Metropolis-Hastings algorithm for a one-way normal random effects model

Description

Simulates realisations from the posterior distribution for the population mean and precision components in a one-way normal random effects model with a semi-conjugate prior. The method marginalises over the random effects and uses univariate normal or log normal random walk proposals for the precision components.

Usage

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  mhReffects(N, initial, intau, innu, priorparam, m, n,
    ybar, s, show = TRUE, innLogscale = FALSE)

Arguments

N

length of MCMC chain

initial

starting values for the algorithm

intau

standard deviation of normal random walk innovation for data precision parameter tau

innu

standard deviation of normal random walk innovation for random effects precision parameter nu

priorparam

prior parameters a,b,c,d,e,f

m

number of treatments

n

vector containing the number of observations on each treatment

ybar

vector containing the mean of observations on each treatment

s

vector containing the standard deviation of observations on each treatment

show

logical. If true then acceptance rate for the proposals will be given

innLogscale

logical. If true then proposals are made on a log scale

Examples

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data(contamination)
n=tapply(contamination$acc,contamination$keyboard,length)
ybar=tapply(contamination$acc,contamination$keyboard,mean)
s=sqrt(tapply(contamination$acc,contamination$keyboard,var)*(n-1)/n)
mcmcAnalysis(mhReffects(N=100,initial=c(200,2e-5,1),intau=1e-5,innu=7.9,priorparam=c(200,0.1,0.1,0.1,0.1,0.1),m=10,n=n,ybar=ybar,s=s,show=TRUE),rows=3)

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