It is so common that data structures are in multilevel in terms of correlative errors across different units. I find it very help to conduct statistical analysis in my research area. Here is a short intro to how! Obviously, complexity will increase along with research directions.

**Running a multilevel analysis in R: **

1) First, make sure that “R2WinBUGS” packages are installed in your R directory.

install.packages(“R2WinBUGS”)

library(R2WinBUGS)

2) Second, have a program (bugs).file ready. This model requires *.bugs file as described below for example:

model {

for (j in 1:J){

y[j] ~ dnorm (theta[j], tau.y[j])

theta[j] ~ dnorm (mu.theta, tau.theta)

tau.y[j] <- pow(sigma.y[j], -2)

}

mu.theta ~ dnorm (0.0, 1.0E-6)

tau.theta <- pow(sigma.theta, -2)

sigma.theta ~ dunif (0, 1000)

}

3) Third, you also need a data file (*.txt) to work with step 4 as described below for example:

school estimate sd A 28 15 B 8 10 C -3 16 D 7 11 E -1 9 F 1 11 G 18 10 H 12 18

4) Do the following command in R to run multilevel analysis finally:

schools <- read.table (“schools.dat”, header=TRUE)

J <- nrow(schools)

y <- schools$estimate

sigma.y <- schools$sd

data <- list (“J”, “y”, “sigma.y”)

inits <- function() {list (theta=rnorm(J,0,100), mu.theta=rnorm(1,0,100), sigma.theta=runif(1,0,100))}

parameters <- c(“theta”, “mu.theta”, “sigma.theta”)

schools.sim <- bugs (data, inits, parameters, “schools.bug”, n.chains=3, n.iter=1000)

Step 1 – Step 4 are a simple example given by Andrew Gelman (see his http://www.stat.columbia.edu/~gelman/bugsR/runningbugs.html)

**Reference on Bayesian inference Using Gibbs Sampling method **

http://www.mrc-bsu.cam.ac.uk/bugs/

I read these two books closely to run multilevel analysis in R. Hope you find them all interesting and helpful. Of course, step 1 – step 4 are a short excerpt from mostly Gelman and Hill (2007) . It will get you enough starting what those individual codes would mean.