BMS (version 0.3.5)

gdensity: Posterior Density of the Shrinkage Factor

Description

Calculates the mixture marginal posterior density for the shrinkage factor (g/(1+g)) from a BMA object under the hyper-g prior and plots it

Usage

gdensity(x, n = 512, plot = TRUE, addons = "zles", addons.lwd = 1.5, ...)

Value

gdensity returns an object of the class density

detailing the posterior mixture density of the shrinkage factor.

Arguments

x

A bma object (see bms).

n

The integer number of equally spaced points at which the density is to be estimated. see 'Details' below

plot

logical. If TRUE (default), the density is plotted; if FALSE then gdensity only returns the estimated posterior density without plotting.

addons

character, defaulting to "zles". Specifies which additional information should be added to the plot via low-level commands (see 'Details' below).

addons.lwd

scalar, default 1.5. Line width to be used for the low-level plotting commands specified by addons. Cf. argument lwd in par

...

Additional arguments for plot.default with sensible defaults

Details

The function gdensity estimates and plots the posterior density for the shrinkage factor \(g/(1+g)\)
This is evidently only possible if the shrinkage factor if not fixed, i.e. if the bma object x was estimated with a hyper-g prior - cf. argument g in bms
The density is based only on the best models retained in the bma object x, cf. argument nmodel in bms
A note on argument n: The points at which the density is estimated start at \(max(0,E-5*SD)\), where \(E\) and \(SD\) are the expected value and standard deviation of the shrinkage factor, respectively. For plotting the entire domain \((0,1)\) use xlim=c(0,1) as an argument for gdensity.

The argument addons specifies what additional information should be added to the plot(s) via the low-level commands lines and legend:
"e" for the posterior expected value (EV) of the shrinkage factor,
"s" for 2 times posterior standard deviation (SD) bounds,
"m" for the posterior median,
"f" for posterior expected values of the individual models whom the density is averaged over,
"z" for a zero line, "l" for including a legend
The following two are only possible if the bma object collected statistics on shrinkage, cf. argument g.stats in bms "E" for posterior expected value under MCMC frequencies (see argument exact in coef.bma),
"S" for the corresponding 2 times standard deviation bounds (MCMC),

Any combination of these letters will give the desired result. Use addons="" for not using any of these.

See Also

density.bma for computing coefficient densities, bms for creating bma objects, density for the general method

Check http://bms.zeugner.eu for additional help.

Examples

 data(datafls)
 mm=bms(datafls,g="hyper=UIP")

 gdensity(mm) # default plotting
 
 # the grey bars represent expected shrinkage factors of the individual models
 gdensity(mm,addons="lzfes") 
 
 # #plotting the median 'm' and the posterior mean and bounds based on MCMC results:
 gdensity(mm,addons="zSEm",addons.lwd=2)

# plot the posterior shrinkage density only for the very best model
 gdensity(mm[1],addons="esz")


#using the calculated density for other purposes...
 dd=gdensity(mm,plot=FALSE)
 plot(dd)