spike.slab.glm.prior {BoomSpikeSlab} | R Documentation |

A Zellner-style spike and slab prior for generalized linear models. It is intended as a base class for LogitZellnerPrior, PoissonZellnerPrior, and potential future extensions.

```
SpikeSlabGlmPrior(
predictors,
weight,
mean.on.natural.scale,
expected.model.size,
prior.information.weight,
diagonal.shrinkage,
optional.coefficient.estimate,
max.flips,
prior.inclusion.probabilities)
SpikeSlabGlmPriorDirect(
coefficient.mean,
coefficient.precision,
prior.inclusion.probabilities = NULL,
expected.model.size = NULL,
max.flips = -1)
```

`predictors` |
The design matrix for the regression problem. No missing data is allowed. |

`weight` |
A vector of length |

`mean.on.natural.scale` |
Used to set the prior mean for the intercept. The mean of the response, expressed on the natural scale. This is logit(p-hat) for logits and log(ybar) for Poissons. |

`expected.model.size` |
A positive number less than |

`prior.information.weight` |
A positive scalar. Number of observations worth of weight that should be given to the prior estimate of beta. |

`diagonal.shrinkage` |
The conditionally Gaussian prior for beta (the "slab") starts with a
precision matrix equal to the information in a single observation.
However, this matrix might not be full rank. The matrix can be made
full rank by averaging with its diagonal. |

`optional.coefficient.estimate` |
If desired, an estimate of the regression coefficients can be supplied. In most cases this will be a difficult parameter to specify. If omitted then a prior mean of zero will be used for all coordinates except the intercept, which will be set to mean(y). |

`max.flips` |
The maximum number of variable inclusion indicators the sampler will attempt to sample each iteration. If negative then all indicators will be sampled. |

`prior.inclusion.probabilities` |
A vector giving the prior
probability of inclusion for each variable. If |

`coefficient.mean` |
The prior mean of the coefficients in the maximal model (with all coefficients included). |

`coefficient.precision` |
The prior precision (inverse variance) of the coefficients in the maximal model (with all coefficients included). |

A Zellner-style spike and slab prior for generalized linear
models. Denote the vector of coefficients by `\beta`

, and the
vector of inclusion indicators by `\gamma`

. These are linked
by the relationship `\beta_i \ne 0`

if ```
\gamma_i =
1
```

and `\beta_i = 0`

if ```
\gamma_i =
0
```

. The prior is

`\beta | \gamma \sim N(b, V)`

`\gamma \sim B(\pi)`

where `\pi`

is the vector of
`prior.inclusion.probabilities`

, and `b`

is the
`optional.coefficient.estimate`

. Conditional on
`\gamma`

, the prior information matrix is

`V^{-1} = \kappa ((1 - \alpha) x^Twx / n + \alpha diag(x^Twx / n))`

The matrix `x^Twx`

is, for suitable choice of the weight vector
`w`

, the total Fisher information available in the data.
Dividing by `n`

gives the average Fisher information in a single
observation, multiplying by `\kappa`

then results in
`\kappa`

units of "average" information. This matrix is
averaged with its diagonal to ensure positive definiteness.

In the formula above, `\kappa`

is
`prior.information.weight`

, `\alpha`

is
`diagonal.shrinkage`

, and `w`

is a diagonal matrix with all
elements set to ```
prior.success.probability * (1 -
prior.success.probability)
```

. The vector `b`

and the matrix
`V^{-1}`

are both implicitly subscripted by `\gamma`

,
meaning that elements, rows, or columsn corresponding to gamma = 0
should be omitted.

The "Direct" version is intended for situations where the predictors are unavailable, or if the user wants more control over the prior precision matrix.

Returns an object of class `SpikeSlabGlmPrior`

, which is a list
with data elements encoding the selected prior values.

This object is intended for use as a base class for
`LogitZellnerPrior`

and `PoissonZellnerPrior`

.

Steven L. Scott

Hugh Chipman, Edward I. George, Robert E. McCulloch, M. Clyde, Dean
P. Foster, Robert A. Stine (2001),
"The Practical Implementation of Bayesian Model Selection"
*Lecture Notes-Monograph Series*, Vol. 38, pp. 65-134.
Institute of Mathematical Statistics.

[Package *BoomSpikeSlab* version 1.2.6 Index]