It would be Example 8.13 but without the CATEGORICAL statement and with intercepts instead of thresholds. So refer to the intercept as [u21] rather than the threshold as [u21$1].
Anonymous posted on Wednesday, May 05, 2004 - 10:57 am
Anonymous posted on Saturday, December 11, 2004 - 11:18 am
Is the model in example 8.13 exactly the same as the one in Reboussin, et.al 1998?
bmuthen posted on Sunday, December 12, 2004 - 11:05 am
It looks from page 460 of the Reboussin et al article that they do not allow c1 and x to interact as shown in Ex 8.13. The broken arrow from c1 to the arrow from x to c2 is not accounted for in their model because the page 460 formula does not have subscript k on the gamma slope for x. Otherwise the models are the same.
Anonymous posted on Monday, December 13, 2004 - 2:26 pm
Thank you Dr. Muthen for answering my previous question. Continuing with the example 8.13, I ran the program with 3 classes in the model and set class 3 as the reference class then I should have 6 specific transition parameters (beta_km, k=1,2,3,m=1,2) like the paper said. But in the Mplus output I only got 4 parameters (k=1,2; m=1,2). How about the transition from the reference class to the other two classes?
I have conducted a multigroup longitudinal LCA (2 occasions, gender as "knownclass"). It appears from the output that Mplus constrains the latent transition probabilities (t1 class --> t2 class) to be equal across gender (since they are only reported for the entire sample). Is there a way to set these probs free (it would be interesting for me to study whether the groups differ with respect to the tansition probs)? Thank you.
bmuthen posted on Tuesday, May 03, 2005 - 10:02 am
To obtain gender differences, you want to regress the true class variables (c1 and c2, say) on the gender knownclass class variable (cg, say):
I'm sorry, I'm asking this again, but I think it's an important question (maybe also for others) and I have not yet received a satisfying answer.
I have estimated a LTA model with 5 classes and 12 indicators on each of 2 occasions as a multigroup model (i.e., I have used gender as a knownclass variable). I assumed measurement invariance across groups and across occasions.
Now there are different constraints that I'm interested in. First I have estimated a model with unequal initial class proportions delta but equal latent transition probabilities (tau) across genders. No problem, the number of parameters (89) is correct, the fit and the estimates are the same as in PANMARK. Then I wanted to test a less restrictive model in which not only the delta's are allowed to vary across genders but also the tau's. This seemed to work also, since I got the correct number of parameters (109) and exactly the same fit as in PANMARK. However, Mplus reported only a single tau-matrix, while PANMARK reports separate matrices for both genders. I wonder whether it is a bug or if I'm missing something.
Furthermore, I would like to know if there is a possibility to get standard errors for delta's and tau's in Mplus
And - a very simple question: What is the correct citation for Mplus (sorry, if it's on the homepage - I just couldn't find it)?
Thank you once again for your excellent support!
BMuthen posted on Saturday, November 12, 2005 - 6:10 pm
Mplus does not print a tau matrix for each gender but instead the marginal transition matrix mixing the two genders. If you want the gender-specific tau matrix, you will have to compute it using the parameter estimates. This can be done in line with Chapter 13.
Mplus does not provide standard errors for taus but they can be computed using the Delta method.
The citation for Mplus is the citation of the user's guide which is shown on the second page of the user's guide.
I am working on a latent transition analysis with more than two timepoints. Do you know of any LTA examples or papers that use more than two timepoints that I can use as a guide? I am unsure how to build the model. Thanks in advance for your help!
bmuthen posted on Tuesday, January 10, 2006 - 8:53 am
I know of references with multi-timepoint LTA using a single indicator per timepoint (which is also referred to as Markov Modeling). Here are two articles for which we also have the Mplus inputs:
Langeheine, R. & van de Pol, F. (2002). Latent Markov chains. In Hagenaars, J.A. & McCutcheon, A.L. (eds.), Applied latent class analysis (pp. 304-341). Cambridge, UK: Cambridge University Press.
Mooijaart, A. (1998). Log-linear and Markov modeling of categorical longitudinal data. In Bijleveld, C. C. J. H., & van der Kamp, T. (eds). Longitudinal data analysis: Designs, models, and methods. Newbury Park: Sage.
I am trying to run a LTA model with 4 time points, 3 variables with three categories, and 4 latent classes. I have run the model once and have then used the model thresholds as starting values for further model runs. However, in this rerun the TECH 8 output is indicating that each interation is taking about 20 minutes or so (time = approx. 1600.00). Is there any way in which I can speed this up. Would fixing those thresholds that are very large (- or +) reduce the estimation time.
The generality of the current LTA implementation allows for not only 1st-, but also 2nd-order and higher-order Markov processes. This generality makes the computing slow with many time points. Essentially, with 4 time points and 4 latent classes, you end up with a latent class model with 256 classes. This is on our list to simplify. In the meanwhile, looking at fewer timepoints at a time saves time.
Boliang Guo posted on Wednesday, March 29, 2006 - 7:20 am
in mplus 4 ex8.14 the if the logit of c2#1 was fix at -15, same as for u11$1-u14$1, the result will change, same siuation when change 20 to 15. what is the rule for fixing the logit, logistics coefficient to an extram vale for 0 or 1 probability? what is the difference betwen -15 and -10, and -4(i remember you mention -4 else where), exp(-10. -15)are both extrem small! thanks.
Using 10 or 15 for extreme logits is (almost) equivalent. Using 5 (or 4) is only approximate. In this example, we fix [c2#1@-10] and in Model c we fix c2#1 ON c1#1@20. Because of this, c2 gets the logit -10 for c1=0 and +10 (= -10+20) for c1=1. So the difference between -10 and +20 (=10) is what is critical here; it should be at least 10. We could have used -15 and +30 instead.
I am trying to run a LTA with covariates. I have a question about that how to get the latent transition probabilities in the output. The transition probabilities of each individual is expressed by Reboussin et al. (1998). In the output, is this the ¡§average¡¨ transition probability of individuals? In Mplus, how is computed about the estimation of transition probabilities in literatures? Are there literatures about the estimation of transition probabilities in Mplus?
Transition probabilities are population parameters in the LTA model, not individual characteristics. Mplus prints the estimates of these parameters. The Mplus User's Guide has several references to LTA that define transition probabilities; see e.g. the Mooijaart ref. If you think that Reboussin et al computes individual values, please send an email with a pdf of the article and point me to the page.
Thank you for answering my previous question. But I have not yet received a satisfying answer. Maybe I don¡¦t give you a clear expression about my question, I¡¦m asking this again. I fit the latent transition model with individual covariates similar to ex8.13 of Mplus version 3, that c2 is depend on c1 and Xi, i=1,¡KN. I get the latent transition probabilities based on the estimated model in output. How is computed about these transition probabilities in output of Mplus?
In the page 317 of Mplus user's guide, the transition probabilities are expressed as
P(c2=r |c1=1) = exp(a_r +b_r1)/ sum, and so on.
But the model without individual covariates is not my model. The transition probabilities of the model with individual covariates was expressed in the page 461 of Reboussin et al. (1998), such as
Are the transition probabilities based on the estimated model in Mplus output computed as
I did an LCA on 9 binary indicators of risky behaviors in a sample of N=2500, and found that 4 latent classes best fitted the data, based on BIC, entropy, etc., and theoretically it fits well too.
I have these data for 3 time points, and the same 4 class solution fits the data over time.
Now I want to do a LTA for transitions between the latent classes over time.
I am referring to the LTA Example 8.13 in your Mplus Version 3 Manual (April 2004)
Would I have to specify c1 (4) C2 (4) and c3 (4) in an LTA, or do I have to import the class membership variables from the LCA in a data file? I just don't get whether I can put the number of classes in myself, or whether I should do something different.
Furthermore, I am interested whether the LTA would use the same classes as indicated by the LCA.
You would specify c1 (4) C2 (4) and c3 (4) as you say, not import class membership. The classes that you found in the LCA for each time point should be found by Mplus also in the LTA without any problem if those classes are well-defined. Try it. Start with 2 time points.
You don't have to put in any numbers. But you can if you want to indicate which class is which - and that is discussed in the LCA examples in the User's Guide in the context of threshold starting values.
AnNA, Just shar something on LTA becasue I jsut finish my LTA ANALYSIS. AS Prof. Muthen said above, you must be clear now 'which class is which' based on the conditional probability pattern. c1 in time1 may not the the c1 in time 2, you MUST check the conditional probability pattern/intercept pattern to make tsure what is the class mean in each time!!
Read the Version 4 User's Guide which is on our web site, Chapter 13, pages 357-359. Bottom of page 358 gives a table with logit components and page 359 gives you the corresponding Mplus names. For example, this makes it clear that c2#1 ON c1#1 is the logit slope b_11. If positive, this says that membership in class 1 at time 1 makes it more likely to be a member of class 1 also at time 2. The regular output also gives the translation of these logits into the corresponding transition probability table.
No, you don't have to run with 4 different reference classes - the transition table should be all that you need.
Also look at the Mplus UG references to LTA and Markov modeling.
I wondered whether it is possible to use grouping variables in MPlus LTA (e.g., look to see if latent statuses, prevalences, and/or transitions differ across group, for example if women difer from men in transition probabilities) and whether it is possible to do a significance test for this in MPlus.
i bet there are 4 class in time 1, 5 class in time2 and time3. which the death as the 5th class,and the death class can not be 'transited',am I right? you can right the mplus code following the general way. 4 class in first time, 5 class in 2nd and 3rd time.then, maybe fix the tranison posibility from 4th death to 5th death to 1 or not let them transite. say, there is no transition from 4th death to 5th death class.
As Boliang said, the absorbing state is such that later transition probabilities are 1 for staying in this death class. Also, the conditional item probabilities for the death class should be zero for observed categories other than missing data. See also chapter 13 for more information on transition probability modeling.
I have 6 continuous indicators, and each of the 6 indicators are measured at two timepoints. Based on LPA analyses at each time point, there appear to be 3 latent classes at each time point. Here is what I want to know: 1) What are the class-specific parameters (means, variances, covariances) at each time point? 2) What are the transition probabilities of being in a particular class at time 2 given membership in a certain class at time 1?
From what I can tell, example 8.13 in the Mplus manual is the best to follow. I did this, and have two questions: 1)I do not understand what to put for the for the Model, %overall% on statement. Could I just say "c2 on c1"? 2) In the output, I did not see the class-specific parameters I mentioned above at each time point. I only saw the class-specific parameters for each of the 9 possible sequences of change. How can I obtain the class specific parameters for the 3 classes at each time point?
so that you refer to all parameters of the multinomial logistic regression; the last class is not referred to (see Chapter 13).
2) If you follow ex 8.13, you will see that the class-specific parameters for the 3 classes at each time point (in your case means of continuous outcomes) are repeated over different patterns of classes. So with 3 classes and 6 variables, you only get 3x6=18 distinct means. This is due to measurement invariance across time (as specified by ex8.13).
Thank you so much for your responses to my 11/16/06 post. I have a follow up question. First of all, I should have clarified that we are NOT assuming measurement invariance as example 8.13 does. Thus, we did NOT get 18 distinct means, as you mentioned we should in your response to my 11/13 post. Rather, we got 54 distinct means at each time point, 108 total (9 latent sequences x 12 indicators for each latent sequence). Besides this fact that we are not assuming measurement invariance across time, and that our indicators are continuous as opposed to categorical, our analysis should follow that of 8.13.
