multi_prior_setup: Prior setup for multiple Gaussian responses
In glmbayes: Bayesian Generalized Linear Models (IID Samples)

multi_prior_setup

R Documentation

Prior setup for multiple Gaussian responses

Description

Prior setup for multiple Gaussian responses

Usage

multi_prior_setup(
  formula,
  family = gaussian(),
  data = NULL,
  weights = NULL,
  subset = NULL,
  na.action = na.fail,
  offset = NULL,
  contrasts = NULL,
  pwt = NULL,
  pwt_default_low = 0.01,
  pwt_default_high = 0.05,
  n_prior = NULL,
  sd = NULL,
  dispersion = NULL,
  intercept_source = c("null_model", "full_model"),
  effects_source = c("null_effects", "full_model"),
  mu = NULL,
  k = 1,
  ...
)

Arguments

`formula`	an object of class `"formula"` (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under ‘Details’.
`family`	a description of the error distribution and link function to be used in the model.
`data`	an optional data frame, list or environment (or object coercible by `as.data.frame` to a data frame) containing the variables in the model. If not found in `data`, the variables are taken from `environment(formula)`, typically the environment from which `glm` is called.
`weights`	an optional vector of ‘prior weights’ to be used in the fitting process. Should be `NULL` or a numeric vector.
`subset`	an optional vector specifying a subset of observations to be used in the fitting process. (See additional details about how this argument interacts with data-dependent bases in the ‘Details’ below.)
`na.action`	how `NAs` are treated. The default is first, any `na.action` attribute of data, second a `na.action` setting of options, and third `na.fail` if that is unset. The `factory-fresh` default is `na.omit`. Another possible value is `NULL`.
`offset`	this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be `NULL` or a numeric vector of length equal to the number of cases. One or more `offset` terms can be included in the formula instead or as well, and if more than one is specified their sum is used. See `model.offset`.
`contrasts`	an optional list. See the `contrasts.arg` of `model.matrix.default`.
`pwt`	Weight on the prior relative to the likelihood function at the maximum likelihood estimate. If supplied, this value is used directly (scalar or one value per coefficient). If `n_prior` is provided and `pwt` is still a scalar and `sd` was not supplied, `pwt` is set to `n_prior / (n_prior + n_effective)`. If `length(pwt) > 1` (including from `sd`) or `sd` was supplied, `n_prior` does not overwrite `pwt`; it is used only as a scalar for Gamma / S_marg steps. If `sd` is provided, `pwt` is computed from the prior standard deviations. If none of these are supplied, `pwt` defaults to `pwt_default_low` for models with fewer than 14 coefficients, and `pwt_default_high` otherwise.
`pwt_default_low`	Default prior weight used when `pwt` is not supplied and the model dimension is below 14. Defaults to 0.01.
`pwt_default_high`	Default prior weight used when `pwt` is not supplied and the model dimension is 14 or greater. Defaults to 0.05.
`n_prior`	Optional scalar effective prior sample size (on the `n_effective` scale). If provided with scalar `pwt` and without `sd`, `pwt` is recomputed from `n_prior`. With vector `pwt` or with `sd`, `pwt` is left unchanged and `n_prior` is used for the Gamma prior on precision and related Gaussian calibration only. If missing and `pwt` is scalar, `n_prior = (pwt/(1-pwt))*n_effective`.
`sd`	Optional vector argument with the prior standard deviations for the coefficients
`dispersion`	Optional scalar dispersion override (default `NULL`). For now, this is documented as an optional argument used to scale the `Sigma` (variance-covariance) matrix; see Details for additional context.
`intercept_source`	Specifies the method through which the prior mean for the intercept term is set. Options are based on the null intercept only model (null_model) or full_models. The default is the null model which is safer if variables are not centered.
`effects_source`	Specifies the method through which the prior means for the effects terms are set. Options are null_effects (prior means set to zero) or full_model (effect means set to match maximum likelihood estimates).
`mu`	Optional vector argument with the prior means for the coefficients
`k`	Scalar (default `1`), non-negative (`k \geq 0`), with `k + p \geq 2` where `p` is the number of coefficients (columns of the model matrix). `k` controls the tail behavior and effective degrees of freedom of the variance prior. It does not change the posterior mean of `\sigma^2` or the covariance of `\beta`, but larger `k` makes the prior and posterior for `\sigma^2` more concentrated and less heavy-tailed. Not yet used in calibration; passed through to `compute_gaussian_prior` for future use.
`...`	For `glm`: arguments to be used to form the default `control` argument if it is not supplied directly. For `weights`: further arguments passed to or from other methods.

Value

A named list of class "multi_PriorSetup". Each element is a Prior_Setup result for one column of the response (names from colnames(y) or Y1, Y2, ...).