Sorry, but perhaps I've answered my own question -- I just re-ran my model setting STARTS = 0 with the same starting values I'd used, specified 100 iterations, and got the identical results. So, I take it that in addition to running the # of models with random seeds, Mplus also runs one model with the specified starting values, and that one happened to give me the smallest LL? If so, what does it mean that that one is not replicated even with as many as 300 random starts? Thanks, Bruce
Your 2nd question is hard to answer without seeing the problem run. Sometimes the model is just too complex for the data and doesn't replicate - a simpler model should then be chosen. Sometimes there are messages that not all perturbed runs converged, in which case switching to stscale=1 might help. Sometimes more numerical precision is needed with numerical integration and it helps to increase the number of integration points.
Thanks so much for your quick reply, Bengt! I think my first posting didn't get posted because I failed to click the correct button after reviewing it, but the results that generated my question were that I got the lowest LL = -3873.278 with the unperturbed starting values, then (asking for STARTS = 300 20, STITERATIONS = 40), got 19 subsequent solutions with the identical LL = -3878.458. So, the solution did replicate for all the models with random seeds, but the one with the unperturned starting values was smaller. (Only 2 out of 300 perturbed starting values did not converge in the initial stage.) I'll try STSCALE=1 and then numerical integration if that doesn't work. Best, Bruce
nina chien posted on Friday, June 27, 2008 - 3:23 pm
In running an LCA with 600 10 random starts, the largest loglikelihood is always the unperturbed starting value (and of course is not replicated). The next 9 best loglikelihoods are identical. Does this indicate the model is unreliable?
Thank you for your prompt reply way last May, Linda. Rather than burden you with unnecessary work, I decided to do more reading and more analyses before bothering you. So, I was able to get the smallest LL of -3874.155 to repeat -- twice in addition to the unperturbed solution, with
STARTS = 1500 50; STITERATIONS = 100;
The two next smallest LL = -3877.816, then the next 45 were LL = -3878.458. Although the solution with the smallest LL interpretable, such results raise the question how trustworthy a solution is with only 3/1500 replications? Doesn't that suggest a local maximum even so? Wouldn't the LL with so many solutions be more reliable?
Sorry, wrong term. I mean I got the same smallest LL in only 3 out of 1500 starts, with 2 being random starts and the 3rd being with unperturbed starting values -- all with starting values I specified based on a prior model. This was for a 4-class GMM. (Is that the right way to say it?)
I ran the model as you suggested without starting values, allowing intercept and linear slope variances to differ across classes. (I set quadratic slope variances to zero for the model.) I used 5000 random starts and got the same largest LL AND class assignments as for only 100 random starts, and in both models got the same warning about the covariance matrix in one class being non-positive definite. This is not the smallest class, but it is small (C4 n=17; the other three classes are C1=215, C2=8, and C3=13). This sort of problem is why I specified starting values before, and solved the problem with the one class by setting slope variance = 0, which seemed reasonable given the tests for the slope variances -- all had p-values < 0.06 except for the problem class, for which the p-value was 0.945.
I want to be able to go to the next step and test whether 4 is better than 3 classes (the plots look interesting and plausible) but can't without getting the model to fit and replicate. It seems to me that the best next step is to use the estimates for the means and variances from this model as starting values, specifying the slope variance as zero for the problem class. However, that's what I did before that led to my question on July 2nd. The model fit then, but with only a very small number of replicated largest LL even with 1500 starts -- only two in addition to the unperturbed, specified starting values.
I would first run with the default of class-invariant variances. Then plot the model-estimated mean curve together with the observed individual curves classified into most likely class to see if there is a need for class-specific variance for a class. If so, free say the intercept variance only for that class. Models with all variances class varying can be hard to replicate.
Another trick is to force variances to be greater than zero. This is done by labeling a variance parameter such as the random slope variance:
Thanks very much, Bengt. This is very helpful. But in the interest of time -- assuming you have more time for a response! -- I understand that you are suggesting that I use a GMM with i s & q variances the same across classes (the default model), then examine the actual individual (spaghetti) plots against the mean plots for the classes. If any look like there is within-class variation not accounted for by the default model, then free up the intercept variances, one at a time, as suggested by the empirical vs est. mean plots, and examine fit for improvement in the less constrained model. Stop when model fit doesn't improve much -- say -- using the BIC and/OR SABIC, and perhaps the CFI and RMSEA?
Also, thanks for the note about how to prevent negative slope variances (a type of Heywood case, right?) if nothing else seems to work. Although I assume that, as with other latent variable models, this strategy would not be as good as fixing a problem leading to the negative variance?
Thanks very much. I've been working on the problematic data set, starting over with the default model and working my way up through the class numbers to find the model that fits best. The individual spaghetti plot variations around the class mean plots do not look that different in the amount of variation across classes.
I have another question now about selecting the number of classes, but I think that should be in a different thread.
Thanks for all your help with this set of questions! Bruce
It probably means that the data cannot support as many as 5 classes. But it doesn't mean that the 4-class model should necessarily be be chosen. For example, if a model different than LCA is the right model, then reducing the number of classes is not sufficient. As one example of a model alternative, factor mixture modeling may be used, adding a factor to the LCA that explains correlations among items within class. Our web site has several papers on FMM.
I am running an LCA with covariates, using 500+ starts. The lowest LL is consistently replicated but with one of the seeds 'unperturbed'. I cannot find an explanation for this in the User Guide. Could you please suggest a reference, and advise if the following model is acceptable?
Final stage loglikelihood values at local maxima, seeds, and initial stage start numbers:
The model is estimated once with the default starting values. Then these values are randomly perturbed to obtain other sets of starting values.
Yuchun Peng posted on Tuesday, February 15, 2011 - 8:12 am
Hi Bengt and Linda,
I am running a 2-cluster LCGA model with 11 binary variables. The warning message I got is like '60 perturbed starting value run(s) did not converge', regardless the starting values and stiterations used.
Although the highest likelihood replicated many times.
I tried to solve this problem by specifying the scale of the random perturbation to 2 and it worked.
Is there anything I need to be aware when specifying a low level scale of perturbation?
By 2-cluster LCGA I think you mean an analysis with 2 latent class variables, rather than a 2-level model with only 2 clusters. Models with more than one latent class variable sometimes need a more gentle perturbation of the random starts to not get wild starting values. You may want to experiment with also using a little larger value between 2 and the default 5 to make sure you don't find a better loglikelihood. Other than that, it should be fine.
Hello, I am running exploratory LPA right now and have started with 3 classes. The following is the input
CLASSES = c (3); Analysis: TYPE = MIXTURE;
I got a number of error messages including the following.
1. Final stage loglikelihood values at local mxima, seeds & initial stage start numbers.
2. Unperturbed starting value run did not converge
3. Best loglikelihood not replicated.
4. One or more parameters fixed to avoid singularity
5. Standard errors of model parameter estimates may not be trustworthy.
6. Entropy is .925
The continuous indicators are decimal numbers because they are proportions. Do you recommended resaling the numbers for eaiser estimation? (for example, one indicator is the proportion of lone mothers in the individuals neighbourhood. Which is being combined with other neighbourhood varialbes t run in the LPA for a latent variable of community adversity). Any suggestions you have would be helpful. ***Melissa