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 Dennis Li posted on Thursday, July 28, 2016 - 2:06 am
I am running an analysis with 8-10 binary milestone variables measured over 5 time periods. Once a milestone becomes 1, there's no transitioning backwards to 0. Also, the proportion of 1s starts high >80% for most milestones. Without adding covariates yet, I put all 50 variables into a RMLCA to see if it would run, and, to my surprise, the models converged. I was able to calculate VLMRLRT and BLRT for all models, and entropy values for k=1-5 were >.96, with fairly substantive interpretations.

However, for models k>2, I received a NON-POSITIVE DEFINITE FIRST-ORDER DERIVATIVE PRODUCT MATRIX error, with the issue being a threshold parameter and a small condition number. Scouring the message boards, I found an old discussion (URL copied below) in which Bengt says "Thresholds that go large like that are harmless causes of the non-pos def message" but also "You don't want a very small condition number and [-0.783D-15 in this case] is very small."

Should I just take that my models are non-identified and not even look at the results? Is it even a good idea to run multiple indicators with multiple time points in the same model? I am quite new to LCA and am stumbling with some of the basic ins and outs. Thanks.

The post I was referring to is:
 Bengt O. Muthen posted on Thursday, July 28, 2016 - 9:27 am
If you have very large thresholds that weren't fixed by Mplus, that can give you a small condition number. This is not necessarily harmful, however. Your model may well be identified.

A bigger issue is perhaps that your model does not reflect the no transitioning backwards from 1 to 0. That feature is characteristic of discrete-time survival analysis (although that is typically done for a single variable).
 Tessa posted on Thursday, December 13, 2018 - 9:31 am
Dear Prof. Muthén,

Currently I'm doing an RMLCA, and figured that the input needs to be like I state below (examining response patterns in 3 classes on a victimization measure across 3 time points). However, I don't understand what the $1 thresholds mean. What determines whether I should indeed set those to 1, and what does that (in 'substantive' words) mean? Does it mean that I am estimating the likelihood that someone answers 0 versus 1 on my item, for example?

Thanks in advance!
Best, Tessa

categorical are vict1 vict2 vict3;
auxiliary = sex(r3step);

TYPE = mixture ;
STARTS 1000 400;

 Bengt O. Muthen posted on Thursday, December 13, 2018 - 12:10 pm
The $1 refers to the first threshold of a categorical variable. With a binary variable, it is the only threshold. The threshold relates to the probabilities of the categorical variable's outcomes. See our Short Course Topic 2 on our website.
 Tessa posted on Friday, December 14, 2018 - 8:00 am
Thanks, that makes sense! My measure has 3 categories and so perhaps I should change the threshold to 2 (for example [vict1$2-vict3$2]).
However, I don't understand whether that is really needed, because in the model in which I had the threshold at $1 (the script in my previous post) the output of Model results showed both thresholds for vict$1 and vict$2, and probabilities for all 3 categories. So it seems that also with the threshold set to 1, it does recognize all three categories.

The reason I'm asking whether it's needed to change my script to $2 is because the model with the $2 is already running for 8 hours now (while the one with $1 was estimated in 5 minutes). So I'd prefer the more simple one and wanted to know whether that would be a problem. Also, some of my thresholds were changed in -15 and 15 anyway, because the thresholds approached extreme values.

Thanks again! Best, Tessa
 Bengt O. Muthen posted on Friday, December 14, 2018 - 11:53 am
With a 3-category variable you have 2 thresholds; they are referred to as $1 and $2. You give starting values of 1 for the first threshold (I don't know why). Note that you don't have to give starting values at all.

If this doesn't help, send relevant files to Support along with your license number.
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