That being said, we understand that in the output we get the class counts and proportions for each time point.
We also understand that we get a transition probability matrix in the output, followed by the parameters (means, variances, and covariances), for each of the 9 cells/sequences of change in the transition probability matrix.
However, we also want to obtain the parameters (means, variances, covariances) for each of the 3 latent classes at time 1, and each of the three latent classes at time 2. It is these parameters that will help us name and define our latent classes.
Question: Is there a way to get Mplus to give us these class-specific parameters at each time point?
I am interested in estimating a latent transition analysis over three waves, with individuals nested within neighborhoods. i am interested in finding out whether the transition probabilities vary between neighborhoods. I initially thought the most appropriate model would be the multilevel latent transition analysis as you have it in the MPLUS 4.2 addendum (example 7). However, I think I may also need a random slope, and I'm not sure how to specify it within the model. Is this the appropriate model, or would model 8 be better?
Moreover, when I estimate the model following example 7, I get a message saying "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."
I would start with example 7. Ex 8 is more advanced.
The message you get is not related to 2-level LTA per se but can also be seen with regular LCA with covariates. It means most often that some classes do not have variation in some covariates so regression coefficients cannot be determined. That is ok and often good in that it means that classes are clearly different wrt to the covariate.
Thank you for your response. I will use example 7 then. But I still think I need to add a random slope to determine whether the transition probabilities vary by neighborhood. Am I right? If so, how would I do that? If not, what parameters from example 7 would tell me how the transition probabilities vary between neighborhoods?
Is there any paper that you are aware of that applies examples 7 and 8? The problem is that I can't find any resource that interprets the output, so I am trying to put bits and pieces together from different sources to interpret it.
You are at the research frontier here, so little is written so far. The 2006 Asparouhov-Muthen paper on our web site has a first application.
I would do ex7 first. If that works out well, I would turn to ex8 to look at transition probabilities that vary across neighborhoods. The "cb" latent class variable allows different within-level "c2 on c1" relationships in different types of neighborhoods. It is not a random slope, but the slope is allowed to have distinct values in different cb classes (non-parametric representation of a random slope).
I have a question regarding missing data and latent transition analysis. Specifically, I have a 6 continuous variables measured at 2 time points. I have 1,300 at time point 1 and 1,000 at time point 2. A total of 612 respondents have scores at both time points. I ran a latent profile analysis at both time points and found 3 classes (which were nearly the same: same pattern & magnitude of means).
I am now going to run the LTA to examine the probability of moving across classes over time. My question concerns the use of a missing data technique. Basically, I expect that readers will question if it makes sense to model all data if only 619 had actual data at both time points. However, I suspect I should use the 1,300 data points at time 1 and the 1,000 at time 2 with a missing data technique when running the LTA. Specifically, I suspect that this would be advised over using only the 619 who had data at both time points for the LTA. Is this true? If so, is it because the transition probabilities would be less biased (more accurate) when using the missing data technique than using the smaller sample of 619?
The best approach is to use all available information: those who have data at both occasions+those who have data at only one of the 2 occasions. This is accomplished in Mplus using Type=Missing. Although the data for those who have information at only one of the 2 occasions do not contribute to the estimation of the transition parameters, they do contribute to estimating the time-specific parameters and therefore help giving better results.
Sara posted on Wednesday, March 28, 2007 - 10:58 am
Thanks for the information Bengt. We ran this model. We believe we have an issue with sparseness of cells. We have three classes at T1 (freshman) and T2 (sophomores). We got the following warning. 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: 56 57
This transition matrix is produced. FRESHPWB Classes (Rows) by SOPHPWB Classes (Columns) 1 2 3 1 1.000 0.000 0.000 2 0.114 0.818 0.068 3 0.025 0.202 0.773
Parameter 56=change in log odds of being in Soph Class 1 compared to Soph Class 3 if a respondent is in Freshman Class 1 vs. Class 3. Parameter 57=change in log odds of being in Soph Class 2 vs. 3 if a respondent is in Freshman Class 1 vs. 3.
No need to do anything, just let Mplus fix these - the large values give the probabilities of
1 0 0
in the first row, and these probabilites are clearly interpretable.
Sara posted on Wednesday, March 28, 2007 - 11:19 am
With respect to the model above and your comments on missing data, I have an additional question:
I understand that the latent transition probabilities are estimated using only the subset of sample that has data at both occasions. Examining the number of respondents in each latent class pattern, it is classifying all respondents. It seems that this table isn't interpretable given that 1/2 the respondents don't have data at one point. Is this correct? FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS BASED ON THE ESTIMATED MODEL Latent Class Pattern 1 1 166.75043 0.10009 1 2 0.00000 0.00000 1 3 0.00000 0.00000 2 1 90.04993 0.05405 2 2 645.00756 0.38716 2 3 53.56662 0.03215 3 1 17.64928 0.01059 3 2 143.66123 0.08623 3 3 549.31494 0.32972
Also, we get a warning that says WARNING in Model command. All variables are uncorrelated with all other variables within class. Check that this is what is intended.
We didn't intend to set all variables to be uncorrelated within a class. We set the within class correlations to be equal across classes and time. Looking at the results it appears that the latter is what happened but this warning concerned us.
The table is totally interpretable. Estimated probabilities for people with information at only one timepoint are based on information from people with information at both timepoints who are like the people with one timepoint at that timepoint. This is the strength of the method.
The warning about variables being uncorrelated is given for analysis variables that are not mentioned in the MODEL command. I would have to see the output and your license number at firstname.lastname@example.org to give specific information about your analysis.
I have a quick question concerning latent transition probabilities. I want to test a LTA model with 2 categorical latent variables (c1 and c2; each with 5 classes) in which no change occurs. Thus I tried to constrain the transition matrix to be an identity matrix using the following statement:
However, this does not seem to be fully correct as some of the tau's are estimated > 0 or < 1, and also the number of parameters is larger than expected. How can I constrain ALL tau's to 1 / 0? Thank you, Christian
You are forgetting about the intercept parameters that are referred to in brackets. See Examples 8.13 and 8.14 and the last section in Chapter 13, Parameterizations of Model With More Than One Categorical Latent Variable. If you don't have the most recent user's guide, see the one on the website.
I am running three independent LCA models for criminal offending types (7 indicators with zero-inflated counts) at three time points as a precursor to running an LTA. For two of the years I found that a four class solution was reasonable (although thresholds were fixed by MPlus in one of those years). For the third year, I was having trouble with local maxima and used the OPTSEED approach suggested in the manual. I found a (twice) replicated log likelihood about two points below the highest LL. The estimates are similar. Should I accept those estimates? If so, are there any special considerations that I have to make in the subsequent LTA to account for this?
Did you try STARTS=1000 100; or greater? If you did not, try more starts. Another factor to consider is if all final stage starts converged?
If you did use many starts and compared the results from the best loglikelihood to one of the replicated second best loglikelihoods and they look the same, I think you can trust them. Are these results also similar to times 1 and 2? It may be that the class structure is not as clear at time 3.
You may find that when you impose measurement invariance in your LTA this will help stabilize the model.
Thank you. I attempted to run the LTA as suggested but received the following error messages:
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE FIRST-ORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.347D-10. PROBLEM INVOLVING PARAMETER 95.
ONE OR MORE PARAMETERS WERE FIXED TO AVOID SINGULARITY OF THE INFORMATION MATRIX. THE SINGULARITY IS MOST LIKELY DUE TO THE MODEL IS NOT IDENTIFIED, OR DUE TO A LARGE OR A SMALL PARAMETER ON THE LOGIT SCALE. THE FOLLOWING PARAMETERS WERE FIXED: 20 98
My workshop notes indicate that identification in such models can be difficult, but I was unsure of exactly how to go forward from here or further check the model.
Follow up to May 2006, re: whether LTA uses the "same" classes as indicated by a LCA model:
I am using LTA to examine transitions between classes of victimization with former and current partners. A 3 3 model best fits the data; the first class for each latent variable is fixed such that all lc probs are 0.
I can calculate the CP of each category and have given appropriate "names" to each class.
The problem comes when I add in covariates. First, I guess I don't know quite how to calculate the CP for each class (the output reports thresholds rather than the lc pattern probs which I used to calculate CP).
But, does the ordering of each of the latent classes remain the same? I've looked at the final class counts for the lc and it *seems* that the classes change order for C2 even though I have done nothing but add the covariates, i.e. C 2 1 now becomes C 2 2 (substantively) in the LTA model, based on the final class counts, and so on.
Questions: 1) How to calculate the conditional probabilities when covariates are included. (And would it be more appropriate to report those as opposed to the unconditional model?) 2) How can I be sure that my classes in the conditional model are substantively the same as in the unconditional model?
I apologize for any repeats of previous postings and for my naivete; thanks in advance for your response.
When you add covariates, do you regress the categorical latent variable on the covariates or the latent class indicators on the covariates? I am assuming it is the categorical latent variable.
You can choose the order of the classes by using user-specified starting values. There are several examples of this in Chapter 7. You take the starting values from a previous analysis.
1. The formula is shown in Technical Appendix 8 formula 153. Note that an intercept is the negative of a threshold. See also the section on Calculating Probabilities from Logistic Regression Coefficients in Chapter 13.
2. You can check whether class counts change and see also if the thresholds of the latent class indicators change.
I am working on a LTA and I am using the KNOWCLASS command to model gender (c) differences. CLASSES = c(2) c1(4) c2(4); I have managed to calculate different tau matrixs and different rho values for the two groups, but still cannot manage to calculate different delta values.
Where should I specify that I want different delta for male and female?
See the section at the end of Chapter 13 called Parameterization of Models With More Than One Categorical Latent Variables.
Sarah Dauber posted on Tuesday, November 27, 2007 - 10:15 am
Hello, I am running a LTA model with 2 timepoints and 4 latent classes at each timepoint. I am trying to follow example 8.13 in the user's guide. I got the following error and don't know what it means:
*** ERROR in Model command Ordered thresholds 1 and 2 for class indicator QUANTITY1 are not increasing. Check your starting values.
This appears in reference to several of my latent class indicators. I'm not sure what it means or what to do.
I'm comparing time1 to time2 latent profile transition models. Two meaningful models work: 2-class to 2-class, and 2-class to 3-class solutions. AIC goes down with the 2-2 compared to 2-3 solution (7070 to 7034, rounded), but the BIC goes up (7215 to 7237). LL goes from -3489.937 to -3453.896. If I understand these correctly, the AIC indicates that the 2-3 class transition fits better, but the BIC indicates the 2-2 class transition fits better. Ns are reasonable for both solutions. Any suggestions about how to choose the model to report? Thanks!
I think I'm having a brain failure! I have done an LTA for 4 continuous variables measured at two times to identify transitions in latent profile classes. I've been thinking that C1 represented the latent class variable for the 4 indicators at time 1, and C2 likewise for time 2. It appears that they really just represent 2 latent class variables that together define class membership for the 8 indicators (same 4 at the two times). I realize this from seeing that the solution for C1(3) and C2(2) is exactly the same as the solution for C1(2) and C2(3) regarding class memberships.
