of these threshold values in order to be able to apply them to my model?

thanks a lot in advance,

 Linda K. Muthen posted on Friday, October 12, 2007 - 9:41 am
The values of a and b should be selected such that the sum is a large value, for example, if a is -15 b should be 30 so that the sum is 15. If a is 15 b should be -30 so that the sum is 15. The sum is used as the logit value determining the probability of transitioning.
 Luca Mariotti posted on Friday, October 12, 2007 - 10:47 am
thanks Linda,

thus, a sum (a+b) equal to -15 represent a probability of 1, whereas a sum equal to +15 represent a probability of 0. Is it correct?
Then, if this is the case, what is the menaing of values larger than -+15?
Has -+10 the same meaning as -+15?
Furthermore, represent -+3 very low and very high probabilities?

thanks again

 Linda K. Muthen posted on Friday, October 12, 2007 - 3:22 pm
Yes. Plus or minus 10 or plus or minus 15 doesn't matter. It just needs to be a large value. Plus or minus 3 may not be large enough.
 Luca Mariotti posted on Saturday, October 13, 2007 - 10:00 am
Thanks Linda,

It seems to work when I claculate a LTA for two time points. In this case if I check the "most likely latent class pattern" I see clearly that the "stayer" class reports values only for the "stayer" patterns, i.e. 2111, 2222, 2333, 2444. The rest is zero. The corrsponding patterns for the "mover" class are close to zero. Is it a clue that my model is corectly specified???

However, when i calculate a model with three time points the "stayer" patterns are all zero but for the 2111 pattern. Furthermore, the same patterns for the "mover" class (i.e. 1111,1222,1333,1444) have in this case relatively large values. Shouldn't these individuals be classified in the "stayer" class???

I really don't know how to interpret these results!!

thanks a lot in advance

 Linda K. Muthen posted on Saturday, October 13, 2007 - 10:33 am
Please send your output and license number to
 Stephanie Fitzpatrick posted on Friday, March 13, 2009 - 8:11 am
I am running LTA following Nylund et al. exactly. I have 3 timepoints and 3 classes made from two continuous variables. I fixed my intercepts at -15 for the stayers as well as the b coefficients at 30 and -45 just as in Nylund et al. However, I keep getting this message:

20 22 26 15 21

Do I need to fix the parameters for the movers as well b/c perhaps there is not much movement at least between time 1 and time 2?
 Bengt O. Muthen posted on Friday, March 13, 2009 - 2:44 pm
Can't be diagnosed without seeing the context - please send your input, output, data and license number to
 Christian M. Connell posted on Monday, May 16, 2011 - 11:42 am
I am setting-up a mover-stayer model using the Nylund dissertation example from appendix H as a guide. I have 2 timepoints, 3 classes per wave.
A problem is recurring where I get a subset of movers (c#1) who are actually stayers in the reference condition. Since you can't include references to the slope of the reference class, is there a way to reduce/eliminate the possibility of stayers being mis-classified as movers?
 Linda K. Muthen posted on Tuesday, May 17, 2011 - 8:51 am
Please send your output and license number to
 Levent Dumenci posted on Monday, August 01, 2011 - 7:11 am
I would like to run example 8.14 with continuous outcome variables. What should I replace the logit tresholds (e.g., @-15) with?
 Bengt O. Muthen posted on Monday, August 01, 2011 - 11:02 am
The c on c logits aren't affected by the type of outcome, but perhaps you refer to the u logits. In ex8.14 they are used to specify that "the stayers represent individuals who do not exhibit problem behaviors." I don't know that this tying together stayers with problem-free responding is a necessary feature of mover-stayer modeling or could be eliminated (see the references we give). I don't know how to handle that feature with continuous outcomes unless you use a two-part model for the outcomes and specify that these individuals are in the zero portion.
 Julia Lee posted on Thursday, April 12, 2012 - 2:34 pm
Hi Linda,
I wrote to you about my LTA mover-stayer question quite some time back. You provided an excellent explanation about OVERALL and MODEL C. However, I am still not clear about the interpretation of the syntax below:
1. Would you kindly explain what is the interpretation of the model specific (i.e., MODEL C.C1 at time 1) thresholds for the stayer group based on this syntax below?
2. If it is a 5-class model, would it then be 2, 1, 0, -1, -2?
Thank you.

