density.bma {BMS}  R Documentation 
Coefficient Marginal Posterior Densities
Description
Calculates the mixture marginal posterior densities for the coefficients from a BMA object and plots them
Usage
## S3 method for class 'bma'
density(
x,
reg = NULL,
addons = "lemsz",
std.coefs = FALSE,
n = 300,
plot = TRUE,
hnbsteps = 30,
addons.lwd = 1.5,
...
)
Arguments
x 

reg 
A scalar integer or character detailing which covariate's
coefficient should be plotted. If 
addons 
character. Specifies which additional information should be added to the plot via lowlevel commands (see 'Details' below). 
std.coefs 
logical. If 
n 
numeric. the number of equally spaced points at which the density is to be estimated. 
plot 
logical. If 
hnbsteps 
even integer, default 30. The number of numerical
integration steps to be used in case of a hyperg prior (cf. argument

addons.lwd 
scalar, default 1.5. Line width to be used for the
lowlevel plotting commands specified by 
... 
Additional arguments for 
Details
The argument addons
specifies what additional information should be
added to the plot(s) via the lowlevel commands lines
and
legend
:
"e"
for the posterior expected value (EV) of
coefficients conditional on inclusion (see argument exact=TRUE
in
coef.bma
),
"s"
for 2 times posterior standard
deviation (SD) bounds,
"m"
for the posterior median,
"b"
for posterior expected values of the individual models whom the density is
averaged over,
"E"
for posterior EV under MCMC frequencies (see
argument exact=FALSE
in coef.bma
),
"S"
for
the corresponding SD bounds (MCMC),
"p"
for plotting the Posterior
Inclusion Probability above the density plot,
"l"
for including a
legend
, "z"
for a zero line, "g"
for adding a
grid
Any combination of these letters will give the desired result. Use
addons=""
for not using any of these.
In case of
density.zlm
, only the letters e
, s
, l
, z
,
and g
will have an effect.
Value
The function returns a list containing objects of the class
density
detailing the marginal posterior densities for each
coefficient provided in reg
.
In case of density.zlm
, simple
marginal posterior coefficient densities are computed, while
density.bma
calculates there mixtures over models according to
posterior model probabilities.
These densities contain only the density
points apart from the origin. (see 'Note' below)
As long as plot=TRUE
, the densities are plotted too. Note that (for
density.bma
) if the posterior inclusion probability of a covariate is
zero, then it will not be plotted, and the returned density will be
list(x=numeric(n),y=numeric(n))
.
Note
The computed marginal posterior densities from density.bma
are
a Bayesian Model Averaging mixture of the marginal posterior densities of
the individual models. The accuracy of the result therefore depends on the
number of 'best' models contained in x
(cf. argument nmodel
in
bms
).
The marginal posterior density can be interpreted as 'conditional on inclusion': If the posterior inclusion probability of a variable is smaller than one, then some of its posterior density is Dirac at zero. Therefore the integral of the returned density vector adds up to the posterior inclusion probability, i.e. the probability that the coefficient is not zero.
Correspondingly, the posterior EV and SD specified by addons="es"
are
based on 'best' model likelihoods ('exact') and are conditional on
inclusion. They correspond to the results from command
coef.bma(x,exact=TRUE,condi.coef=TRUE,order.by.pip=FALSE)
(cf. the
example below).
The lowlevel commands enacted by the argument addons
rely on colors
of the palette
: color 2 for "e"
and "s"
, color 3
for "m"
, color 8 for "b"
, color 4 for "E"
and
"S"
. The default colors may be changed by a call to
palette
.
Up to BMS version 0.3.0, density.bma
may only cope with builtin
gprior
s, not with any userdefined priors.
See Also
quantile.coef.density
for extracting quantiles,
coef.bma
for similar concepts, bms
for creating
bma objects
Check http://bms.zeugner.eu for additional help.
Examples
data(datafls)
mm=bms(datafls)
density(mm,reg="SubSahara")
density(mm,reg=7,addons="lbz")
density(mm,1:9)
density(mm,reg=2,addons="zgSE",addons.lwd=2,std.coefs=TRUE)
# plot the posterior density only for the very best model
density(mm[1],reg=1,addons="esz")
#using the calculated density for other purposes...
dd=density(mm,reg="SubSahara")
plot(dd)
dd_list=density(mm,reg=1:3,plot=FALSE,n=400)
plot(dd_list[[1]])
#Note that the shown density is only the part that is not zero
dd=density(mm,reg="Abslat",addons="esl")
pip_Abslat=sum(dd$y)*diff(dd$x)[1]
#this pip and the EV conform to what is done by the follwing command
coef(mm,exact=TRUE,condi.coef=TRUE)["Abslat",]