Perhaps I really want a "mover/stayer" model, but I haven't figured out how to make the syntax work for continuous indicator despite notes here about it and information in the manual. Do you have any examples for this sort of LTA on latent profile classes for continous variables I could work from?
Your LTA should not allow c1 to influence the 4 indicators at time 2, and not allow c2 to influence the 4 indicators at time 1. See UG ex8.13. Here, "not influence" implies that the means do not vary over those classes.
Thanks, Bengt - I've been using ex8.13 but not correctly, it seems. I have meaningful LPA classes at T1 (3) and T2 (2), but I can't get even a 2-2 LTA to work. I can live with zero corr within classes, but my attempts to specify even equal diag matrices at each time haven't worked. Going with the defaults for covar matrices, this syntax gives a class at each time with no cases.
If you get a meaningful 3-class LPA at t1 and a 2-class at t2 - with BIC supporting those choices - it would seem that an input like the one you have here (although with 3 classes at t1) should work fine (I assume the starting values come from the individual LPA's). If using many random starts doesn't get you a solution that looks like the individual LPAs at each time point, perhaps (a) those solutions weren't stable enough, or (b) the sample size is rather small, or (c) putting the two time points together creates a model misfit, such that the correlations among indicators across time are not well modeled by the conventional LPA. One example of (c) would be that a given indicator has a residual correlation with itself across time.
It is hard to say more than that without doing analyses.
Thank you Bengt - I've revised my models a bit more trying to get a solution when specifying starting values from the prior LPAs, but I am still getting strange results -- one class gets fixed as having 0 obs at each time, after this warning:
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE FIRST-ORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.371D-15. PROBLEM INVOLVING PARAMETER 26. (The ALPHA(C) for C2#1)
This happens with a 2c to 2c and a 3c to 2c model. When I allow Mplus to choose its own starting values, I get solutions both ways. Any ideas what is going on? Eg, MODEL c1: %c1#1% [t1v1*6 t1v2*5 t1v3*68 t1v4*19]; %c1#2% [t1v1*1 t1v2*3 t1v3*46 t1v4*10]; MODEL c2: %c2#1% [t2v1*6 t2v2*4 t2v3*63 t2v4*17]; %c2#2% [t2v1*1 t2v2*3 t2v3*50 t2v4*12];
It's hard to say without seeing the outputs and running it ourselves. For example, I don't know if you have used a large number of random starts or use the default and I don't know how they loglikelihoods compare across the models.
The non-identification message clearly appears when you have empty classes, since you don't have people supporting parameters in those classes. The results you show indicate no transitions.
A good way to start an LTA is to do the two LCA's first with K1 and K2 classes and then cross-classify people into a K1 x K2 frequency table to see if people fill the cells so that you have transitions.
You say "When I allow Mplus to choose its own starting values, I get solutions both ways." -if that result comes from many random starts with the best LL replicated several times and better than the LL of the solution you show here, then that's what the LTA gives.
Kim D'zatko posted on Thursday, October 30, 2008 - 1:31 pm
Hello all, I ran an LTA with three classes each over three timepoints. I included two covariates, as well. This converged in ~2.5 hours. The current model includes a mover/stayer latent variable, but no covariates. After 36 hours, it has progressed through only 22 sets of starting values. Is this typical or should I stop the run and check my code? Take care
It's hard to say without more information. If you are not using Version 5.1, I suggest that you do. If you are, please send the output from the model with covariates, the input and data for the model without covariates, and your license number to email@example.com.
I receive the following message when running an IRT mixture model with 2 latent classes: ----- ONE OR MORE PARAMETERS WERE FIXED TO VOID SINGULARITY OF THE INFORMATION MATRIX .... ----- In this case, the singularity is due to empty cells in the joint distributions of some of the categorical variables. Consequently, the SEs for the fixed parameters can not be computed. However, the values of the fixed parameter estimates are provided in the output. How are the values of the fixed parameter estimates determined given that there are empty cells in the joint distributions?
I can imagine that a univariate outcome gets prob zero or one in a certain class and therefore a large or small threshold that gets fixed. The choice of value of this fixing is innocous because say 15 or 20 gives the same zero probability. A joint distribution being the cause seems odd to me given the IRT mixture model. If this doesn't help, feel free to send input, output, data, and license number to firstname.lastname@example.org.
I have 2 questions about how to specify measurement non-invariance and correlations among continuous manifest indicators in the context of LTA. I'm running an LTA with 2 timepoints with 5 classes at time1 and 4 at time2. (Those solutions are supported theoretically and statistically following your recommendations with LCAs for continuous indicators at each timepoint.) I am trying to follow UG 8.13 and the very helpful Nylund (2007), but I don't know how to:
1) Allow correlations within class 2) Account for measurement non-invariance across time
I'm interested in the transition probabilities and want to allow the means to differ across time. I apologize if I have missed this answer here or in the user guide. I'd appreciate any direction from you or recent references. Abbreviated model syntax is pasted below:
1) You can accomplish that by adding a factor measured by the items at each time. See the chapter on our web site:
Muthén, B. (2008). Latent variable hybrids: Overview of old and new models. In Hancock, G. R., & Samuelsen, K. M. (Eds.), Advances in latent variable mixture models, pp. 1-24. Charlotte, NC: Information Age Publishing, Inc.
2) You can use the "dot" option in the Model statement:
Thank you for your quick response. I have gone back to your 2008 chapter on hybrids and it sounds like you are suggesting an FMA-LTA approach in preference to the conventional LTA. This makes sense to me and your data example in the chapter makes a compelling case.
Can you direct me to syntax examples of how to run FMA-LTA? Would I just add these lines to the model command:
I have a total of 7 time points, and am working on LTA analyses with 3 classes at each time point. I have successfully completed the LTA with 3 time points, but when I add a 4th time point it takes a VERY long time to iterate (more than a day with a single processor). Can MPlus handle more than 3 timepoints for LTA right now? Should I try to use a computer with numerous processors to decrease the iteration time? Or do I just need to do a series of 3 timepoints at different combinations to get the transition tables I want? Any suggestions?
I described LTA results in a recent paper. A reviewer wants to know whether it is possible to provide standard errors for the latent transition probabilties. I could not find any information on this and tried to bootstrap CI's ("Bootstrap" in Analysis command and "Cinterval" in output command). However, Mplus would not provide bootstrapped CI's for the posterior probabilities. Is it possible (and how) to obtain the CIs given that bootstrapping does not work?
It is hard to say without knowing your data analysis situation. I don't know how many random starts you have used and how many times the best LL was replicated. It is not clear from your question that you had the same covariates in the model for a given time point and for the two time points togther.
Generally speaking, however, when you put the two time points together your model has more content than for each time point - you are saying for example that c1 does not influence the c2 indicators directly but only indirectly via c2. This means that results can change. Typically, this does not happen with a well-defined solution for each time point.
I am attempting to establish measurement invariance for a LTA across three time points. I was wondering if there is an empirical indicator of which constraints might be particularly problematic in the analysis (e.g., an LM test). I have not yet been able to establish invariance and will likely have to settle for partial invariance, but am not sure how to empirically decide which constraints to free in order to improve model fit.
Thank you very much Dr. Muthen for your quick reply. I did try to run the model with the MODINDICES option in the output section, but received the following message. Is there another way to obtain these?
*** WARNING in OUTPUT command MODINDICES option is not available for TYPE=MIXTURE with more than one categorical latent variable. Request for MODINDICES is ignored.
That's what I was afraid of. Thank you very much for clarifying this for me.
Evgenia posted on Friday, February 12, 2010 - 1:52 am
Hello. I'm trying to fit a hybrid model with two latent classes with binary indicators. In one class I want to fit a two parameter logistic model and the other class is assumed homogeneous without any latent structure, with given probability of a positive response on item i, for a subject belongs to this class (similar to classic Latent Class model). Is it possible to fit this type of model in Mplus? Can I simulate data from this model? Thank you .
I think in the IRT mixture literature a similar situation arises when one class of subjects use their knowledge (a factor f, say) to solve a problem and another class of subjects guesses. The second class would then be specified with
to eliminate the factor in that class. This would make for independent items in that class, which may make sense with guessing.
One could also contemplate other models in the second class. A totally unrestricted model for the second class is hard to estimate by ML because it would involve correlating all items (ML for categorical outcomes does not allow WITH), although the use of many factors could approximate this.
I have a LTA model with three time points and three classes at the first two timepoints and four classes at the last time point. Although I could not achieve statistical invariance for any of the classes in their entirety, the conditional response probabilities indicate that three of the classes are very similar and that a fourth emerges at the final time point. However, the ordering of the classes seems to change at the fourth time point.
After identifying the latent class orders at each time point, I ran an LTA, but the transition probabilities did not seem valid. I checked some of the conditional response probabilities for the specific class membership patterns and concluded that the order seemed to have changed again when the LTA was run. Is this possible? Is there a way to get CRPs for each class at each time point to confirm? I appreciate your feedback about this issue.
Thank you Linda! So I assume that I should enter the CRPs from each measurement model as start values for each threshold and turn off the random starts in order to assure that my class orders do not change. Is this correct?
Thank you very much Linda, I tried this and it worked very nicely. However, not I am trying to add a distal outcome that will be regressed on my final four class variable at my third time point. There did not seem to be much in the User's Guide about this issue, so I read through Karen Nylund's dissertation and her syntax example and added my continuous distal outcome variable the same way. In the output, it seems that means and variances are estimated for each latent class pattern, but I could not find means for each class of the final latent class variable. In other words, I was hoping for three means and ended up with 36. Is there an easy way to get the means that I am looking for or are they printed in another section of the output? Thank you so much for all of your help with this.
You need to impose equality constraints using the . labelling feature which is described on pages 560-61 of the user's guide and in Example 8.14. For further help on this, contact email@example.com.
I am attempting to run a LTA (mover-stayer model) using example 8.14 in the Mplus user's guide. I've run the model with constraints (which allowed for a graph) and free--without constraints (which did not allow for a graph). However, even when I remove the constraints (1-3) (4-6) are there some default constraints that Mplus imposes? I ask because even though all the mean estimates are no longer held to be the same for one latent class, it appears that their are patterns of means which are identical across latent classes.
Also, Based on the constrained model there are are 74 movers and 356 stayers. Based on the free to vary model there are 333 movers and 97 stayers. Why would the number of movers and stayers change so much?
I am following Karen Nylund's papers which reports size of classes, % of individuals in each pattern (movers then stayers), etc.
It's hard to say what is going on without looking at your 2 runs. There are default constraints when using Model c1, Model c2, etc, namely what you would expect: time 1 means only change as function of c1 classes, not c2 classes, etc.
If the model is correctly set up, the changing numbers of movers and stayers might indicate a model misfit.
Is it possible to have more than 2 latent classes for the higher order latent variable "c" in the mover-stayer model (8.14)?
Specifically, is it possible to create a 4 class latent variable c? This way instead lumping all movers and all stayers together (respectively), you could estimate: stayer type 1, stayer type 2, mover type 1 and mover type 2.
After finding out that LTA with more than 3 time points is very computational demanding, I've decided to pool the data, and do the analysis in a multilevel LTA framework, in which the different transitions are nested in individual cases.
