Dear R-listers,

I have a few questions about how to specify priors. My questions are listed
below:

(1). I have a set a data with a continuous response variable, two 2-level
fixed effects, and two random effects - 'subj' and 'item'. In lmer, I would
fit a model like the one below:

model.lmer = lmer(response ~ fixed1 * fixed2 + (1 + fixed1 * fixed2 | subj)
+ (1 + fixed1 * fixed2 | item), data=Dataset)

Based on the Course notes for MCMCglmm, I fitted the model below:

prior1 = list(R=list(V=diag(1), nu=0.002),   G=list(G1 = list(V=diag(4),
nu= 0.002),  G2 = list(V=diag(4), nu= 0.002)))

model.mcmc1
= MCMCglmm(response~fixed1*fixed2, random=~us(1+fixed1*fixed2):subj +
us(1+fixed1*fixed2):item,

 data=Dataset,  verbose=F,  prior=prior1)

I wonder if the prior is appropriate.

(2). In an old post (couldn't find the link...), Jarrod Hadfield mentioned
that if V is set to a very small value, and nu is set to -2, the output
should be similar to the result based on REML, while setting V to any value
and nu to 0 will produce a result similar to one based on ML. I attempted
to do so:

prior2 = list(R=list(V=diag(1)*1e-6, nu=-2), G=list(G1 =
list(V=diag(4)*1e-6, nu= -2),  G2 = list(V=diag(4)*1e-6, nu= -2)))

model.mcmc2
= MCMCglmm(response~fixed1*fixed2,  random=~us(1+fixed1*fixed2):subj +
us(1+fixed1*fixed2):item,

 data=Dataset,  verbose=F,  prior=prior2)

prior3 = list(R=list(V=diag(1)*, nu=0),  G=list(G1 = list(V=diag(4), nu=
0),  G2 = list(V=diag(4), nu= 0)))

model.mcmc3 = MCMCglmm(response~fixed1*fixed2,
random=~us(1+fixed1*fixed2):subj + us(1+fixed1*fixed2):item,

 data=Dataset, verbose=F,   prior=prior3)

However, both resulted in this error message:

"Error in MCMCglmm(response ~ fixed1 * fixed2, random = ~us(1 +
fixed1*fixed2):subj+  :  ill-conditioned G/R structure: use proper priors
if you haven't or rescale data if you have"

I wonder what I can do (to either the priors or my data) to make the
function work properly.


(3). My third question concerns the argument 'rcov'. If I assume that the
different combinations of the two fixed effects have different residual
variances, how should I specify 'rcov'? I attempted
rcov=~us(fixed1*fixed2):units and rcov=~us(1+fixed1*fixed2):units to no
avail as I got error messages saying that R/G-structures were not specified
properly.


(4). The last question is a general question about how to make priors more
informative. As I recall based on what I've read, the V=1, nu=0.002
specification is a general approach and may not be very informative. I
wonder if there are any articles that you can suggest that may help me
understand how to determine relatively informative priors.



Thank you in advance.

Best,
Xiao

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