[R-sig-ME] Choosing appropriate priors for bglmer mixed models in blme

[Ben Bolker]

Josie Galbraith <josie.galbraith at ...> writes:

> 

[snip]

> 
> I'm after some advice on how to choose which priors to use.  I gather I
> need to impose a weak prior on the fixed effects of my model but no
> covariance priors - is this correct?  Can I use a default prior (i.e. t, or
> normal defaults in the blme package) or does it depend on my data?  What is
> considered a suitably weak prior?

   If all you're trying to do is deal with complete separation (and not,
e.g. singular estimates of variance components [typically indicated
by zero variances or +/- 1 correlations, although I'm not sure those
are necessary conditions for singularity]), then it should be OK
to put the prior only on the fixed effects.  Generally speaking a
weak prior is one with a standard deviation that is large relative
to the expected scale of the effect (e.g. we might say sigma=10 is
large, but it won't be if the units of measurement are very small
so that a typical value of the mean is 100,000 ...)

> I am running binomial models for epidemiology data (response variable is
> presence/absence of lesions), with 2 fixed effects (FOOD: F/NF; SEASON:
> Autumn/Spring) and a random effect (SITE: 8 levels).  The main goal of
> these models is to test for an effect of the treatment 'FOOD.'  I'm
> guessing from what I've read, that my model should be something like the
> following:


This seems fairly reasonable at first glance.  Where were you seeing
the complete separation, though?   I would normally expect to
see at least one of the parameters still being reasonably large
if that's the case.
 
> bglmer (LESION ~ FOOD*SEASON +(1|SITE), data = SEYE.df, family = binomial,
> fixef.prior = normal, cov.prior = NULL)
> 
> This is the output when I run the model:
> 
> Fixef prior: normal(sd = c(10, 2.5, ...), corr = c(0 ...), common.scale =
> FALSE)
> Prior dev  : 18.2419
> 
> Generalized linear mixed model fit by maximum likelihood (Laplace
> Approximation) [
> bglmerMod]
>  Family: binomial ( logit )
> Formula: LESION ~ FOOD * SEASON + (1 | SITE)
>    Data: SEYE.df
> 

[snip]
 
> Random effects:
>  Groups Name        Variance Std.Dev.
>  SITE   (Intercept) 0.3064   0.5535
> Number of obs: 178, groups: SITE, 8
> 
> Fixed effects:
>                     Estimate Std. Error z value Pr(>|z|)
> (Intercept)          -3.7664     1.4551  -2.588  0.00964 **
> FOODNF                0.5462     1.6838   0.324  0.74567
> SEASONSpring          1.7529     1.4721   1.191  0.23378
> FOODNF:SEASONSpring  -0.8151     1.7855  -0.456  0.64803
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> 

[snip]