As I'm not interested in cross-level interactions, and just want to control for the fact that the cases are not statistically independent, I've read I can use the "TYPE=COMPLEX MIXTURE" option, and specifying the variable by which the nesting is indicated. However, as the individuals are also nested in families, I have actually 2 nesting variables, something "TYPE=COMPLEX MIXTURE" cannot handle. Instead, I found out I should use the "TYPE=TWOLEVEL COMPLEX MIXTURE" option.
The model is running fine with this last option. However, there are 2 problems I run into. (BTW, I'm using MPlus v5.0)
1) The output only reports the thresholds for the item probabilities. Is there someway to also get the item probabilities themselves, or should I calculate these by hand?
2) The output does not report the chi square test of model fit. Is there someway to get these nonetheless?
Again, please keep in mind that I'm not interested in any cross-level interactions, but that I just want to adjust the standard errors for the nested structure of the data.
We don't give probabilities at this time when numerical integration is involved. You cannot compute the probabilities by hand in this case. You may find the following paper which is available on the website helpful:
Henry, K. & Muthén, B. (2009). Multilevel latent class analysis: An application of adolescent smoking typologies with individual and contextual predictors. Forthcoming in Structural Equation Modeling.
If the chi-square tests are not given automatically, there is no way to request them.
Thanks for your quick reply and the helpful reference.
Examining the results in more detail, I seem to find the same fit indices and thresholds for the 'fixed effects model' (in which I control for the clustering of the cases in families) and the 'random effects model' in which I add a third level (cases nested in individuals). Am I doing something wrong in the syntax?
The fixed effects model syntax looks like:
USEVARIABLES ARE x1 x2 x3 x4 x5 x6 x7 x8 x9 x10; CATEGORICAL ARE x1 x2 x3 x4 x5 x6 x7 x8 x9 x10; CLUSTER = FAM; CLASSES = c(#); MISSING ARE all (-9999);
ANALYSIS: TYPE = COMPLEX MIXTURE MISSING;
The random effects model syntax looks like:
USEVARIABLES ARE x1 x2 x3 x4 x5 x6 x7 x8 x9 x10; CATEGORICAL ARE x1 x2 x3 x4 x5 x6 x7 x8 x9 x10; WITHIN ARE x1 x2 x3 x4 x5 x6 x7 x8 x9 x10; CLUSTER = FAM ID; CLASSES = c(#); MISSING ARE all (-9999);
ANALYSIS: TYPE = TWOLEVEL COMPLEX MIXTURE MISSING;
Again, please keep in mind, that I only want to adjust the standard errors for the nested structure of the data, and that I am not interested in any cross-level interactions.
With four continuous variables and one categorical variable, I generated a four class LPA solution, good fit, makes sense. My question: Is it proper to use cross-sectional LPA class means to constrain latent variables, each with a four class solution in an LTA? syntax:
CATEGORICAL = male latino aa coh_one coh_plus;
classes = c1(4) c2(4);
ANALYSIS: TYPE = MIXTURE; MITERATIONS = 1000; Starts= 100 10;
MODEL: %overall% c2 ON c1 male latino aa coh_one coh_plus; c1 ON male latino aa coh_one coh_plus;
I want to estimate the effect of three tx conditions on four classes at 2 time points. My observed variables are continuous. I have been using the example from your Berlin lectures, slides 48-51 "LTA with Intervention studies." However, my model differs in that my knownclass would have three tx groups in it and there are four classes at both T1 and T2. I am having difficulty with programming the model language to reflect this, can you assist me in the most efficient way to state this model? Also, can covariates (i.e. race & gender) be included in this model?
Is there a way to calculate the regression estimates and significance levels for the reference class and the reference tx condition in a LTA with an intervention model? I have a three class model at two time points for 4 tx conditions, and I am unable to know the estimates and significance levels for the third class at each time point and for the fourth tx condition. Also, the output does not explain the regression coeffs for my gender and race covariates. Thank you in advance!
I have been working on the model that you reviewed several weeks ago for me. If you recall, I am treating 4 tx groups as a latent variable with two time points using six continuous measures with high reliabilities. So, in a 3 class model, there are 3x3= 9 cells for 4 tx groups = 36 transition patterns, and a model with 4 classes will produce a 4x4= 16 cells for 4 tx groups = 48 transition patterns.
So, I have excellent fit indices and entropy over .92 for models with 2-5 classes. However, the 3 class model has the largest drop in BIC magnitude from a 2 group model (over 1,200 pts lower from a 2 class model) compared to the other models (less than 500 pts diff between a 3 and 4 group model and 250 diff between 4 and 5 groups). In addition, the model w/ 4 groups has a comparable entropy to the 3, but many empty cells. Kline would suggest a more parsimonious model would be the way to go, but...
1. Is there a citation I can go to that would discuss the drop in magnitude in the BIC as a criteria for deciding on model selection?
2. Do models with empty transition cells/patterns produce stable estimates? I have good fit with a four group model, and there is literature to support the meaning of the class, but 25% of the cells are empty in the 4 group model.
3. Are there are citations that you are aware of investigating the stability/instability of models with empty cells?
Wasserman (2000) in J of Math Psych gives a formula (27) which implies that a BIC-related difference between two models is logBij where B is the Bayes factor for choosing between model i and j. Wasserman's (27) says that logBij is approximately what Mplus calls minus 1/2 BIC. This means that 2log Bij is in the Mplus BIC scale apart from the ignorable sign difference.
Kass and Raftery (1995) in J of the Am Stat Assoc gives rules of evidence on page 777 for 2log_e Bij which say that >10 is very strong evidence in favor of the model with largest value.
So, to conclude, this says that an Mplus BIC difference > 10 is strong evidence against the model with the highest Mplus BIC value (I hope I got that right).
Raftery has a Soc Meth chapter from around 1995 (?) that talks about Bij from a SEM perspective
Rob Dvorak posted on Wednesday, July 14, 2010 - 6:45 pm Hi Michael,
Here's the Raftery cite:
Raftery, A. E. (1995). Bayesian Model Selection in Social Research. Sociological Methodology, 25, 111-163.
Thank you for the great resources. I hate to belabor this point, but I am a stickler for accuracy and I am an intervention researcher - not a mathematician. Last summer, I took an ICPSR course and learned about the Raferty citation for calculating a more interpretable BIC using the Mplus chi2 in the formula "chi2-df (ln(N))". This calculation produces a BIC that is comparable across nonnested models following the Raferty rule >10.
However, as Mplus LTA output does not give a chi2, but only a LgLkd chi2, I am assuming that I can not use this statistic in this calculation, am I correct in my understanding?
Therefore, following your suggestions using the results from my models, 2ln of the BIC (19355.681) for model i = 19.741, 2ln of the BIC (18956.107) for model j = 19.699. The difference between Bij is less than 10. Thus, according to your explanation, this is is "strong" statistical evidence for retaining the more parsimonious model with the larger BIC (i.e. keep model i over model j). Is my interpretation of this accurate?
Comparing models using the formula "chi2-df (ln(N))" is the same as using the Mplus BIC = -2logL + p*ln(N), where p is the number of parameters. Note that
chi2 = -2(logL_a - logL_b),
where a is a model nested within b. In the usual SEM case b is the totally unrestricted model called H1. Note also that
df = p_b - p_a,
where p is the number of parameters.
So when you look at the difference between the BIC of two models using the formula chi2-df (ln(N)) there is a canceling out of the terms -2logL_b and of the terms p_b*ln(N). This means that BIC differences are the same for both formulas. And this means that we should view a BIC difference > 10 as strong evidence that the model with lower BIC is better.
Dana Wood posted on Wednesday, September 15, 2010 - 12:59 am
I have a question about how to interpret the latent classes in my latent transition analysis.
When I ran the preliminary latent class analyses, Mplus provided results both in terms of thresholds and in probability scale. However, when I ran the latent transition analysis, only the thresholds were provided. Is it possible to manually convert these thresholds to probability scale? All indicator variables for the latent classes are ordered categorical variables (3 categories in each). Thank you.
The computation of probabilities for ordered polytomous variables is shown in Technical Appendix 1 on the website.
csulliva posted on Sunday, October 10, 2010 - 3:11 pm
I am attempting to run a two stage LTA model with latent classes comprised of categorical, censored, and count measures. When I try to incorporate equality constraints over time, I get a series of warnings stating "There are more equality labels given than there are parameters" and a termination message that reads "***FATAL ERROR EQUALITIES BETWEEN PARAMETERS ARE NOT POSSIBLE IN THIS SITUATION." I was wondering what these messages mean and whether anything can be done about them.
I am conducting an LTA w/ 3 classes at 2 time points. The measurement model is LPA. I added gender as a covariate. Every time I run the model w/ gender included, the output has the 1st class as the largest class. Unfortunately, I would like for this class (a normative group) to be the last class so I can use it as the reference group in the logistic regression.
Based on earlier posts, I tried to re-order classes by putting the original start values for the last class (i.e., the mean estimates (Nu)) as the start values for 1st class, & using 0 random starts. When I do this, the largest (reference) class becomes class 2 and I get an error: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE FIRST-ORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NoNIDENTIFICATION. THE CONDITION NUMBER IS 0.851D-10. PROBLEM INVOLVING PARAMETER 69. 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: 90
Should I be using different start values or is there another way to reorder classes? Any suggestions you have are appreciated.
You should be using the ending values from the results section of the first analysis as starting values in the second analysis. IF you continue to have problems, send the relevant outputs and your license number to firstname.lastname@example.org.
I attended the August mixture modeling course in Baltimore, and I have a question about an LTA I am trying to do. In following the steps outlined in the course handout (page 42 topic 6), I am on step two. I also have been following the Nylund (2007) dissertation, and I am a bit stuck.
To explore transitions based on cross sectional results, I am unsure about how to do this. In the handout and in the dissertation, they talk about cross-tabs based on most likely class membership. Is this something I would synthesize from my LCA output files from each time point?
If this is not the case, I am wondering if I need to run a new model, such as example 8.14 in the version 6 user’s guide (but without model constraints)?
For each LCA, you can use the CPROBABILITIES option of the SAVEDATA command to save the posterior probablities and most likely class membership. You can use the CROSSTABS option of the OUTPUT command to do crosstabs between most likely class membership for time 1 and 2, 2 and 3, etc. to see what the transitioning looks like.
I am at the point in the LTA building process where I am testing for invariance between fully constrained and partially constrained models (I have a 3 class solution at 3 time points). While I am able to free and constrain classes at different time points, I am having trouble figuring out how to constrain individual variables in each class at each time point in my analysis.
I have written the following syntax. Is this how I would constrain individual variables in each class at a single time point?
What you show under MODEL C1 is the default where thresholds are free across classes. With mixture modeling if you want to test the equality of thresholds, instead of constraining the thresholds to be equal across classes which can cause the classes to change, label the threshold parameters and use MODEL TEST to test the equalities.
I have a question about the model Mplus estimates when running an LTA with covariates. Based on my reading of the Nylund (2007) dissertation, the coefficients for the multinomial regression that occurs when a covariate is included in the model are for the latent status at a given time point. Stated otherwise, it is the effect of the covariate on latent class/status membership at a given time point. Other programs (e.g., PROC LTA, Collins & Lanza, 2010), provide the effect of the covariate on the transitional probabilities. Thus, in Mplus we get the effect on class membership at a given time point for a covariate, whereas in PROC LCA and others it is the effect of transitioning in to a given class membership at a given time point. Am I correct in the way I am distinguishing these effects and the model I understand Mplus to be running? If so, is there a way to make it so that Mplus runs the model where the effect of the covariate on transitional probabilities is tested?
