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, ...)

## S3 method for class 'zlm'
density(x, reg = NULL, addons = "lesz", std.coefs = FALSE,
n = 300, plot = TRUE, hnbsteps = 30, addons.lwd = 1.5, ...)
```

### Arguments

 `x` A bma object (see `bms`) or a `zlm` object. `reg` A scalar integer or character detailing which covariate's coefficient should be plotted. If `reg=NULL` (default), then all regressors are plotted one after the other, waiting for user interaction. `addons` character. Specifies which additional information should be added to the plot via low-level commands (see 'Details' below). `std.coefs` logical. If `TRUE` then the posterior density is estimated for standardized coefficients (representing the case where all variables have mean zero and standard deviation 1) - default is `FALSE`. `n` numeric. the number of equally spaced points at which the density is to be estimated. `plot` logical. If `TRUE` (default), the density is plotted; if `FALSE` then `density.bma` only returns the estimated posterior densities without plotting. `hnbsteps` even integer, default 30. The number of numerical integration steps to be used in case of a hyper-g prior (cf. argument `g` in `bms`). Increase this number to increase accuracy. `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 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 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 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 `"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 built-in `gprior`s, not with any user-defined priors.

### Author(s)

Martin Feldkircher and Stefan Zeugner

`quantile.coef.density` for extracting quantiles, `coef.bma` for similar concepts, `bms` for creating bma objects

### Examples

```
data(datafls)
mm=bms(datafls)

density(mm,reg="SubSahara")
density(mm,1:9)

# plot the posterior density only for the very best model

#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[])

#Note that the shown density is only the part that is not zero