Ramu Sudhagoni writes:
I am working on combining three longitudinal studies using Bayesian hierarchical technique. In each study, I have at least 70 subjects follow up on 5 different visit months. My model consists of 10 different covariates including longitudinal and cross-sectional effects. Mixed models are used to fit the three studies individually using Bayesian approach and I noticed that few covariates were significant. When I combined using three level hierarchical approach, all the covariates became non-significant at the population level, and large estimates were found for variance parameters at the population level. I am struggling to understand why I am getting large variances at population level and wider credible intervals. I assumed non-informative normal priors for all my cross sectional and longitudinal effects, and non-informative inverse-gamma priors for variance parameters. I followed the approach explained by Inoue et al. (Title: Combining Longitudinal Studies of PSA, Biostatistics,2004, 483-500).
My reply:
I don’t know but I’d recommend you graph your data and fitted model so you can try to understand where the estimates are coming from.
Also, get rid of those inverse-gamma priors, which aren’t noninformative at all! (See my 2006 paper.)
Could you have an identifiability problem with one of the variances? Is the data non-gaussian, if so is there a marginal/conditional transformation happening when you add a level to the model?
If you are ambitious you could try to follow the example on page 395 of Gelman
and Hill (i.e. plot the priors and posteriors)
Could this be related to the phenomenon of increased population variation as a result of adding an individual-level covariate (as discussed in Gelman and Price (1998) and Gelman and Hill pg 480)? In that case an increase in the apparent residual variance was caused by a correlation between the predictors at the lower level and the errors at the upper level of a two-level hierarchy. The instance described in the post is different in that a level was added on top rather than a covariate at the bottom, but perhaps something similar is going on.
[...] guess I need to go figure out why Gelman says that inverse-gamma priors for variance parameters are informative and therefore suggests (I’m assuming based on my previous approach) half-t priors. I guess [...]