Mplus does allow for transition probabilities to vary as a function of a covariate.
Essentially such a phenomenon is an interaction between the latent class variable say c1 at time 1 and the x covariate in their influence on the latent class variable c2 at time 2. As usual, an interaction can be viewed as a moderated effect, either by (1) c1 moderating the effect of x on c2 or (2) by x moderating the effect of c1 on c2. Estimates from either approach can be used to compute estimates from the other approach. In Mplus, the transformation can be done in Model Constraint.
Approach (1) is shown in UG ex 8.13 with the broken line from c1 to the arrow from x to c2 indicating the interaction through c1 moderating x's influence on c2.
Approach (2) is shown in UG ex 8.14, where c takes the role of x. The c variable can be latent as shown in that example (this is not possible in proc lta as far as I understand), or it can be observed-categorical. The observed case is handled by using the Knownclass approach making the observed x identical to the latent class variable. An example of this approach is given in the Topic 6 handout of 8/17/2009, slides 48-50. That's an example where x is a binary treatment/control variable in an intervention. Various intervention effects of interest are expressed using new parameters defined in Model Constraint.
Approach (2) is used in proc LTA and does not use a latent c. An illustration is given in the Lanza-Collins (2008) article in Dev Psych. Their x is binary, representing past-year drunkenness. This model can also be done in Mplus.
Thank you very much for the reply and for directing me to the handout. As a follow up, is it also possible to do this with an observed continuous variable instead of an observed categorical? Presumably Knownclass wouldn't be the appropriate choice there, but something else?
In principle yes, via approach (1) - the Mplus approach (2) could not be used unless you categorize it (more than 2 cat's possible). But it is probably wise to first dichotomize it and use the approach (2) of the handout approach. As you saw in the Lanza-Collins article even approach (2) with a binary x sometimes has problems in practice.
I should add that a more advanced way of doing approach (2) with a continuous covariate x in Mplus is to use the Constraint=x option in the Variable command. This is then applied to the c2 on c1 regression. For an example, look for quantitative trait locus in the index of the UG.
F Lamers posted on Wednesday, April 06, 2011 - 10:06 am
I’m modeling an LTA with 3 classes at two time points and I am in the process of evaluating measurement invariance. The 3 classes have the same interpretation at the two time points, but some of the items turn out not to be invariant across measurements, so if I understand correctly I should use partial measurement invariance in my final LTA model. The 3 items (out of 10) that aren’t invariant don’t change the interpretation of the classes. I’ve seen some studies having the same situation enforce full MI in the final model, because of the conceptual similarity of classes and to aid interpretability. Is assuming full MI justifiable in such a situation? Are there any serious drawbacks to this approach?
I would not enforce full invariance if you found partial invariance. I would allow for the partial invariance. The interpretation of the transitions are still valid if you model the partial invariance.
I am fitting an LTA with 3 manifest indicators, 3 classes and 6 time points. I am trying to establish if there is stationarity and measurement invariance over time. Based on BIC, I come to the conclusion that item response probabilities do not vary over time but transition probabilities are time heterogeneous. I get though the following msg with 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.
I checked through TECH1 which parameters these are and they all refer to the betas of when we regress the latest time point latent variable to the previous one. All of them have s.e=0. 1) Shall I worry? If yes shall impose restrictions to the transition probabilities? 2)Can I try the same model with 4 latent classes?
Having an LTA with 30 time points would be very computationally demanding. I would suggest using fewer time points, for example, early, middle, and late. The varying number of time points can be handled by missing data.
I am trying to fix the transition probability C1#2 - C2#1 (0.011) at zero. I am not sure what the model specification is:
[c2#1]; c2 ON c1;
Do you know where I could find an example? I am trying to deal with inconsistencies when a respondent reports having some experience with a drug, and then at a later occasion reports never having tried it.
Dear Professors, I am trying to replicate Example 10.12. I do not want yet to include any covariates at the individual or cluster level. I have CLASSES = C1(3) C2(3) C3(3) C4(3) C5(3); In the overall part of the between part of the model, I wonder if the following code for my problem is correct: C2#1 ON C1#1; C3#1 ON C2#1; C4#1 ON C3#1; C5#1 ON C4#1; C1#1 C2#1 C3#1 C4#1 C5#1; If yes then I get the following message: THERE IS NOT ENOUGH MEMORY SPACE TO RUN THE PROGRAM ON THE CURRENT INPUT FILE. THE ANALYSIS REQUIRES 5 DIMENSIONS OF INTEGRATION RESULTING IN A TOTAL OF 0.75938E+06 INTEGRATION POINTS. THIS MAY BE THE CAUSE OF THE MEMORY SHORTAGE. YOU CAN TRY TO FREE UP SOME MEMORY BY CLOSING OTHER APPLICATIONS THAT ARE CURRENTLY RUNNING. NOTE THAT THE MODEL MAY REQUIRE MORE MEMORY THAN ALLOWED BY THE OPERATING SYSTEM. REFER TO SYSTEM REQUIREMENTS AT www.statmodel.com FOR MORE INFORMATION ABOUT THIS LIMIT. I have tried 4 timepoints but the problem persists and then 2 timepoints, the program runs but with warning msgs of non-identification and se's that they cannot be computed. I read the paper entitled ‘Multilevel Mixture Models’ and I wonder if it is a problem the fact that I have 184 clusters with 1-14 individuals in each of them. Any advice from you would help greatly. With Kind Regards, Artemis
Thanks so much for the speedy response; can I just confirm please that I understand correct?
So in the overall part of the between part of the model, is it correct the following code, if all 5 latent class variables have 3 categories? C2 ON C1; C3 ON C2; C4 ON C3; C5 ON C4; C1#1 C2#1 C3#1 C4#1 C5#1; C1#1 C2#2 C3#2 C4#2 C5#2; Can you please advise? All latent variables are categorical. I think I can suspect what you mean about very heavy computations.
refers to the random intercepts (so continuous latent variables) of the within-level categorical latent variables C1-C5. They do not refer to categorical variables. That's a very high dimensionality (=10) which is difficult to work with.
With 2 timepoints you would get 4 dimensions and will already then need a factor trick like in Henry and Muthen (2010).
Thank you so much Prof Muthen for all your valuable comments, I will read again also the paper entitled 'Multilevel Latent Class Analysis: An Application of Adolescent Smoking Typologies with Individual and Contextual Predictors' as I see there are examples of MPLUS codes for both parametric and non parametric approaches for estimating an MLCA. Hopefully I can edit these and estimate a reasonable MLTA. Thanks again!
csulliva posted on Saturday, July 23, 2011 - 8:31 am
I am trying to run a 2-Wave LTA model with covariates but am getting a "nonpositive definite" message regarding the standard errors. Looking at Tech 1, it appears that the problem is with a transition estimate where, if you look at the output, there doesn't seem to be any cases making that designated transition. I did run a model where I tried to fix that parameter but it doesn't seem to have helped with that issue (the same warning appears with a different parameter number). I have two questions: (a) how would I work with that parameter to determine whether it's a problem? It seems that only that part of the multinomial estimates is problematic. (b) This model is intended to be a precursor to a mover-stayer model. Will the use of that type of model alleviate this problem as that second order latent class variable is designed to capture those cases in the stayer class?
Typically, when no one transitions there will be an extreme estimate for a logit parameter and the program fixes it, avoiding the singular information matrix (SE) issue you refer to. So I am not sure why you have a problem here - I think you need to send it to support.
Thank you. Support answered the question. I had a quick follow-up on the Mover-Stayer model. Basically, I'm trying to follow ex. 8.14, but am wondering what changes to the input need to be made to accomodate (a) latent class variables with three rather than two classes and (b) the highlighted portions of the within class specifications on page 226 with alternative levels of measurement(I have categorical, inflated count, and censored items).
We don't have an example of that. Try generalizing it yourself and if you have problems contact email@example.com.
csulliva posted on Sunday, July 31, 2011 - 6:35 pm
After reviewing a comment above in response to a question from 3/2/11, I decided it might be more straightforward to look at covariate interaction effects on the transition probabilities based on example 8.13. It appears that the model runs, but I am getting a message that "the sample covariance of the independent variables in class 2 is singular."
You may want to take a look at the new note we just wrote on this topic,
Muthén, B. and Asparouhov, T. (2011). LTA in Mplus: Transition probabilities influenced by covariates. Mplus Web Notes: No. 13. July 27, 2011.
This explains how ex 8.13 can be used for your purpose.
It sounds like you have covariates and that in class 2 there is no variation in one of them (everybody in this class having the same covariate value). This is ok - at least if it makes substantive sense.
Julia Lee posted on Tuesday, August 16, 2011 - 12:07 pm
I'm in the process of planning my analysis using both latent profile analysis and latent transition analysis in my study. I am trying to understand the use of covariates and concurrent variables in both analyses.
Regarding LTA, the Mplus manual example 8.13 shows a diagram with covariate x. Q1. I am assuming that the covariate is an antecedent variable. Is this correct?
Q2. If I am planning a study that examines the transition of classes from Time 1 (fall of Grade 1) to Time 2 (spring of Grade 1), are concurrent variables i.e., variables that were administered at Time 1-in the fall of Grade 1 feasible?
Because Grade 1 data is all that I have, I am hoping to use the variables in the fall of Grade 1 to predict the latent transition from fall to spring of Grade 1. Based on a paper recommended on the Mplus website, i.e., Marsh et al. (2009), I understand that in Mplus, the term covariate refers strictly to antecedents. I would like to iron out any misconceptions I am still have in my mind.
Q3. I would also be most grateful if you would recommend papers on covariates and concurrent variables and time-varying and time invariant predictors in LTA analyses. Thank you very much!
Julia Lee posted on Thursday, September 08, 2011 - 2:07 pm
I edited the syntax on Example 8.14 on page 226 to analyze 4 classes with continuous variables instead of categorical variables for the LTA mover-stayer model. I would appreciate your input regarding the correct syntax for the Model c.c1 and Model c.c2 for continuous variables. The highlighted sections (i.e., the syntax on measurement error) must be where I had a problem because my Mplus software ran for 8 hours without coming to a convergence and I had to cancel the analysis. This highlighted section is easier to understand in terms of categorical variables; I am still trying to understand it terms of continuous variables. I would be most grateful if you would provide some insight/explanation. Thank you very much.
Hi there, I am running an LTA with two time points with four classes at each time. I have received the:
"THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE FIRST-ORDER DERIVATIVE PRODUCT MATRIX..." message.
Examining the TECH1 output, I see the issue is with a parameter listed in the beta parameterization matrix. In looking at the regression coefficient itself, I don't see an issue, per se. That is, the estimate does not look problematic.
What more can I do to identify and fix the problem? Is there a resource that might have some tips?
I have a question regarding LTA and confounding. I have conducted a multiple group LTA (2 time points and home smoking ban as "known class"). Some of the transition probabilities in my output are counter intuitive and I was wondering if this could be due to possible confounding.
Is confounding an issue in GMM and if it is,then how can I account for confounding in a multiple group LTA, in MPus ?
First be sure you classes are ordered the same in both groups and at both time points. Confounding can be helped by adding a covariate. See Web Note 13 on the website.
