bayesGAM {bayesGAM}

bayesGAM fits a variety of regression models using Hamiltonian Monte Carlo

Description

Based on glm. bayesGAM is used to fit a variety of statistical models, including linear models, generalized lienar models, mixed effect models with random intercept, and semiparametric regression models.

Usage

bayesGAM(
  formula,
  random = NULL,
  family = gaussian,
  data,
  offset,
  beta = list(),
  eps = list(),
  lambda = list(),
  a = list(),
  spcontrol = list(qr = TRUE, mvindep = FALSE, ...),
  store_plot_data = FALSE,
  method = "bayesGAMfit",
  ...
)

Arguments

formula

a formula object describing the model to be fitted.

random

(optional) specify a random intercept in the form '~var'

family

distribution and link function for the model

data

(optional) data frame containing the variables in the model.

offset

Same as glm

beta

(optional) list of priors for the fixed effects parameters. Sensible priors are selected as a default.

eps

(optional) list of priors for the error term in linear regression. Sensible priors are selecteda as a default.

lambda

(optional) list of priors for random effects variance parameters. Sensible priors are selected as a default.

a

(optional) list of priors for the off diagonal of the LDLT decomposed covariance matrix for multivariate response models. Vague normal priors are used as a default.

spcontrol

a list of control parameters for fitting the model in STAN. See 'details'

store_plot_data

a logical indicator for storing the plot data frame after simulation. Defaults to FALSE

method

default currently set to 'bayesGAMfit'.

...

Arguments passed to rstan::sampling (e.g. iter, chains).

Details

Similar to glm, models are typically specified by formula. The formula typically takes the form response ~ terms, where the response is numeric and terms specify the linear predictor for the response. The terms may be numeric variables or factors.

The link function for the Generalized Linear Model is specified with a family object. Currently, this package supports gaussian, binomial, and poisson families with all available link functions.

The list spcontrol currently supports additional parameters to facilitate fitting models. qr is a logical indicator specifying whether the design matrix should be transformed via QR decomposition prior to HMC sampling. QR decomposition often improves the efficiency with which HMC samples, as the MCMC chain navigates an orthogonal space more easily than highly correlated parameters. mvindep is a logical indicator for multivariate response models with random intercepts. This indicates whether the multivariate responses should be considered independent. Defaults to FALSE

Value

An object of class bayesGAMfit. Includes slots:

results: stanfit object returned by rstan::sampling

model: glmModel object

offset: offset vector from the input parameter

spcontrol: list of control parameters from input

References

Hastie, T. J. (1992) Generalized additive models. Chapter 7 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

Dobson, A. J. (1990) An Introduction to Generalized Linear Models. London: Chapman and Hall.

Examples

## 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)
fpois<- bayesGAM(counts ~ outcome + treatment, family = poisson(),
                 spcontrol = list(qr = TRUE))
summary(fpois)