posterior.fit {MSBVAR}R Documentation

Estimates the marginal likelihood and posterior probability for VAR, BVAR, and BSVAR models

Description

Computes the marginal log likelihood other posterior fit measures for VAR, BVAR, and BSVAR models fit with szbsvar and szbvar.

Usage

posterior.fit(varobj, A0.posterior.obj=NULL)
posterior.fit.BVAR(varobj)
posterior.fit.BSVAR(varobj, A0.posterior.obj)

Arguments

varobj Bayesian BVAR or BSVAR object from fitting a model with szbsvar or szbvar
A0.posterior.obj MCMC Gibbs sample object for the B-SVAR model A(0) from gibbs.A0.BSVAR

Details

Estimates the marginal log likelihood, log prior, log posterior for the A_0 and A_1,...,A_p parameters of the model, and the log data density for the sample (after integrating out the model parameters). The approach used is that of Chib (1995).

The computations are done using compiled C++ code as of version 0.3.0. See the package source code for details about the implementation.

Value

BVAR:
A list of the class "posterior.fit.VAR" that includes the following elements:

data.marg.llf Log marginal density, the probability of the data after integrating out the parameters in the model.
data.marg.post Predictive marginal posterior density
Coefficient log likelihood
log.prior Log prior probability
log.llf T x 1 list of the log probabilities for each observation conditional on the parameters.
log.posterior.Aplus Log marginal probability of A(1),...,A(p) conditional on the data and A(0)
log.marginal.data.density Log data density or marginal log likelihood, the probability of the data after integrating out the parameters in the model.
log.marginal.A0k m x 1 list of the log probabilities of each column (corresponding to the equations) of A(0) conditional on the other columns.

Note

The log Bayes factor for two model can be computed using the log.marginal.data.density:

log BF = log.marginal.data.density.1 - log.marginal.data.density.2

Note that at present, the scale factors for the BVAR and B-SVAR models are different (one used the concentrated likelihood, the other does NOT). Thus, one cannot compare fit measures across the two functions. To compare a recursive B-SVAR to a non-recursive B-SVAR model, one should estimate the recursive model with szbsvar using the appropriate ident matrix and then call posterior.fit on the two B-SVAR models!

Author(s)

Patrick T. Brandt

References

Chib, Siddartha. 1995. "Marginal Likelihood from the Gibbs Output." Journal of the American Statistical Association. 90(432): 1313–1321.

Waggoner, Daniel F. and Tao A. Zha. 2003. "A Gibbs sampler for structural vector autoregressions" Journal of Economic Dynamics & Control. 28:349–366.

See Also

szbvar, szbsvar, gibbs.A0.BSVAR, mc.irf, print.posterior.fit

Examples

## Not run: 
varobj <- szbsvar(Y, p, z = NULL, lambda0, lambda1, lambda3, lambda4,
                  lambda5, mu5, mu6, ident, qm = 4)
A0.posterior <- gibbs.A0.BSVAR(varobj, N1, N2)
fit <- posterior.fit(varobj, A0.posterior)
print(fit)
## End(Not run)

[Package MSBVAR version 0.3.2 Index]