R help - Jul 2013 - MCMClogit: Cannot calculate marginal likelihood with improper prior

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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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.
> 
> 
> 
> 
> 
> --
> View this message in context:
http://r.789695.n4.nabble.com/MCMClogit-Cannot-calculate-marginal-likelihood-with-improper-prior-tp4672561.html
> Sent from the R help mailing list archive at Nabble.com.
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.