MCMClogit: Cannot calculate marginal likelihood with improper prior
Hi, what I see so far is that you have specified your user.prior.density correctly. The error comes from the prior precision matrix "B0" in combination with the marginal.likelihood set to "Laplace". B0, if not explicitly specified, defaults to zero, which results in eigenvalues of zero. If "Laplace" is indicated for the marginal.likelihood, the algorithm usually calls an optimization over "logpost.logit" in "BayesianFactors.R" where the matrix B0 is tried to be solved by solve(B0) ... as it is a zero matrix its linear equation system is exactly singular and cannot be solved. The Function MCMClogit knows about this fact and gives out a warning "Cannot calculate marginal likelihood with improper prior" while changing marginal.likelihood to "none". So concluding: Choose your user.prior.density with marginal.likelihood = "none" and all is fine (implicitly it is done so nevertheless). Best Simon P.S. Using a name on a community help list will certainly improve the number of answers to your questions.
On Jul 29, 2013, at 3:00 AM, ba0728 <haleybeck at att.net> wrote:
I'm an undergrad who is new to MCMCpack and I haven't been able to find an
answer to my problem online yet: I'm attempting to run MCMClogit with a
Cauchy proper prior but I'm getting the warning "Cannot calculate marginal
likelihood with improper prior" (my purposes require the marginal likelihood
calculation so I understand that I need to use a proper prior).
I'm trying to simulate the "user-defined independent Cauchy prior with
additional args" as specified in the MCMCpack User Manual (p. 76, April 2013
version). My input data has been standardized (mean = 0, sd = 0.5 for
non-binary variables, and binary variables with mean of 0 and difference of
1 between upper and lower ends) according to the Gelman 2008 paper on
logistic regression
(www.stat.columbia.edu/~gelman/research/published/priors11.pdf?).
When I run the example data set (birthwt) from the User Manual, the
logpriorfun works correctly allowing the marginal likelihood to be
generated. However, when I try running my data with the logprior fun, I get
a warning that the prior is improper. Here is the code I am running:
*logpriorfun = function(beta, location,scale){
sum(dcauchy(beta, location, scale, log = TRUE))
}*
*> MCMC.2= MCMClogit(DEAD ~ YEARS + MALE + x1 + x2 + x3+ x4 +x5 + x6 + x7 +
x8 + x9, tune= 0.65,burnin =500, mcmc=5000, data = dat, marginal.likelihood
= "Laplace", user.prior.density=logpriorfun, logfun=TRUE, location = 0,
scale=2.5)
*
*@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
The Metropolis acceptance rate was 0.27418
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
Warning message:
In MCMClogit(DEAD ~ YEARS + MALE + x1 + x2 + x3 + :
Cannot calculate marginal likelihood with improper prior*
Any advice on how to fix my arguments so it is a proper prior and will allow
me to generate a marginal likelihood using the Laplace approximation? Or how
should I be coding a Cauchy proper prior? I'm having problems defining the
priors.
Thanks, B.
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