Prior_Check: Checks for Prior-data conflicts
In knygren/glmbayes: Bayesian Generalized Linear Models (iid Samples)

Description Usage Arguments Value See Also Examples

Checks if the credible intervals for the prior overlaps with the implied confidence intervals from the classical model that comes from a call to the glm function

Prior_Check(
  formula,
  family,
  pfamily,
  level = 0.95,
  data = NULL,
  weights,
  subset,
  na.action,
  start = NULL,
  etastart,
  mustart,
  offset,
  control = list(...),
  model = TRUE,
  method = "glm.fit",
  x = FALSE,
  y = TRUE,
  contrasts = NULL,
  ...
)

`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. For `glm` this can be a character string naming a family function, a family function or the result of a call to a family function. For `glm.fit` only the third option is supported. (See `family` for details of family functions.)
`pfamily`	a description of the prior distribution and associated constants to be used in the model. This should be a pfamily function (see `pfamily` for details of pfamily functions).
`level`	the confidence level at which the Prior-data conflict should be checked.
`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.
`na.action`	a function which indicates what should happen when the data contain `NA`s. The default is set by the `na.action` setting of `options`, and is `na.fail` if that is unset. The ‘factory-fresh’ default is `stats{na.omit}`. Another possible value is `NULL`, no action. Value `stats{na.exclude}` can be useful.
`start`	starting values for the parameters in the linear predictor.
`etastart`	starting values for the linear predictor.
`mustart`	starting values for the vector of means.
`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 documentation for `model.offset` at `model.extract`.
`control`	a list of parameters for controlling the fitting process. For `glm.fit` this is passed to `glm.control`.
`model`	a logical value indicating whether model frame should be included as a component of the returned value.
`method`	the method to be used in fitting the model. The default method `"glm.fit"` uses iteratively reweighted least squares (IWLS): the alternative `"model.frame"` returns the model frame and does no fitting. User-supplied fitting functions can be supplied either as a function or a character string naming a function, with a function which takes the same arguments as `glm.fit`. If specified as a character string it is looked up from within the stats namespace.
`x`	For `glm`: logical values indicating whether the response vector and model matrix used in the fitting process should be returned as components of the returned value. For `glm.fit`: `x` is a design matrix of dimension `n * p`, and `y` is a vector of observations of length `n`.
`y`	For `glm`: logical values indicating whether the response vector and model matrix used in the fitting process should be returned as components of the returned value. For `glm.fit`: `x` is a design matrix of dimension `n * p`, and `y` is a vector of observations of length `n`.
`contrasts`	an optional list. See the `contrasts.arg` of `model.matrix.default`.
`...`	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.

A vector where each item provided the ratio of the absolue value for the difference between the prior and maximum likelihood estimate divided by the length of the sum of half of the two intervals (where normality is assumed)

Other prior utility Functions: Prior_Setup()

## Dobson (1990) Page 93: Randomized Controlled Trial :
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)
print(d.AD <- data.frame(treatment, outcome, counts))
## Step 1: Set up Prior
ps=Prior_Setup(counts ~ outcome + treatment)
mu=ps$mu
V=ps$Sigma
# Step2A: Check the Prior
Prior_Check(counts ~ outcome + treatment,family = poisson(),
            pfamily=dNormal(mu=mu,Sigma=V))
# Step2B: Update and Re-Check the Prior
mu[1,1]=log(mean(counts))
Prior_Check(counts ~ outcome + treatment,family = poisson(),
            pfamily=dNormal(mu=mu,Sigma=V))