MCMClogit  R Documentation 
This function generates a sample from the posterior distribution of a logistic regression model using a random walk Metropolis algorithm. The user supplies data and priors, and a sample from the posterior distribution is returned as an mcmc object, which can be subsequently analyzed with functions provided in the coda package.
MCMClogit(
formula,
data = NULL,
burnin = 1000,
mcmc = 10000,
thin = 1,
tune = 1.1,
verbose = 0,
seed = NA,
beta.start = NA,
b0 = 0,
B0 = 0,
user.prior.density = NULL,
logfun = TRUE,
marginal.likelihood = c("none", "Laplace"),
...
)
formula 
Model formula. 
data 
Data frame. 
burnin 
The number of burnin iterations for the sampler. 
mcmc 
The number of Metropolis iterations for the sampler. 
thin 
The thinning interval used in the simulation. The number of mcmc iterations must be divisible by this value. 
tune 
Metropolis tuning parameter. Can be either a positive scalar or
a 
verbose 
A switch which determines whether or not the progress of the
sampler is printed to the screen. If 
seed 
The seed for the random number generator. If NA, the Mersenne
Twister generator is used with default seed 12345; if an integer is passed
it is used to seed the Mersenne twister. The user can also pass a list of
length two to use the L'Ecuyer random number generator, which is suitable
for parallel computation. The first element of the list is the L'Ecuyer
seed, which is a vector of length six or NA (if NA a default seed of

beta.start 
The starting value for the 
b0 
If 
B0 
If 
user.prior.density 
If nonNULL, the prior (log)density up to a
constant of proportionality. This must be a function defined in R whose
first argument is a continuous (possibly vector) variable. This first
argument is the point in the state space at which the prior (log)density is
to be evaluated. Additional arguments can be passed to

logfun 
Logical indicating whether 
marginal.likelihood 
How should the marginal likelihood be calculated?
Options are: 
... 
further arguments to be passed 
MCMClogit
simulates from the posterior distribution of a logistic
regression model using a random walk Metropolis algorithm. The simulation
proper is done in compiled C++ code to maximize efficiency. Please consult
the coda documentation for a comprehensive list of functions that can be
used to analyze the posterior sample.
The model takes the following form:
y_i \sim \mathcal{B}ernoulli(\pi_i)
Where the inverse link function:
\pi_i = \frac{\exp(x_i'\beta)}{1 + \exp(x_i'\beta)}
By default, we assume a multivariate Normal prior on \beta
:
\beta \sim \mathcal{N}(b_0,B_0^{1})
Additionally, arbitrary userdefined priors can be specified with
the user.prior.density
argument.
If the default multivariate normal prior is used, the Metropolis proposal
distribution is centered at the current value of \beta
and has
variancecovariance V = T (B_0 + C^{1})^{1} T
, where T
is a the
diagonal positive definite matrix formed from the tune
, B_0
is the prior precision, and C
is the large sample
variancecovariance matrix of the MLEs. This last calculation is done via an
initial call to glm
.
If a userdefined prior is used, the Metropolis proposal distribution is
centered at the current value of \beta
and has
variancecovariance V = T C T
, where
T
is a the diagonal positive definite matrix formed from the
tune
and C
is the large sample variancecovariance matrix of
the MLEs. This last calculation is done via an initial call to glm
.
An mcmc object that contains the posterior sample. This object can be summarized by functions provided by the coda package.
Andrew D. Martin, Kevin M. Quinn, and Jong Hee Park. 2011. “MCMCpack: Markov Chain Monte Carlo in R.”, Journal of Statistical Software. 42(9): 121. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v042.i09")}.
Daniel Pemstein, Kevin M. Quinn, and Andrew D. Martin. 2007. Scythe Statistical Library 1.0. http://scythe.lsa.umich.edu.
Martyn Plummer, Nicky Best, Kate Cowles, and Karen Vines. 2006. “Output Analysis and Diagnostics for MCMC (CODA)”, R News. 6(1): 711. https://CRAN.Rproject.org/doc/Rnews/Rnews_20061.pdf.
plot.mcmc
,summary.mcmc
,
glm
## Not run:
## default improper uniform prior
data(birthwt)
posterior < MCMClogit(low~age+as.factor(race)+smoke, data=birthwt)
plot(posterior)
summary(posterior)
## multivariate normal prior
data(birthwt)
posterior < MCMClogit(low~age+as.factor(race)+smoke, b0=0, B0=.001,
data=birthwt)
plot(posterior)
summary(posterior)
## userdefined independent Cauchy prior
logpriorfun < function(beta){
sum(dcauchy(beta, log=TRUE))
}
posterior < MCMClogit(low~age+as.factor(race)+smoke,
data=birthwt, user.prior.density=logpriorfun,
logfun=TRUE)
plot(posterior)
summary(posterior)
## userdefined independent Cauchy prior with additional args
logpriorfun < function(beta, location, scale){
sum(dcauchy(beta, location, scale, log=TRUE))
}
posterior < MCMClogit(low~age+as.factor(race)+smoke,
data=birthwt, user.prior.density=logpriorfun,
logfun=TRUE, location=0, scale=10)
plot(posterior)
summary(posterior)
## End(Not run)
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