Julia Lee posted on Tuesday, February 28, 2012 - 1:35 pm
I am conducting LTA mover-stayer. I read Nylund's dissertation. On p.57 she wrote that interpretation of the stayers may not be meaningful without measurement invariance. My question: what if full measurement invariance is not observed? Can the LTA mover-stayer still be used? How should the analysis be conducted or interpretation if full measurement invariance is not met? Thanks. I appreciate your response.
You can still do the analysis, but you just change your interpretation since you don't consider movement among the same classes at the different time points. But you should have measurement invariance across the mover-stayer classes for it to make sense.
i want to compute a transition model with unordered categorical variables in three time points. In every timepoint there is only one variable. The variables represent different states of school-/occupational-status and so the categories of the variables aren't equal over time (especially from t1 to t2):
Var2-t2 schooltype5 schooltype6 schooltype7 vocational training
Var3-t3 schooltype5 schooltype6 schooltype7 vocational training unemployed
Is it possible to model the transition between those variables over time in an hidden markov process, or do I have to recode the different categories into dummy variables? I was not able to find an example in the literature that fits to this kind of problem.
If it's possible, do you have a recommendation for an article where such a LTA/hidden markov process is performed?
Dear Linda I have another question. When I conduct the GMM, may I let the Mplus estimate the nonlinear parameters in each class? For example, I set c(4), %c#1% i s | y1@0 y2* y3* y4@1; %c#2% i s | y1@0 y2* y3* y4@1; %c#3% i s | y1@0 y2* y3* y4@1;
How do I interpret the four classes outcome ? Just in FMM, if the factor loadings are different in each class, these four classes have different meanings. Am I right?
In GMM the goal is to find trajectories that differentiate people. You do not expect to find the same trajectory in each class. You do not compare the means, variances, and covariances of the growth factors across classes. To do this you would need measurement invariance which you would have only if the same growth model was found in all classes. You compare the different trajectory shapes.
So, I just can set the nonlinear parameters in %overall% not in all classes. Right? Another problem is that there are many settingg across classes. For example,I can let variances of growth factors free estimated in each class or let residual variancles of Ys in each class free. Then I choose the best model from BIC or some indices. So, it is not necessary that let the variances and covariances of growth facttors equal across classes. Am I right? Thank you.
I am interested in the members of a class A at time 2 and I would like to know in which classes these subjects were at time 1. Therefore, I conducted an LTA and used the final class proportions for the latent class patterns based on the estimated model to calculate class membership probabilities at time 1 conditional on class membership at time 2. Is it statistically correct to do this?
I could not find the RESPONSE option in the OUTPUT command in the users guide. I tried to use the TECH10 option in the OUTPUT command and the RESPONSE option in SAVEDATA command, but both do not work because the indicators in the model are continuous.
Is it possible to use LTA to investigate class membership at time 1 conditional on class membership at time 2?
What part of the output do I need to calculate these probabilities?
I am analyzing the data from a violence prevention intervention study with 4 cohorts. Two cohorts recieved the intervention and two cohorts serve as a comparison group. I am using a latent profile transition model to group participants based on five measures (i.e., overt aggression, social aggression, social competence, cognitive concentration, and liked by peers). Next, the pre to posttest transition of individuals between groups is conditioned on their membership in a knownclass (i.e., treatment or comparison cohort) One of the cohorts in the study is signifcantly different at pretest on the social aggression measure...which leads me to my two questions.
First, are there guidelines for using the social aggression along with soicodemographic measures in both the latent portion of the model and in the autoregressive statements of the model to control for the pretest differences between groups?
Second, (...and since I have already analyzed the model with and without the social aggression measure as a control) if there is no significant change in the model as a result of including the social aggression measure (indicated by no drop in BIC, no change in LgLkd chi square, and a non-significant regression parameter for social aggression) is it defensible to opt for the more parsimonious model without the social aggression measure?
Thank you in advance for your time and consideration.
I am currently trying to create an LTA analysis over 3 different time points. I have already conducted the LCA analysis and have determined that a 3 class solution for T1, a 4 class solution for T2, and a 3 class solution for T3.
My problem is this: The variable structure is not identical across all three time points. For instance, I have 6 variables at T1; at T2, three new variables were added to the 6 at T1; and at T3, a few of the variables from T2 were dropped and a couple more were added. This is appropriate cross-sectionally because the appropriateness of the variables changed as the respondents aged.
I thought that Mplus was capable of conducting a LTA analysis even if the variable structure was not identical across all time points, but I have not been able to find examples of this. Am I incorrect? Must the variables be identical across time points to conduct an LTA? If not, could I be directed to some sample syntax and/or articles?
The variables do not need to be identical over time and can also vary in number. The interpretation of the transitions will be different because you don't have the same classes over time, but that is ok.
All you need to do is to relax the measurement invariance restrictions that are shown in the UG examples for LTA.
Drs. Muthen, Example 8.13 in the current manual is for an LTA model with 2 latent categorical variables with 2 classes each.
It is stated that the regression of c2 on x in the overall model gives the effect in a multinomial logistic regression of x of c2 when comparing class 1 to class 2 of c2.
Similarly, the regression of c1 on x gives the effect in a multinomial logistic regression of x on c1 when comparing class 1 to class 2 of c1.
It is stated that because both c1 and c2 have two classes, there is only one parameter to be estimated for x for each latent categorical variable.
My model has 2 latent categorical variables with THREE classes each. When I regress c1 and c2 on covariates, I receive TWO sets of effects for each covariate for each latent categorical variable. How do I interpret this?
For example, I see: C2#1 ON INTER_AV -0.074 1.246 -0.060 0.952 EXTER_AV -0.137 0.871 -0.157 0.875 ADVERS11 -0.174 0.124 -1.407 0.159
The above output (just pasting effects for c2) shows effects of the three covariates on classes of the latent categorical variable c2, but this is comparing what with what? Class 1 to Class 3, and Class 2 to Class 3 of c2? Is Class 3 similar to an omitted class (as in dummy coding)?
I have a question about a warning I received when conducting a LTA over two time points with 3 classes in each time point. Some of the variables are the same across time, and some are different - I have relaxed the measurement invariance to reflect this. I found that it is helpful to include STScale=1 in other LTAs, so I included it here as well. My stating values are STARTS = 5000 100.
I receive the following warning:
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE FIRST-ORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.122D-10. PROBLEM INVOLVING PARAMETER 47.
Now, I was unable to determine exactly what parameter 47 is (the Tech1 output was not terribly helpful here), but I did notice that only 1 case transitioned from T1C2 to T2C1; only 2 cases from T1C3 to T2C1; and 0 cases from T1C2 to T2C3. I think this must be problematic. Is it possible to "fix" the transition from T1C2 to T2C3 since no one transitions here (should I do this for the other transitions with such low cases)? How would I write that in the input? Do you think this may be the problem causing the warning message? What other sorts of problems might I consider?
Hi Linda, if I see the following in my output, should I be concerned about the p levels of 999.000? Do those numbers indicate a problem in my model, or are these p values so small simply because the SEs are near zero? Thanks.
Linda, I have explored several predictors of class membership in my LTA models. Some predictors improved model fit (AIC, BIC) and had significant effects on class membership; while other predictors worsened model fit slightly and had no significant effect on class membership.
Only one of our predictors was dichotomous: a marker of Ethnicity (0/1) for our two groups. When we added this predictor, we had to specify INTEGRATION=ALGORITHM under the analysis line to accomodate the dichotomous nature of this variable. However, the fit of the model worsened much more dramatically for this predictor than for the other predictors that ended up not having significant effects.
Could this be due to the dichtotomous nature of the predictor, or the INTEGRATION=ALGORITHM? Is the fit of a model with TYPE=ALGORITHM reasonable to compare with our unconditional model, which was estimated without INTEGRATION=ALGORITHM?
Or does the INTEGRATION=ALGORITHM specification make the model very different in nature than a model without this line of code--such that it is not a fair comparison?
Hi, I am running a two time point LTA, three classes at each time point. Is it possible to get confidence intervals or standard errors for the class probability estimates and the transition probability estimates? I read above that there was a formula in Chapter 13, but I think the manual must have changed since then because the page numbers given don't exist in Chapter 13. Thanks
To get SEs of transition probabilities, you have to express transition probabilities in terms of your logit parameters in Model Constraint using the formulas of Chapter 14. Version 7 will have a probability parameterization where such SEs are produced directly.
Hi Bengt, Thanks for the pointers. I am still not sure exactly how to get the standard errors of the transition probabilites. I have been able to use the formulas on page 446 and 447 of the User's Guide to get from the logit parameters output in MPLUS to the transition probabilities also output, so I know that I am using the formulas correctly.
However, I am not sure how to apply these to the standard errors. In the formulas on page 446, the sum is defined as the 'sum of the exponentials across the classes of c2 for c1 = j'. I can do this for the point estimates, for example: sum1 = exp(a1 +b11) + exp(a2 + b21) + exp(a3 + b31) where a1, a2, b11, b12 are all in the output, and a3 and b31 are 0.
However, when I try to do this for the standard errors, I use the standard error values corresponding to a1, a2, b11, b12 in the formula, but I do not know what to use for the the values of a3 and b31, and so I can't calculate the sum.
You get SEs for the latent class statuses expressed as logit parameters. You can transform those logits to probabilities in Model Constraint as described in Chapter 14 of the UG (in version 7 you can request probability parameterization and get this directly).
I am sorry, can you tell me exactly what page in the User's Guide? I have looked in Chapter 14, and I can only find formulas for the latent class statuses conditional on covariate x. I wish to get standard errors for the unconditional latent class status probabilities, as per the output 'FINAL CLASS COUNTS AND PROPORTIONS FOR EACH LATENT CLASS VARIABLE BASED ON THE ESTIMATED MODEL'. Thanks, O
Hi Jon and Bengt, Hmm, thanks, that is what tried to do but it doesn't seem to be working, so I thought I must have been looking at the wrong thing. For example, I have a three class variable c1 at time 1, so I used the following code (extra stuff on transitions omitted):
[c1#1] (a_1); [c1#2] (a_2);
MODEL CONSTRAINT: NEW(tempa_1 tempa_2 proba_1 proba_2 proba_3 suma_12);
Hi Bengt, Sorry I misread your earlier message and thought you said it could be used for the case with covariates. AT least now I know why it wasn't working. Is there a way to calculate the probabilties when covariates are present? O
The formulas on page 444 are for the probabilities at specific values of the covariates - in the two examples, there is the case where all covariates = 0, and then the case when all covariates = 1. However, I have tried both these and neither of these gives me the probabilities output by MPLUS under 'FINAL CLASS COUNTS AND PROPORTIONS FOR EACH LATENT CLASS VARIABLE BASED ON THE ESTIMATED MODEL'. I think what I need is a way to calculate the marginal probabilties (and s.e.), not those for a specific value of the covariates. Basically what I need is a way to calc the s.e. for the 'Proportion for each latent class variable based on the estimated model'. Is there a way to do this?
Jon Heron posted on Monday, September 17, 2012 - 6:33 am
Presumably if your covariate is categorical then this would just be a weighted sum of those two figures you have just derived, with the weights depending on the distribution of your covariate.
