[R-sig-ME] distribution of random effects glmmTMB - covariance structure

[D. Rizopoulos]

Logically, the ranef() gives you the empirical Bayes estimates of the 
random effects. Note that the distribution (and as a result the variance 
and covariances) of these is not the same as the distribution you 
specified in the formula of the model. Namely, the distribution you 
define is the _prior_ distribution of the random effects, whereas the 
empirical Bayes estimates are coming from the posterior of the random 
effects.

In math terms, the choice of us() of diag() specifies the distribution 
[b] of the random effects, whereas from ranef() you get the modes or 
means of the posterior distribution

[b | y] which is proportional to [y | b] * [b],

where y denotes you Count outcome, and [y | b] denotes the distribution 
of your outcome.

Best,
Dimitris


On 9/6/2018 7:59 PM, Vidal, Tiffany (FWE ) wrote:
> I'm unclear about the distributional assumptions regarding the random effects in glmmTMB, using different covariance structures. It is my understanding that the default is unstructured covariance structure. When estimating a vector of random effects, what is the assumption about the distribution of the factor levels within each grouping? I'm usually assuming normality with a mean of 0 and estimated variance. This doesn't seem to hold looking at the ranef(mod) for the different grouping variables.
> 
> For example:
> mod <- glmmTMB(Count ~ us(time + 0|Subject))
> or
> mod <- glmmTMB(Count ~ diag(time + 0|Subject))
> 
> 
> Here, I'm modeling (I think) variability among subjects through time (e.g., a different subject variance in each time step), and assuming that the repeated measures within each individual subject at time t, come from some distribution. If the assumed distribution was normal with a mean of 0, I would expect the sum of the Subject BLUPs in each year to approximate 0, but that doesn't appear to be the case. Any clarification on this would be appreciated.
> 
> Thank you,
> Tiffany
> 
> 
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-- 
Dimitris Rizopoulos
Professor of Biostatistics
Department of Biostatistics
Erasmus University Medical Center

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