prior_factor {BayesTools}

Creates a prior distribution for factors

Description

prior_factor creates a prior distribution for fitting models with factor predictors. (Note that results across different operating systems might vary due to differences in JAGS numerical precision.)

Usage

prior_factor(
  distribution,
  parameters,
  truncation = list(lower = -Inf, upper = Inf),
  prior_weights = 1,
  contrast = "meandif"
)

Arguments

distribution

name of the prior distribution. The possible options are

"point"

for a point density characterized by a location parameter.

"normal"

for a normal distribution characterized by a mean and sd parameters.

"lognormal"

for a lognormal distribution characterized by a meanlog and sdlog parameters.

"cauchy"

for a Cauchy distribution characterized by a location and scale parameters. Internally converted into a generalized t-distribution with df = 1.

"t"

for a generalized t-distribution characterized by a location, scale, and df parameters.

"gamma"

for a gamma distribution characterized by either shape and rate, or shape and scale parameters. The later is internally converted to the shape and rate parametrization

"invgamma"

for an inverse-gamma distribution characterized by a shape and scale parameters. The JAGS part uses a 1/gamma distribution with a shape and rate parameter.

"beta"

for a beta distribution characterized by an alpha and beta parameters.

"exp"

for an exponential distribution characterized by either rate or scale parameter. The later is internally converted to rate.

"uniform"

for a uniform distribution defined on a range from a to b

parameters

list of appropriate parameters for a given distribution.

truncation

list with two elements, lower and upper, that define the lower and upper truncation of the distribution. Defaults to list(lower = -Inf, upper = Inf). The truncation is automatically set to the bounds of the support.

prior_weights

prior odds associated with a given distribution. The value is passed into the model fitting function, which creates models corresponding to all combinations of prior distributions for each of the model parameters and sets the model priors odds to the product of its prior distributions.

contrast

type of contrast for the prior distribution. The possible options are

"meandif"

for contrast centered around the grand mean with equal marginal distributions, making the prior distribution exchangeable across factor levels. In contrast to "orthonormal", the marginal distributions are identical regardless of the number of factor levels and the specified prior distribution corresponds to the difference from grand mean for each factor level. Only supports distribution = "mnormal" and distribution = "mt" which generates the corresponding multivariate normal/t distributions.

"orthonormal"

for contrast centered around the grand mean with equal marginal distributions, making the prior distribution exchangeable across factor levels. Only supports distribution = "mnormal" and distribution = "mt" which generates the corresponding multivariate normal/t distributions.

"treatment"

for contrasts using the first level as a comparison group and setting equal prior distribution on differences between the individual factor levels and the comparison level.

"independent"

for contrasts specifying dependent prior distribution for each factor level (note that this leads to an overparameterized model if the intercept is included).

Value

return an object of class 'prior'.

See Also

prior()

Examples

# create an orthonormal prior distribution
p1 <- prior_factor(distribution = "mnormal", contrast = "orthonormal",
                   parameters = list(mean = 0, sd = 1))