Josie Galbraith <josie.galbraith at ...> writes:
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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
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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
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Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
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