This function fits a Bayesian hierarchical generalized additive model (BGAM) using a spline-based approach. It supports various families, including Gaussian, Binomial, Poisson, and Negative Binomial (NegBin)
bgam(
formula,
family = gaussian,
data,
offset,
weights,
subset,
na.action,
start = NULL,
etastart,
mustart,
control = stats::glm.control(epsilon = 1e-04, maxit = 50),
prior = Student(),
group = NULL,
method.coef,
theta.weights = NULL,
inter.hierarchy = NULL,
inter.parents = NULL,
prior.sd = 0.5,
dispersion = 1,
Warning = FALSE,
verbose = FALSE
)These arguments are the same as in glm
can be all the standard families defined in glm. also can be Negative Binomial (NegBin or "NegBin").
Prior distributions for the coefficients. Four types of priors can be used; Student-t: Student(mean, scale, df, autoscale) (default: mean=0, scale=0.5, df=1, autoscale=TRUE), Double-exponetial: De(mean, scale, autoscale) (default: mean=0, scale=0.5, autoscale=TRUE), mixture double-exponential: mde(mean, s0, s1, b), and mixture Student-t: mt(mean, s0, s1, df, b), s0 < s1, default: mean=0, s0=0.04, s1=0.5, df=1, b=1. The mean, scale, df and b can be a vector. For example, scale = c(a1,a2,...,ak); if k < the total number of predictors, it is internally expanded to c(a1,a2,...,ak, rep(ak,J-k)). If autoscale=TRUE, scale will be modified internally (see details).
a numeric vector, or an integer, or a list defining the groups of predictors. Only used for mde or mt priors. If group = NULL, all the predictors form a single group. If group = K, the predictors are evenly divided into groups each with K predictors. If group is a numberic vector, it defines groups as follows: Group 1: (group[1]+1):group[2], Group 2: (group[2]+1):group[3], Group 3: (group[3]+1):group[4], ..... If group is a list of variable names, group[[k]] includes variables in the k-th group.
jointly updating all coefficients or updating coefficients group by group. The default is jointly updating. If method.coef = NULL or method.coef is missing, jointly updating. If method.coef = K, update K coefficients at a time. method.coef can be a numeric vector or a list of variable names (as defined by group) that defines groups. If the number of coefficients is large, the group-by-group updating method can be much faster than the jointly updating.
Optional weights for the dispersion parameter.
Optional specification for hierarchical interaction terms.
Optional specification for parent-child relationships in hierarchical terms.
Standard deviation for the prior distribution.
Dispersion parameter for the model.
logical. If TRUE, show the error messages of not convergence and identifiability.
logical. If TRUE, print out number of iterations and computational time.
This function returns an object of class "glm", including all outputs from the function glm, and also results for the additional parameters in the hierarchical models.