Specify Priors for a Hurdle Beta-Binomial Model

Creates a prior specification object that controls the prior distributions used in the Stan model. All arguments are optional; unspecified components receive the defaults from default_prior().

Usage

hbb_prior(
  alpha = NULL,
  beta = NULL,
  log_kappa = NULL,
  gamma = NULL,
  tau = NULL,
  lkj_eta = NULL
)

Arguments

alpha: Prior on the extensive-margin fixed effects \(\alpha\) (logit scale). A named list with elements dist (character), mean (numeric scalar), and sd (positive numeric scalar). Currently only dist = "normal" is supported.
beta: Prior on the intensive-margin fixed effects \(\beta\) (logit scale). Same structure as alpha.
log_kappa: Prior on the log-concentration parameter \(\log \kappa\). Same structure as alpha.
gamma: Prior on the policy moderator coefficients \(\Gamma\). Same structure as alpha.
tau: Prior on the random effect scale parameters \(\tau\). Same structure as alpha. Note: in Stan, \(\tau\) is declared with lower = 0, so a Normal(mean, sd) prior becomes a half-normal prior in practice. The mean component is typically set to 0 for half-normal priors.
lkj_eta: Concentration parameter \(\eta > 0\) for the LKJ prior on the Cholesky factor of the correlation matrix \(L_\Omega\). Higher values shrink the correlation toward the identity matrix. A scalar \(\eta = 1\) gives a uniform prior over correlation matrices; \(\eta = 2\) (default) mildly favours the identity.

Value

An S3 object of class "hbb_prior" with components:

alpha: Named list with dist, mean, sd.
beta: Named list with dist, mean, sd.
log_kappa: Named list with dist, mean, sd.
gamma: Named list with dist, mean, sd.
tau: Named list with dist, mean, sd.
lkj_eta: Positive numeric scalar.

Details

Extensibility

The dist field in each component currently accepts only "normal". The structure is designed to accommodate future distributions (e.g., Student-t) without breaking the API.

Model-specific usage

Not all parameters are present in every model variant:

hbb_base and hbb_weighted: use alpha, beta, log_kappa only.
hbb_svc and hbb_svc_weighted: additionally use gamma, tau, and lkj_eta.

Unused prior components are silently ignored by the fitting function.

Examples

# Default priors
default_prior()
#> Hurdle Beta-Binomial Prior Specification
#> ----------------------------------------
#>   alpha     ~ Normal(0, 2) 
#>   beta      ~ Normal(0, 2) 
#>   log_kappa ~ Normal(2, 1.5) 
#>   gamma     ~ Normal(0, 1) 
#>   tau       ~ HalfNormal(0, 1) 
#>   L_Omega   ~ LKJ(2) 

# Tighter prior on fixed effects
hbb_prior(alpha = list(dist = "normal", mean = 0, sd = 1))
#> Hurdle Beta-Binomial Prior Specification
#> ----------------------------------------
#>   alpha     ~ Normal(0, 1) 
#>   beta      ~ Normal(0, 2) 
#>   log_kappa ~ Normal(2, 1.5) 
#>   gamma     ~ Normal(0, 1) 
#>   tau       ~ HalfNormal(0, 1) 
#>   L_Omega   ~ LKJ(2) 

# Custom prior on dispersion and LKJ
hbb_prior(
  log_kappa = list(dist = "normal", mean = 3, sd = 1),
  lkj_eta   = 4
)
#> Hurdle Beta-Binomial Prior Specification
#> ----------------------------------------
#>   alpha     ~ Normal(0, 2) 
#>   beta      ~ Normal(0, 2) 
#>   log_kappa ~ Normal(3, 1) 
#>   gamma     ~ Normal(0, 1) 
#>   tau       ~ HalfNormal(0, 1) 
#>   L_Omega   ~ LKJ(4) 

# Override everything
p <- hbb_prior(
  alpha     = list(dist = "normal", mean = 0, sd = 1),
  beta      = list(dist = "normal", mean = 0, sd = 1),
  log_kappa = list(dist = "normal", mean = 2, sd = 1),
  gamma     = list(dist = "normal", mean = 0, sd = 0.5),
  tau       = list(dist = "normal", mean = 0, sd = 0.5),
  lkj_eta   = 5
)
print(p)
#> Hurdle Beta-Binomial Prior Specification
#> ----------------------------------------
#>   alpha     ~ Normal(0, 1) 
#>   beta      ~ Normal(0, 1) 
#>   log_kappa ~ Normal(2, 1) 
#>   gamma     ~ Normal(0, 0.5) 
#>   tau       ~ HalfNormal(0, 0.5) 
#>   L_Omega   ~ LKJ(5)