Choosing appropriate priors for bglmer mixed models in blme

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]

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