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Hi. We estimated a parallel latent growth model with continuous outcomes over 4 time points examining the directional associations between 2 domains (depression and alcohol use). We wanted to assess: The predictive effect of alcohol use intercept on slope in depression (and vice versa). Given the presence of zerocases (nondrinkers) in the sample we attempted a zeroinflated model. However we were unable to estimate it in the context of a parallel growth model. Given this, it was suggested to us that we exclude all participants who continued to be nondrinkers across the entire timeperiod (approx 25% of the sample). The rationale was that these zero cases were not contributing to the testing of the hypotheses and will interfere with the results. I just wondered whether this is accurate. Do these zero cases provide no important information? and will their inclusion interfere with the interpretation of the results? Even though these cases are providing important information in the alternative domain (depression). Thanks 


You can exclude the cases with zero but perhaps a more interesting approach is a twopart model as described in Olsen and Schafer (2001) and shown in Example 6.16. 


Hi Linda and Bengt, I'm working with an investigator who is proposing a twoarm RCT where the primary outcome will be log10 HIV RNA viral load, a continuous measure, measured at three time points: baseline, 6 months, and 12 months. He is interested in modeling the change in the average trajectory in log10 VL predicted by group assignment. That seems well addressed via an LGM with three time points and a single binary covariate. However, the investigator also wants to simultaneously compute the odds ratio of participants who are zero on the log10 VL outcome at both 6 and 12 month followups versus being nonzero at either 6 or 12 months (this is important because full viral suppression for a year following intervention is a high mark of success for the proposed intervention). My question is whether the twopart modeling framework allows for addressing that type of question and, if so, what the user needs to address this type of research question in Mplus? For instance, if in example 6.16 one assumed u2u4 followed an intervention, how would one assess what the odds of always being zero for u2u4 would be? With best wishes and many thanks in advance for your reply, Tor Neilands 


In principle, twopart modeling would work for your situation. However obtaining the odds ratios is not possible because it requires numerical integration. 


Thanks. Is there an alternative way to obtain the odds ratio in Mplus in this situation, say through growth mixture modeling? 


The issue is allowing zero outcomes by doing a binary growth model (e.g. as part of a twopart model) with random growth factors. The presence of growth factors with nonzero variance leads to numerical integration in order to express probabilities. You need multivariate probabilities, which are inside of the computations in Mplus but are not easily accessible nor printed out, nor easily computed "by hand" due to the need for numerical integration. An alternative would be do represent the binary growth by a mixture that captures the growth factor variation  in that case, the multivariate probabilities don't call for numerical integration but can be computed by hand as a mixture. But that leads to more complex modeling on the other hand. 


Thank you, Bengt, this is most helpful. Would the same limitations and complexity apply if we switched from logit to probit and used a different estimation approach, say Bayesian or WLSMV? 


Maybe Bayes could be of help. You could certainly do a twopart growth model in Bayes in Mplus. We discuss that in our Bayes papers on the web site. Or you could simply focus on just doing a binary growth model with random growth factors. This would be probit currently for Bayes in Mplus. For each binary variable u_t, this analysis generates the continuousnormal underlying latent response variable u*_t (see Bayes MCMC algorithms for binary response in the literature and also our technical Bayes reports). So from this "H0" model you can get say 100 imputed data sets including these u*'s. So in a secondstage analysis, they are now observed continuous variables and for each imputed data set, and then averaged over the 100, you can find the proportion of individuals who are below or above their thresholds  so you get an estimate of the probability of any response pattern of 0's and 1's for the binary u's. 


Thanks, Bengt, that's a very creative idea, and very much appreciated. With best wishes, Tor 

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