Posterior covariance matrix
Message/Author
 Mike Stoolmiller posted on Wednesday, October 16, 2013 - 7:59 am
Mplus exports the empirical bayes estimates of latent log hazards from multilevel continuous time survival models and their standard errors but there are times when I need the entire posterior covariance matrix in models that have 2 or more random effects per subject. Can you provide me with the computational formula so I can do this using the Mplus parameter arrays and the raw data or direct me to an appropriate reference? Thanks.
 Tihomir Asparouhov posted on Wednesday, October 16, 2013 - 4:26 pm
Mike

You should assume normal posterior distribution. If you have more than 20 observations per cluster this will be fine.

Otherwise obtaining the posterior distribution can be computed using the formulas in these two papers but this is a difficult task.

There is another way ... tricks ... but that is not easy either ... using the model estimates in a run with fixed parameters and factors observed by going through the integration points you can get the log-likelihood for each cluster/integration point ... but still you wont be able to fix the basehazard to the original ... so you will have to move to basehazard=on which is fine.

Tihomir
 Mike Stoolmiller posted on Thursday, October 17, 2013 - 5:00 am
Thanks. Actually, I forgot to mention that the model I am running is an exponential model (constant hazard) with basehazard on. I'll take a look at the refs.
 Mike Stoolmiller posted on Friday, October 18, 2013 - 7:05 am
So I have a related question. If I am fitting a very simple multilevel continuous time survival model with a single hazard rate with a constant baseline hazard (i.e., basehazard = on), can Mplus compute either the individual reliabilities (shrinkage factors) of the single level hazard rates or the overall reliability of the single level hazard rates after estimating the multilevel model? Is there a way to use the EB estimates and/or standard errors to do this?
 Tihomir Asparouhov posted on Friday, October 18, 2013 - 5:46 pm
If I understand the question correctly

Exp(EB)*HazRate

Assume independence of the two when computing the total SE using the delta method and eb_se and h_se.