gdensity {BMS} R Documentation

## 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, ...)
```

### 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 `addons` character, defaulting to `"zles"`. Specifies which additional information should be added to the plot via low-level commands (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.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.

### Value

`gdensity` returns an object of the class `density` detailing the posterior mixture density of the shrinkage factor.

### Note

The computed marginal posterior density is a Bayesian Model Averaging mixture of the marginal posterior densities of the shrinkage factor under individual models. The accuracy of the result therefore depends on the number of 'best' models contained in `x` (cf. argument `nmodel` in `bms`).

Correspondingly, the posterior EV and SD specified by `addons="es"` are based on 'best' model likelihoods ('exact') and are conditional on inclusion.

The low-level 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 `"f"`, color 4 for `"E"` and `"S"`. The default colors may be changed by a call to `palette`.

### Author(s)

Martin Feldkircher and Stefan Zeugner

`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="zSEm",addons.lwd=2) #plotting the median 'm' and the posterior mean and bounds based on MCMC results

# plot the posterior shrinkage density only for the very best model