With covariates, the marginal probabilities of the latent classes are not parameters in the model so this is not straightforward to get. As Jon says, the point estimates of the probabilities can be obtained by computing the probabilities for each subject's covariate values and averaging, but I see no easy way to get the SEs. Some would argue that you get the class probabilities and their SEs from the unconditional model and that the conditional model is used for explaining the class membership; problem is that the class probabilities may change between these two models, but the reason for this can be explored.
Check the top of your output to be sure you are using Version 7. You may have more than one version of Mplus on your computer.
Laure posted on Thursday, November 08, 2012 - 1:46 am
Dear Linda and Bengt
I am running a LTA with 15 binary variables, 3 time-points, 3 latent classes and a covariate. I would like to estimate the missing values of the variables based on the existing information of the other time-points. My syntax is based on ex8.13part2.inp and I am using Mplus 7. Could you please give me an example of how to specify the syntax for the imputation of the missing values? Thank you so much.
See Example 11.5 and also the section in the user's guide for DATA IMPUTATION.
Laure posted on Saturday, November 10, 2012 - 5:39 am
Thank you, Linda. Unfortunately, with ex11.5 the following warning occurred:
*** FATAL ERROR THE CONVERGENCE CRITERION IS NOT SATISFIED.INCREASE THE MAXIMUM NUMBER OF ITERATIONS OR INCREASE THE CONVERGENCE CRITERION.
PROBLEM OCCURRED DURING THE DATA IMPUTATION.YOU MAY BE ABLE TO RESOLVE THIS PROBLEM BY SPECIFYING THE USEVARIABLES OPTION TO REDUCE THE NUMBER OF VARIABLES USED IN THE IMPUTATION MODEL.SPECIFYING A DIFFERENT IMPUTATION MODEL MAY ALSO RESOLVE THE PROBLEM.
I would not like to reduce the number of variables, unless it would be absolutely necessary. What can I do to remedy this issue? For information: With only two time-points ex11.5 works fine.
Hi! I am running LTA following Nylund Dissertation. But….
ONE OR MORE 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 VARIABLES IN THE MODEL THE FOLLOWING PARAMETERS WERE FIXED…
Also I am running a Mover-stayer LTA for three time points using a probability parameterization (following example 8.15). But…
THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ILL-CONDITIONED FISHER INFORMATION MATRIX. CHANGE YOUR MODEL AND/OR STARTING VALUES. THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NON-POSITIVE DEFINITE FISHER INFORMATION MATRIX. THIS MAY BE DUE TO THE STARTING VALUE BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS -0.375D-16. THIS MAY ALSO BE DUE TO LARGE THRESHOLDS. DECREASING (INCREASING) LOGHIGH (LOGLOW) MAY RESOLVE THIS PROBLEM. LARGE THRESHOLDS WERE FOUND…
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: 37 38 39 40 41 42 43 44
========================================= Could you please help me with this problem? thank you so much!
Hope this is the right topic heading. What kind of analysis is the following: Categorical variables measured at baseline (e.g. big, heavy, smart, wise) would give you something like two latent classes -> say, weight and IQ; you also measure change (i.e. not using the same set of variables as at baseline) as in bigGER, heavIER, smartER and wiseR at some point later on -> that also gives two classes, as in weightIER and IQ-IER ;). What's of interest is how class membership at baseline affects the class membership of change - and how these are associated with a later outcome, say life expectancy (could be categorical or continuous). Would it be latent transition analysis with distal outcomes - of sorts? Can one model it? Would one use the AUXILIARY setting? Cheers!
I've a question concerning a Hidden Markov Chain Model with more that 2 unordered (nominal) categories in the variables.
I've two nominal variables, one in each timepoint. Before building a markov chain I have to define a latent variable in each timepoint with the nominal variable as an indicator.
My question is now, how do I have to set up the measurement model? Do I have to define for each category a latent class with the number of thresholds (k-1) defined like in the examples for ordinal variables, just replacing the $ with #?
Here my example for the first timepoint (nominal variable 5 categories)
Tania Wood posted on Wednesday, January 30, 2013 - 6:46 am
Dear Mplus team,
I'm working on an LTA model with covariates and have tried to follow the input used by Nylund in her thesis. My input looks like this:
MODEL: %OVERALL% ptype4 ON ptype2;
MODEL ptype2: ptype2#1 ptype2#2 ptype2#3 ptype2#4 ON zwrkhrs2 sw2anx; ptype4#1 ptype4#2 ptype4#3 ptype4#4 ON zwrkhrs4 sw4anx anybaby ONSSECch;
MODEL ptype2: %ptype2#1% etc, etc.
I keep getting the error message: *** ERROR in MODEL command No OVERALL or class label for the following MODEL statement(s): PTYPE2#1 PTYPE2#2 PTYPE2#3 PTYPE2#4 ON ZWRKHRS2 SW2ANX;
and I can't work out what I'm doing wrong. I've tried putting the model statement on the same line and adding % to the class labels but I get the same error message. I'd be really grateful for any ideas.
I am running a LTA model with continuous covariates and would like to utilize the new LTA calculator function. The model runs without error, but I am unable to click on the LTA calculator in the drop down menu. Is there something I need to write in the syntax to make this option available? Thanks!
I am running SEM analysis using WLSMV estimation method. I have three latent variables for IVs and three mediating variables (they are all continuous) and one latent variable for DV (three items were categorical).
I have a question about the indirect effect. The M-plus example code shows that I can include a code for indirect effect.
However, when I read over posting on the website, so many people talk about the bootstrapping method. It was my understanding that the indirect effect on the output can be used for the report of the results, correct?
Or should I use the code for bootstrapping to test the indirect effects? If I need to use this bootstrapping method, how to set the code?
Hello, I am having some with an LTA with 3 time points. There are 3, 3 and 4 classes at the respective time points the classes represent psychological disorder classes. I have two covariates, gender and a continuous, time varying covariate. I have been through examples 8.13 and 8.14 as well as the webnote and have developed the following input (excluding threshold constraints to save space): MODEL: %Overall% C1 ON Gender ACES04; C2 ON C1 Gender ACES04 ACES48; C3 ON C2 Gender ACES04 ACES48 ACES812; MODEL C1: %C1#1% C2 ON Gender ACES04 ACES48; %C1#2% C2 ON Gender ACES04 ACES48; %C1#3% C2 ON Gender ACES04 ACES48; MODEL C2: %C2#1% C3 ON Gender ACES04 ACES48 ACES812; %C2#2% C3 ON Gender ACES04 ACES48 ACES812; %C2#3% C3 ON Gender ACES04 ACES48 ACES812; I have tried this both parameterizations from the webnote. Both gave me the logits and odds ratios predicting class membership at each time point and for transitioning to each class, given specific Latent Class Patterns (i.e., 111, 121, 131, 211, 311). However, what I am really looking for is whether or not the transition probabilities from each of the two transition matrices (3X3 and 3X4) are dependent on my covariates. Do these parameters have to be created manually or is there a way to print them?
I am trying to run an LTA with two concurrent growth models (ie., childhood ADHD and Depression symptoms) that predict a second set of two concurrent growth models (ie., early adolescent ADHD and Depression symptoms). I am evaluating the transitions from childhood symptoms to adolescent symptoms. I also have binge eating in late adolescence as an outcome.
My problem is with testing significant mean differences on the outcome among classes within each growth model. I was able to identify how to place binge eating in the model as an outcome, based on syntax referenced in Karen Nylund's dissertation. However, I understand from the discussion board that I need to use the Wald test in Model Test to identify statistical means differences across classes. Unfortunately, I keep getting this warning: "WALD'S TEST COULD NOT BE COMPUTED BECAUSE OF A SINGULAR COVARIANCE MATRIX." I may have too many empty cells for these tests to be estimated. Do you have any suggestions for how to remedy this?
Nylund (2007, p. 100) notes that in LTA "It is important to explore measurement invariance of the classes before imposing structure on their relationship across time (i.e., through the autoregressive relationship)."
The examples on invariance that I have seen, however, seem to include the autoregressive paths (UG ex 8.13, posting of May 12, 2009).
Should I omit the "on"-statements between the classes in the %OVERALL% section for exploring invariance?
I am running a LTA with two time points. The measurement model is LCA with four binary indicators and 3 classes at Time 1, 2 classes at Time 2. When I run the analysis, I get the same error message reported by several others above:
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: 23 24 25
Based on the Tech 1 output, I believe the parameters correspond to the following: 23 = Alpha(c) c2#1 24 = Beta(c) c1#1:c2#1 25 = Beta(c) c2#1:c1#2
The transition matrix produced is as follows: 1 2 1 0.00 1.00 2 1.00 0.00 3 1.00 0.00
My questions are: 1) How can I determine whether the singularity is due to empty cells or to the model not being identified? 2) What is the meaning of the alpha and beta values? 3) How problematic is this error message in terms of the validity of my model?
Not necessarily. The two time points are not independent.
Oliver Perra posted on Thursday, September 19, 2013 - 6:00 am
I am reading with interest the paper regarding the 3-step approach implemented in Mplus 7 (see Mplus Web Noes No.15, version 7).
I have a couple of general questions and I would appreciate your comments.
1-When applying this method to LTA, what is the best way to test for measurement invariance across occasions? Looking at the two examples in the webnote (one with and one without measurement invariance), I cannot figure out how one would compare models with and without measurement invariance.
2. Assuming one has partial measurement invariance (e.g. two classes invariant in a 3-class model), what would be the best strategy to apply the 3-step method? Would one estimate the SVALUES for the invariant part in step 1 and then use them to fix parameters for the invariant part as one would do for a completely invariant model? Thanks Oliver
Hello, do indicators of classes in an LTA have to be categorical, or can they be continuous? Typically, I see indicators as categorical in LCA and LTA because the classes are determined by probability of endorsement on the group of indicators.
I also saw the examples in the Mplus manual for GMM and LCGA (also in the family of mixture modeling), where indicators can be continuous. But for those, continuous indicators are measured multiple times in the growth model, which is different.
But can indicators be continous in LCA and LTA, such as ratings on items on a scale from 1 to 100, or age, or a percent score? I would think that the answer is no, because I don't see that as allowing classes to be defined according to endorsement probabilities. Only categorical indicators lend to probabilistic interpretations. Is this right?
Very interesting! Dated literature on LTA (e.g., Collins et al. 1994) describes it as being based on categorical items only. This is intriguing, but I appreciate this expansion to the method. It is as if the analysis has changed in definition since then, perhaps because of expanded software capabilities. Thank you.
Tait Medina posted on Wednesday, September 25, 2013 - 2:59 pm
I am wondering if a model such as this can be estimated and if you think it makes sense: Say I have 3 time periods. I allow the conditional item probabilities to be non-invariant over time, but I fix the transition probabilities to be 1 on the diagonal (everyone in c1 at t1 is in c1 at t2 and t3, everyone in c2 at t1 is in c2 at t2 and t3, etc.). I want to do this b/c the LCAs estimated separately at each time reveal interesting and reasonable differences in conditional item probabilities for classes with the same substantive meaning. Absent the data, I also think this makes sense theoretically. I am trying to capture developmental trajectories during emerging adulthood (the period from 18 to 24 yo). If we think of a "normative class," we can envision the probability of leaving the parents' house, finishing college, working full-time, having a first child to increase over this time period. We can also think of a "u-turn" class who leave the parents' house and begin full-time employment only to later return home and enroll in school. I believe the above model will be able to capture this, but am not sure if it is a reasonable approach.
