Dear Dr. Bengt Muthen, I am currently using MPLUS to run a latent growth model that examines the impact of parental divorce on depression trajectories. Divorce will be a dichotomous time-varying predictor. I am using your paper from 1998 (Curran, Muthen, & Harford, 1998 "The Influence of Changes in Marital Status on Developmental Trajectories of Alcohol Use in Young Adults") as a guide for my model, and thus examining the time incremental change for the divorce predictor (Similar to your 'Model 2'). In the article, you state "The relation between changes in drinking trajectories and changes in marital status was modeled using techniques developed by Muthen (in preparation)". Unfortunately, I am having a hard time finding the published version of the paper that was in preparation. Would you mind pointing me in the direction of resources that will help me with how to model this?
Dr. Muthen, Thank you very much for your response. Your short course slides and the corresponding video on this topic were very helpful. I never explored your short courses before, and I look forward to watching all of them in their entirety! I do have one question that I am still unsure about, and then a question about the equation- 1) Why is the incremental change a latent construct, and not just the observed status? Why does the observed status get regressed on the latent change construct?
1) I don't think the 4 latent constructs are necessary. You can get the same effect by holding the slopes in the regressions of the outcomes equal across time as I show in 2). The input doesn't show residual variances of zero for these 4 constructs but I think that has to be specified to be identified.
2) The equations would look like
y_i1 = i + lambda1*s + beta1*t1 + res1 y_i2 = i + lambda2*s + beta1*t1+beta2*t2 + res2 y_i3 = i + lambda2*s + beta1*t1 + beta2*t2 +beta3*t3 + res3
etc where the lambda's are the time scores and the t's are the 4 status variables. You see the equalities in the beta's here that I mentioned in 1).
Dr. Bengt Muthen, Thanks again for all of your help a few weeks ago with my original questions. I have a follow-up question after I ran a few simple preliminary analyses.
I ran a simplified version of this model, with divorce (time-varying) predicting depression over time. I am having an issue about list-wise deletion, where MPLUS is automatically deleting participants who do not have all 4 datapoints for divorce. In my original question, I had asked why in your 1998 paper, you modeled the change in divorce as a latent construct rather than just an observed variable. Initially, you said that I could probably just model it as observed. As I looked into this issue of list-wise deletion further, I read about the idea of 'phantom variables', where I would make my predictor variable a latent construct to prevent MPLUS from deleting my missing. Is this, perhaps, the reason why you had originally modeled divorce as a latent construct?
You don't need to introduce latents if missing on x at time t implies missing on y at time t. In this case, the observation does not contribute to the estimate of y_t on x_t. Therefore, we recommend the trick of changing the missingness flag for x to something not identified as missing. Then these subjects are not deleted.
Dr. Muthen, Unfortunately I am gathering my x (divorce) information from the mother, and the y (depression) information from the child, therefore I have cases in which the mother did not respond but the child did, so I do have some cases in which I am not missing on y but missing on x, and visa versa.
Dr. Muthen, I have done as you suggested and added my x variables into the model by mentioning their variances. I have checked for identification a few times and had my advisor also count, and we both agree that is should not be an identification issue. However, I now receive the following error and I am unsure how to proceed:
THE MODEL ESTIMATION TERMINATED NORMALLY
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL. PROBLEM INVOLVING THE FOLLOWING PARAMETER: Parameter 25, DIV1819 WITH S1
THE CONDITION NUMBER IS -0.160D-12.
THE ROBUST CHI-SQUARE COULD NOT BE COMPUTED.
FACTOR SCORES WILL NOT BE COMPUTED DUE TO NONCONVERGENCE OR NONIDENTIFIED MODEL.