metropolis_glm {metropolis}

Use the Metropolis Hastings algorithm to estimate Bayesian glm parameters

Description

This function carries out the Metropolis algorithm.

Usage

metropolis_glm(
  f,
  data,
  family = binomial(),
  iter = 100,
  burnin = round(iter/2),
  pm = NULL,
  pv = NULL,
  chain = 1,
  prop.sigma.start = 0.1,
  inits = NULL,
  adaptive = TRUE,
  guided = FALSE,
  block = TRUE,
  saveproposal = FALSE,
  control = metropolis.control()
)

Arguments

f

an R style formula (e.g. y ~ x1 + x2)

data

an R data frame containing the variables in f

family

R glm style family that determines model form: gaussian() or binomial()

iter

number of iterations after burnin to keep

burnin

number of iterations at the beginning to throw out (also used for adaptive phase)

pm

vector of prior means for normal prior on log(scale) (if applicable) and regression coefficients (set to NULL to use uniform priors)

pv

vector of prior variances for normal prior on log(scale) (if applicable) and regression coefficients (set to NULL to use uniform priors)

chain

chain id (plan to deprecate)

prop.sigma.start

proposal distribution standard deviation (starting point if adapt=TRUE)

inits

NULL, a vector with length equal to number of parameters (intercept + x + scale ;gaussian() family only model only), or "glm" to set priors based on an MLE fit

adaptive

logical, should proposal distribution be adaptive? (TRUE usually gives better answers)

guided

logical, should the "guided" algorithm be used (TRUE usually gives better answers)

block

logical or a vector that sums to total number of parameters (e.g. if there are 4 random variables in the model, including intercept, then block=c(1,3) will update the intercept separately from the other three parameters.) If TRUE, then updates each parameter 1 by 1. Using guide=TRUE with block as a vector is not advised

saveproposal

(logical, default=FALSE) save the rejected proposals (block=TRUE only)?

control

parameters that control fitting algorithm. See metropolis.control()

Details

Implements the Metropolis algorithm, which allows user specified proposal distributions or implements an adaptive algorithm as described by Gelman et al. (2014, ISBN: 9781584883883). This function also allows the "Guided" Metropolis algorithm of Gustafson (1998) doi: 10.1023/A:1008880707168. Note that by default all parameters are estimated simulataneously via "block" sampling, but this default behavior can be changed with the "block" parameter. When using guided=TRUE, block should be set to FALSE.

Value

An object of type "metropolis.samples" which is a named list containing posterior MCMC samples as well as some fitting information.

Examples

dat = data.frame(y = rbinom(100, 1, 0.5), x1=runif(100), x2 = runif(100))

res = metropolis_glm(y ~ x1 + x2, data=dat, family=binomial(), iter=1000, burnin=3000, 
adapt=TRUE, guided=TRUE, block=FALSE)
res
summary(res)
apply(res$parms, 2, mean)
glm(y ~ x1 + x2, family=binomial(), data=dat)
dat = data.frame(y = rnorm(100, 1, 0.5), x1=runif(100), x2 = runif(100), x3 = rpois(100, .2))

res = metropolis_glm(y ~ x1 + x2 + factor(x3), data=dat, family=gaussian(), inits="glm", 
iter=10000, burnin=3000, adapt=TRUE, guide=TRUE, block=FALSE)
apply(res$parms, 2, mean)
glm(y ~ x1 + x2+ factor(x3), family=gaussian(), data=dat)