This sounds similar to the mover-stayer model of UG ex 8.15.
Tait Medina posted on Thursday, September 26, 2013 - 9:32 am
Thank you for your reply. Doesn't the model of UG ex 8.15 assume measurement invariance across time for the five latent class indicators? So it would be the same as 8.15 if measurement non-invariance of latent class indicators was allowed and everyone was in the stayer class. Is this reasonable?
I'm trying to conduct an LTA with count and continuous indicators & a continuous covariate as in Ex. 8.14. I am getting the errors "There is at least one count variable that has only one unique value..." and "One or more variables in the data set have no non-missing values." referring to T2 indicators. When I check these variables in Stata, they have few missing values. Here's part of the output:
What's very confusing is that there should be roughly 992 observations at each time point (although some may be missing one or more indicators).
You need to check the data set that Mplus is reading not the Stata data set. It sounds like you may be reading the data set incorrectly in Mplus. Check the data set for blanks and be sure the number of variable names in the NAMES statement is the same as the number of columns in the data set.
I am very new to Mplus (only got it this week in fact) but I have a few (probably basic) questions. I have done my best to look through the discussions above but I may have missed solutions to my problems. I am trying to fit an LTA model, quite simply, I have 2 time points, 7 indicator variables. I want to know the number of classes to select and then to interpret what I have found. I have some notes from an Mplus course I attended, and have been looking at the User’s guide a fair bit. Anyway, my questions are: a) Is it possible to use an ordinal indicator to form the latent variable (as each of my indicator variables are on a scale (most 5 levels)) instead of binary? If so, how are they coded? b) Is it possible to get the Bootstrapped Likelihood Ratio Test (BLRT) for LTA. In the notes I have, it is possible to get it with the TECH14 command for LCA, however, when I run it, it doesn’t accept it in the LTA. c) From what I have read, one of the key parameters in LTA is the item-response probabilities (Rho’s). From the output, I can’t see clearly where they are. I have found the proportions in the classes and transitional probabilities but can’t find the bit for the rhos. Those are my queries for now- I hope they aren’t too trivial! Many thanks, Dan
a) Yes; just declare the variables as categorical and Mplus will find how many categories you have. You don't need to code the variables in any special way.
b) No, we don't have BLRT when there is more than one latent class variable. Do LCA BLRT for each time point separately. Or, use BIC for either LTA or LCA. I find that BIC is so much easier to work with.
c) The rho's are the thresholds for each class and variable. See our Topic 5 teaching handouts and videos on our website covering LCA and Topic 6 on LTA.
Hello, Example 8.13 in the Mplus manual shows an interaction between c1 and x on c2 in a two-class, two time point LTA as follows.
MODEL c1: %c1#1% [u11$1-u14$1*1] (1-4); c2 ON x; %c1#2% [u11$1-u14$1*-1] (5-8); MODEL c2: %c2#1% [u21$1-u24$1*1] (1-4); %c2#2% [u21$1-u24$1*-1] (5-8);
Why is the regression of c2 on x shown in the MODEL c1 portion of code, rather than in the MODEL c2 portion of code, given that it is an interaction on the c2 factor? I like this model very much, but am confused about the placement of that one line in the code. What would be modeled if it were placed in the MODEL c2 portion of code? Thank you.
Actually, I think the above code was from a prior version of the manual, but I suppose the concept is the same. Apologies--I am checking the current manual now, but am still interested in the question above. Thank you.
Hello, in example 8.13 there is an option for using PARAMETERIZATION = PROBABILITY. When transition from class 1 to class 2 is considered it gives the following results: P(C2=2|CG=1,C1=1)=0.547 for cg1 P(C2=2|CG=2,C1=1)=0.475 for cg2 The probabilities of staying in class 1 are: P(C2=1|CG=1,C1=1)=0.194 for cg1 P(C2=1|CG=2,C1=1)=0.244 for cg2
When cg2 is a reference class: OR=(0.547/0.194)/(0.475/0.244)=1.4 That OR means that members of cg1 group in comparison to cg2 group are more likely to move from class 1 to class 2 (rather than stay in class 1). Am I getting this right?
Is it possible to calculate the significance level of this OR in Mplus as in the web note 13 using model constraint command, but with the probability parametrization instead of logit parametrization? Thank you.
Thank you very much for your advice. I've tried to label the probability parameters: MODEL cg: %cg#1% c2#1 ON c1#1 (t011); c2#1 ON c1#2 (t021); c2#1 ON c1#3 (t031); c2#2 ON c1#1 (t012); c2#2 ON c1#2 (t022); c2#2 ON c1#3 (t032); ..and the same for x=1
Then I used the model constraint to get ORs using the code below:
t013 = 1-(t012+t011); t023 = 1-(t021+t022); t033 = 1-(t032+t031); ..and the same for x=1
oddsx012 = t012/t011; oddsx013 = t013/t011; oddsx021 = t021/t022; oddsx023 = t023/t022; oddsx031 = t031/t033; oddsx032 = t032/t033; ..and the same for x=1
The results seem to give me correct calculation of ORs. But they are based on the transition probabilities that differ a lot from the model without model constraint command. I will be very grateful for your suggestions how to solve this problem.
Thank you for your answers to my previous questions. I will be grateful for your opinion about yet another thing. I have a LTA model with assumed measurement invariance. Adding a second order path to this model resulted in significant improvement of fit based on -2*loglikelihood test, but the BIC for the second order model is still higher (difference = 4.03). How would you interpret these results? In theory it makes sense to add the second order path. Thank you
I have a couple of queries regarding the LTA investigations I am running at the moment.
I have about 9700 observations in my dataset, and I am currently looking at 9 binary indicator variables measured at 2 time points. The number of classes that is optimum is 3 classes, of which have latent class proportions roughly (class 1- 16%, class 2- 67%, class 3- 17%). So am I correct in thinking that 67% of the 9700 (so about 6500 observations) belong to class 2? I would presume this, however, when I look at the item-response probabilities, class 2 has these at or nearly at 1.00, so that would imply there are 6500 observations in my dataset that have a '1' for all of the 9 variables? But I know that that isn't correct by a long way. Only about 600 observations have a '1' in every indicator variable. The majority of the dataset have '0' in the indicator variables as I have coded them such by design. Am I getting muddled with what this means or is my data not being read into Mplus correctly?
My second question, is that I am using the save cprob command which gives me the probabilities in a txt file. Is there a program that I can open this file in so that I can re-arrange the data and create frequencies etc?
Also, if I extend Example 8.14 to three time points, would the transition that occurs between time points 2 and 3 be independent of the transition that occurred between points 1 and 2?
This idea is reflected in literature for latent trajectory analysis, but I was unsure whether it applies to this latent transition analysis model.
For example, for latent trajectory analysis: "For a given trajectory class j, conditional independence is assumed for the sequential realizations of the elements of Yi, yit [i.e., the dependent variables] over the T periods of measurement."
Kathleen posted on Friday, January 31, 2014 - 5:53 pm
Hello, I'm looking at UG 8.15, but would like to know how to constrain transitions without specifying a mover or stayer class, more along the lines of the description of the ECLS-K LTA? I would like to do this with the probability parametrization in Mplus 7.1.
We have 2 time points with 4 classes at each time point. Looking at our results from latent class analysis at time 1 and 2 in cross tabs, there are some transitions that hardly happen (e.g.,0.3% of the sample).
Related to the above is how to specify the transition constraints for the 4th class, since it is the reference class and therefore not mentioned in the multinomial regressions.
Ex 8.1 can be extended to any number of time points.
The different transition matrices are different as the default in Mplus.
Jane Smith posted on Thursday, February 06, 2014 - 6:53 am
I have an LTA model with 3 time points and a second-order effect, and would like to compute the transition probabilities between time 2 and time 3 based on class membership at time 1. Can the new LTA calculator be used compute transition probabilities across different levels of a given latent class membership? If not, can I use the equations for computing transition probabilities across covariates?
Yes, the LTA calculator should be able to do this. Maybe I have examples in one of my talks that are posted (e.g Utrecht, August 2012).
Kathleen posted on Sunday, February 09, 2014 - 9:50 am
Sorry if this is a repost; I thought I had posted but cannot find it on the board. I have two questions: 1) After reading Webnote 15 and Chapter 14 in the UG, I’m not able to figure out how to constrain transition probabilities in the last class in an LTA. I’d like to constrain movement from class 3 at Time 1 to class 4 at Time 2, and vice versa. In the logit parameterization, “c2#4 on c1#3@0;” is not allowed. How could I specify this with a model constraint command? I seek to do this is because the transition patterns for these groups are too small for analysis. I thought my options would be to either constrain the model or examine the item response probabilities and re-classify respondents post-hoc. Which do you think is the better approach?
2) I am not using a covariate in my LTA, as I have no theoretical reason or substantive reason to do so. But I’d still like to improve the model due to misclassification at each time point. I applied the manual 3 step approach, saving class probabilities at each time point in 2-time point LTA, and applying the logits in the LTA to the nominal variable. The BIC and ABIC of the model increased, but the entropy also increased substantially compared to results without the 3 step procedure. Would I compare the models using the measurement invariance LRT test with the scaling correction factor?
Dear Dr.Muthen, I have a question about your model in Mplus user's Guide Chapter 8 page 236 Variable cg you use circles and squares overlap symbols, this variable it mean know class variable right? If I apply this model to use in my research. I can use this right, if I have know class variable. Could you tell me about this symbol.
I also want to test if there is a difference between males and females.
I can see I will also struggle with the covariate prediction stage as well. The users guide seems to be the best example I can find, but my data isn't clustered (or two-level as phrased in the example). Do I simply remove the terms that are related to the clustering for it to work?
Jane Smith posted on Tuesday, February 11, 2014 - 9:41 am
Thanks for your quick response to my last question. I was able to use TECH15 to get the transitions split by class membership at the first time point. I then added continuous covariates to my model and the TECH15 output gave me ten outputs with slightly different numbers but all with the same heading--"ESTIMATED CONDITIONAL PROBABILITIES FOR THE CLASS VARIABLES EVALUATED AT THE SAMPLE MEAN FOR ALL COVARIATES." Which output is most appropriate to use? Is this perhaps because I use multiple imputation?
I am examining the moderating effect of a continuous covariate on transition probabilities, similar to the model shown in the Muthen & Asparouhov web notes entitled “LTA in MPlus: Transition Probabilities Influenced By Covariates.” I am using the LTA Calculator function to produce the transition probabilities at different values of the covariate. My question: Is there any available estimate of the statistical significance of the moderation effect, or are the apparent differences in transition probabilities at different values of the covariate merely descriptive?
I am running one- and two-level LTA models with dichtomous indicators.
When I ran 1-level LTA models, I received class endorsement probabilities in both threshold and probability scales.
In my 2-level LTA output, I see class endorsement probabilities only in the threshold scale, without the conversion to probability scale.
What command may I use to obtain the class endorsement probabilities for my 2-level LTA in the probability scale, as seen below from the 1-level models? Alternatively, is there a way to convert them by hand?
RESULTS IN PROBABILITY SCALE Latent Class Pattern 1 1 1 ALCYEAR1 Category 1 0.768 0.019 39.478 0.000 Category 2 0.232 0.019 11.926 0.000