Description Usage Arguments Details Value Author(s) References Examples
In this function the transition kernel proposed by Gamerman (1997) is implemented for a Metropolis Hastings algorithm, in order to sample the posterior distribution of the regression parameters given de data in a poisson regression. A normal Prior is assumed for the regression parameters. For now only the log link is implemented.
1 2 3 4 5 |
formula |
an object of class formula: a symbolic description of the model to be fitted. |
data |
A data frame containing the variables in the model. |
... |
When using poissmh.formula, the formula object encapsulates the arguments y and X of poissmh.default, thus ... represents all other arguments needed in poissmh.default to be poissmh to binommh.formula |
y |
Response variable, a vector of counts. |
X |
Design matrix. |
b |
Mean of the normal prior distribution of the regression parameters. |
B |
Covariance matrix of the normal prior distribution of the regression parameters. |
N |
Number mcmc simulations of the posterior distributions of the regression parameters given de data. |
flag |
Logical, if TRUE iterations and acceptance ratio of the samples is printed to monitor the mcmc progress. |
See Gamerman, 1997 for the details.
A list with the following objects:
chain |
A matrix where mcmc simulations of the posterior distributions of the regression parameters given the data is stored. Rows correspond to mcmc simulation and columns correspond to the regression parameters. |
Deviance |
a vector with -2*l(y,chain[i,]), where l(.,.) is the log-likelihood of the model. |
Accepted_samples |
An integer with the number of samples accepted by the M-H algorithm. |
Nicolas Molano-Gonzalez, Edilberto Cepeda-Cuervo
Gamerman, D. 1997. Sampling from the posterior distribution in generalized linear mixed models. Statistics and Computing, 7, 57-68.
1 2 3 4 5 6 7 8 | library(faraway)
data(gala)
g2<-glm(Species ~ .,family=poisson, gala)
#####use N > 8000 for more accurate results
bmen<-poissmh(Species ~ .,data=gala,N=1000)
#####compare Bayesian estimation vs classical
round(data.frame(R.coef=coef(g2),R.sd=sqrt(diag(summary(g2)$cov.unscaled)),
mh.mean=apply(bmen$chain,2,mean),mh.sd=apply(bmen$chain,2,sd)),4)
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