distribution of random effects glmmTMB - covariance structure
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 [[alternative HTML version deleted]]
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Dimitris Rizopoulos Professor of Biostatistics Department of Biostatistics Erasmus University Medical Center Address: PO Box 2040, 3000 CA Rotterdam, the Netherlands Tel: +31/(0)10/7043478 Fax: +31/(0)10/7043014 Web (personal): http://www.drizopoulos.com/ Web (work): http://www.erasmusmc.nl/biostatistiek/ Blog: http://iprogn.blogspot.nl/