[x11-x15] (1-5);
[x11-x15] (6-10);
[x11-x15] (11-15);
[x11-x15] (16-20);

[x11-x15*2] (21-25);
[x11-x15*1] (26-30);
[x11-x15*-1] (31-35);
[x11-x15*-2] (36-40)
 Linda K. Muthen posted on Friday, April 13, 2012 - 8:24 am
See the following FAQ which is on the website:

LTA with Movers-Stayers
 Brian Meekins posted on Monday, May 04, 2015 - 12:40 pm
I have a somewhat different mover-stayer model to model four time points with one dichotomous indicator at each time point. I am most concerned with measurement error from underreporting. In order to estimate this model I have a number of assumptions (equal transition probs, no false positive reports, equal probability of misreporting across time points). However, because I am most concerned with this underreporting I wish to have a 3-level mover-stayer latent variable, representing stayer (m=1) non-purchaser (1 1 1 1, m=2), stayer-purchaser (2 2 2 2, m=3), and mover (all other patterns). In my data the indicators of the four time points are indic1, indic2, indic3, indic4 corresponding to latent constructs: pur1, pur2, pur3, pur4.
The problem is that I canít fully specify the relationship between the mover-stayer latent variable and the four latent variables. If I do I get the error message that I canít refer to the reference class or last class). Glad to send you program, but too long for this post.
 Bengt O. Muthen posted on Monday, May 04, 2015 - 1:19 pm
Please send to support along with your license number.
 Caspar van Lissa posted on Wednesday, July 27, 2016 - 2:57 am
Dear Bengt and Linda, I am trying to construct a nearly identical model to Brian Meekins above:
Four time points, one dichotomous indicator at each time point. The data show three roughly equal groups: 1) A low stayer class of about 250 people who score 1 in all waves, 2) A high stayer class of about 250 people who score 2 in all waves, and 3) Several smaller classes who show different mover patterns. I would like to model the high and low stayer classes separately, so that I can compare them on levels of a covariate. Would you be so kind to share the solution to Brian Meekins' question above so I can try to apply it to my problem as well? Sincerely, Caspar
 Bengt O. Muthen posted on Wednesday, July 27, 2016 - 12:24 pm
You might be helped by the 2 FAQs on our website:

LTA with Movers-Stayers

LTA with transition probs varying as a function of covariates
 Caspar van Lissa posted on Tuesday, August 02, 2016 - 3:47 am
Dear Bengt, thank you for your response. I've already worked through these documents and the examples in the User's Guide, but unless I'm missing something, I don't see the specification of a high vs low stayer class in there. Brian Meekins published an article about the problem discussed in this thread where he describes the constraints used (see below). However, I don't understand how to implement these constraints in the MPlus language:

"Let M = 1 denote a stayer-purchaser, M = 2 a stayer-nonpurchaser,
and M = 3 a mover.
To reflect this structure in the model, the following constraints
are imposed on the purchase status latent variables (W, X, Y, Z)
conditionally on M:
(a) if M = 1, then Pr(W =1) =Pr(X =1)=Pr(Y =1)=Pr(Z =
(b) if M = 2, then Pr(W =1) =Pr(X =1)=Pr(Y =1)=Pr(Z =
1)=0; and
(c) if M = 3, Pr(W), Pr(X), Pr(Y), and Pr(Z) are unconstrained."
Ref: Beamer, Tucker, & Meekins, 2011
 Bengt O. Muthen posted on Tuesday, August 02, 2016 - 6:10 pm
It sounds like you would be helped by using the Parameterization = Probability feature. Some applications of that are shown on slide 82 and onwards for the V7Part handout for the 2012 Utrecht course:

Mplus Version 7 workshop and Dutch Mplus Users Group, Utrecht, August 2012

Videos and handouts from 3-day Version 7 workshop.

which you find at
 Caspar van Lissa posted on Wednesday, August 03, 2016 - 9:33 am
Dear Bengt, thanks you for the excellent video course! I worked through the examples in V7part2.pdf. In the slides, I read: "The latent class variable c1 which is the predictor has probability parameters [c1#1 c1#2]". I imagine I have to fix this probability for my high- vs low-stayer class? So I included syntax like this:
%movstay#2% !Stayer class with probability 1 of being in class 1. Probability of transitioning is 1 on the diagonal of the probability matrix, and 0 off-diagonal
c2#1 ON c1#1@1; c2#1 ON c1#2@0;
c3#1 ON c2#1@1; c3#1 ON c2#2@0;
c4#1 ON c3#1@1; c4#1 ON c3#2@0;

%movstay#3% !Stayer class with probability 0 of being in class 0.

However, this gives a series of errors like:
The following MODEL statements are ignored:
* Statements in Class %MOVSTAY#2.C1#1.C2#1.C3#1.C4#1% of MODEL:
[ C1#1 ]
 Bengt O. Muthen posted on Wednesday, August 03, 2016 - 2:28 pm
Follow the approach in slides 91-94.
 Amanda Hagman posted on Thursday, January 12, 2017 - 3:20 pm
Dear Drs. Muthen,

I am fairly new to Mplus and mixture models. Could you help me understand how continuous variables are treated in the mover-stayer model?

I am running a Mover-Stayer model with 3 time points and 4 classes at each time point. My observed variables are continuous.

In Kaplan, 2008 when the Model c.c# are specified thresholds are set to 15 or -15. For example part of the stayer group is set up as follows:

Are you able to use similar code with continuous variables, but instead of setting a threshold, you set the mean?

