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?
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.
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?
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!!
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:
ONE OR MORE MULTINOMIAL LOGIT PARAMETERS WERE FIXED TO AVOID SINGULARITY OF THE INFORMATION MATRIX. THE SINGULARITY IS MOST LIKELY BECAUSE THE MODEL IS NOT IDENTIFIED, OR BECAUSE OF EMPTY CELLS IN THE JOINT DISTRIBUTION OF THE CATEGORICAL LATENT VARIABLES AND ANY INDEPENDENT VARIABLES. THE FOLLOWING PARAMETERS WERE FIXED: 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?
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?
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.
Hi, 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.
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
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 = 1)=1; (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
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 [c1#1@1]; 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. [c1#1@0]; etc.
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 ]
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.