gblr {bsamGP}  R Documentation 
This function fits a Bayesian generalized linear regression model.
gblr(formula, data = NULL, family, link, mcmc = list(), prior = list(),
marginal.likelihood = TRUE, algorithm = c('AM', 'KS'), verbose = FALSE)
formula 
an object of class “ 
data 
an optional data frame. 
family 
a description of the error distribution to be used in the model: The family contains bernoulli (“bernoulli”), poisson (“poisson”), negativebinomial (“negative.binomial”), poissongamma mixture (“poisson.gamma”). 
link 
a description of the link function to be used in the model. 
mcmc 
a list giving the MCMC parameters.
The list includes the following integers (with default values in parentheses):

prior 
a list giving the prior information. The list includes the following parameters
(default values specify the noninformative prior):

marginal.likelihood 
a logical variable indicating whether the log marginal likelihood is calculated. The methods of Gelfand and Dey (1994) is used. 
algorithm 
a description of the algorithm to be used in the fitting of the logistic model:
The algorithm contains the Gibbs sampler based on the KolmogorovSmirnov distribution ( 
verbose 
a logical variable. If 
This generic function fits a Bayesian generalized linear regression models.
Let y_i
and w_i
be the response and the vector of parametric predictors, respectively.
The model is as follows.
y_i  \mu_i \sim F(\mu_i),
g(\mu_i) = w_i^T\beta, ~ i=1,\ldots,n,
where g(\cdot)
is a link function and F(\cdot)
is a distribution of an exponential family.
For unknown coefficients, the following prior is assumed for \beta
:
\beta \sim N(m_{0,\beta}, V_{0,\beta})
The prior for the dispersion parameter of negativebinomial regression is
\kappa \sim Ga(r_0, s_0)
An object of class blm
representing the generalized Bayesian linear model fit.
Generic functions such as print
, fitted
and plot
have methods to show the results of the fit.
The MCMC samples of the parameters in the model are stored in the list mcmc.draws
,
the posterior samples of the fitted values are stored in the list fit.draws
, and
the MCMC samples for the log marginal likelihood are saved in the list loglik.draws
.
The output list also includes the following objects:
post.est 
posterior estimates for all parameters in the model. 
lmarg 
log marginal likelihood using GelfandDey method. 
family 
the family object used. 
link 
the link object used. 
methods 
the method object used in the logit model. 
call 
the matched call. 
mcmctime 
running time of Markov chain from 
Albert, J. H. and Chib, S. (1993) Bayesian Analysis of Binary and Polychotomous Response Data. Journal of the American Statistical Association, 88, 669679.
Holmes, C. C. and Held, L. (2006) Bayesian Auxiliary Variables Models for Binary and Multinomial Regression. Bayesian Analysis, 1, 145168.
Gelfand, A. E. and Dey, K. K. (1994) Bayesian Model Choice: Asymptotics and Exact Calculations. Journal of the Royal Statistical Society. Series B  Statistical Methodology, 56, 501514.
Roberts, G. O. and Rosenthal, J. S. (2009) Examples of Adaptive MCMC. Journal of Computational and Graphical Statistics, 18, 349367.
############################
# Poisson Regression Model #
############################
# Simulate data
set.seed(1)
n < 100
x < runif(n)
y < rpois(n, exp(0.5 + x*0.4))
# Fit the model with default priors and mcmc parameters
fout < gblr(y ~ x, family = 'poisson', link = 'log')
# Summary
print(fout); summary(fout)
# Plot
plot(fout)
# fitted values
fitf < fitted(fout)