For example a stayer class might look like this if you didn't want c2#3 individuals in your stayer group:
(to be clear -15 is not a possible number for my data set)
 Bengt O. Muthen posted on Thursday, January 12, 2017 - 6:25 pm
The -15 setting is specific to categorical outcomes where you want prob=1 or 0 for a certain outcome category. So it does not have to do with the latent class variables but the observed variables as a function of latent class variables. The -15 matter doesn't carry over to continuous outcomes. See UG ex 8.15 for an approach to mover-stayer modeling - just delete the $ symbols and you will refer to the continuous outcome intercepts (in this case you apply measurement invariance over time).

See also the handout (V7part2) of our short course in Utrecht Aug 2012.
 Maja Flaig posted on Monday, March 20, 2017 - 4:16 am
I am trying to estimate a 2x4 mover-stayer LTA using logit parameterization with the model from Nylund's dissertation as a template.


Also, appr. 10 people show the pattern "144" which should not be possible as c=1 are movers.

I double checked the model specification, it seems correct. A model without the mover-stayer variable fits the data well and there are people with mover and stayer patterns.
Is it possible that the mover-stayer model is empirically underidentified or is it more likely that there is a mistake in the model specification?
 Bengt O. Muthen posted on Monday, March 20, 2017 - 5:29 pm
The mover class has no parameter restrictions that forbid staying. It means that those stayers are more like people in the movers class than people in the stayer class.

If you have further questions, send output to Support along with your license number.
 Jacqueline Kim posted on Monday, February 26, 2018 - 1:46 pm
Hello, I am planning on regressing a distal outcome on the mover/stayer latent variable. Meanwhile, I have a few questions about mover/stayer.

Is it possible to have more than one mover latent class?

So, if there are 4 time points with 3 classes each, differentiating those who moved from class 1 to 3 (1133) vs. a reverse pattern (3311), rather than lumping them all into one ďmoverĒ latent class. This would mean ending up with 2 mover latent classes with a specified pattern and 1 stayer latent class.

If yes, how would I do this in the syntax?

thank you very much for your help.
 Bengt O. Muthen posted on Monday, February 26, 2018 - 2:59 pm
Yes, you can have more than one mover class. You can specify different patterns in line with our FAQ on the web site:

LTA with Movers-Stayers
 Amanda Hagman posted on Sunday, January 26, 2020 - 2:52 pm
Hello Drs. Muthen,

I am running a mover-stayer analysis and am hoping to include distal outcomes and covariates.

My model has 4-mover-stayer options from 3-time points. At each time point, there are 4 latent profiles. M(4) C1(4) C2(4) C3(4)

To configure the mover-stayer with continuous indicator variables, is it possible to use the logit parameterization so that I can incorporate distal outcomes and covariates (it's my understanding that the probability parameterization does not allow for covariates and distal outcomes)? Can you give some guidance on how to do this if it is possible?

Thank you,
 Bengt O. Muthen posted on Monday, January 27, 2020 - 4:40 pm
Yes, you can use logit parameterization to do Mover-Stayer modeling - it's just a little more work. See the FAQ on our website:

LTA with Movers-Stayers
 Berenice Anaya posted on Tuesday, January 28, 2020 - 11:56 am
Hello Drs Muthen,
I am running an LTA with 5 times and 4 classes. I followed Nylund and Muthen (2007) and I am having trouble with the mover-stayer portion.
I related C1,C2,and C3 to the Movers, and C2,C3,and C4 to the Stayers.

%c#1% !movers
!Time 2 on Time 1
C2#1 on C1#1 (111);
C2#1 on C1#2 (112);
C2#1 on C1#3 (113); continuing this pattern for C2#2 and C2#3 and the other time points.

%C#2% !stayers
!Time 2 on Time 1
C2#1 on C1#1@30 (111);
C2#1 on C1#2@25 (112);
C2#1 on C1#3@-70 (113);

C2#2 on C1#1@30 (114);
C2#2 on C1#2@25 (115);
C2#2 on C1#3@-70 (116);

C2#3 on C1#1@30 (117);
C2#3 on C1#2@25 (118);
C2#3 on C1#3@-70 (119);

Are these transition probabilities correct?
Thank you for your help,
 Bengt O. Muthen posted on Wednesday, January 29, 2020 - 5:22 pm
See the FAQ on our website for how to do this using the default logit parameterization:

LTA with Movers-Stayers

Otherwise, use Parameterization=Probability as in the UG example 8.15.
 Amanda Hagman posted on Saturday, February 15, 2020 - 9:42 am
Hello Drs. Muthen,

I would like to add a distal outcome to a mover-stayer model where the mover-stayer class (M) predicts the outcome (distal). I wrote this in the %Overall% model as:

distal on M;

I get the error "One or more MODEL statements were ignored. note that ON statements must appear in the OVERALL class before they can be modified in class-specific models"

I'm confused about where I must specify the regression. Can you give some additional guidelines?

Thank you,
 Bengt O. Muthen posted on Saturday, February 15, 2020 - 4:29 pm
When a class variable is a predictor, you don't use ON but instead see how the DV mean or threshold changes over the classes. It is saying the same thing. You can use Model Constraint to see if mean/thresholds are different across classes.
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