R: Football priors distributions and options

priors {footBayes}

R Documentation

Football priors distributions and options

Description

This prior specification is just a duplicate of some of the priors used by the rstanarm package.

These prior distributions can be passed to the stan_foot function, through the arguments prior and prior_sd. See the vignette Prior Distributions for rstanarm Models for further details (to view the priors used for an existing model see prior_summary). The default priors used in the stan_foot modeling function are intended to be weakly informative in that they provide moderate regularlization and help stabilize computation.

You can choose between: normal, cauchy, laplace, student_t.

Usage

normal(location = 0, scale = NULL, autoscale = TRUE)

student_t(df = 1, location = 0, scale = NULL, autoscale = TRUE)

cauchy(location = 0, scale = NULL, autoscale = TRUE)

laplace(location = 0, scale = NULL, autoscale = TRUE)

Arguments

`location`	Prior location. In most cases, this is the prior mean, but for `cauchy` (which is equivalent to `student_t` with `df=1`), the mean does not exist and `location` is the prior median. The default value is `0`.
`scale`	Prior scale. The default depends on the family (see Details).
`autoscale`	A logical scalar, defaulting to `TRUE`.
`df`	Prior degrees of freedom. The default is `1` for `student_t`, in which case it is equivalent to `cauchy`.

Details

The details depend on the family of the prior being used:

Student t family

Family members:

normal(location, scale)
student_t(df, location, scale)
cauchy(location, scale)

Each of these functions also takes an argument autoscale.

For the prior distribution for the intercept, location, scale, and df should be scalars. For the prior for the other coefficients they can either be vectors of length equal to the number of coefficients (not including the intercept), or they can be scalars, in which case they will be recycled to the appropriate length. As the degrees of freedom approaches infinity, the Student t distribution approaches the normal distribution and if the degrees of freedom are one, then the Student t distribution is the Cauchy distribution.

If scale is not specified it will default to 10 for the intercept and 2.5 for the other coefficients.

If the autoscale argument is TRUE (the default), then the scales will be further adjusted as described above in the documentation of the autoscale argument in the Arguments section.

Laplace family

Family members:

laplace(location, scale)

Each of these functions also takes an argument autoscale.

The Laplace distribution is also known as the double-exponential distribution. It is a symmetric distribution with a sharp peak at its mean / median / mode and fairly long tails. This distribution can be motivated as a scale mixture of normal distributions and the remarks above about the normal distribution apply here as well.

Value

A named list to be used internally by the stan_foot model fitting function.

Author(s)

Leonardo Egidi legidi@units.it

References

Gelman, A., Jakulin, A., Pittau, M. G., and Su, Y. (2008). A weakly informative default prior distribution for logistic and other regression models. Annals of Applied Statistics. 2(4), 1360–1383.